statistics in clinical trials: how to interpret published data … · 2014-04-16 · 30...

1

STATISTICS IN CLINICAL TRIALS

How to interpret published data

correctly

Adam Svobodniacutek

This presentation is financially supported by GlaxoSmithKline

CZDUTT002212

2

Information sources

3

Information sources Books

Clinical Trials A Methodological Perspective Piantadosi S ISBN 0471163937

Clinical Trials A Practical Approach Pocock SJ ISBN 0471901555

Clinical Trials Design Conduct and Analysis Meinert CL ISBN 0195035682

Clinical Trials in Oncology Green S Benedetti J Crowley J ISBN 1584883022

Design and Analysis of clinical Trials Concepts and Methodologies Chow SCh Liu J

ISBN 047113404X

Guide to clinical Trials Spilker B ISBN 0881677671

Design of Clinical Trials-------------------------------------------------------------------------------------------------

Data Analysis in Clinical Trials ------------------------------------------------------------------------------------- Analyzing survival Data from Clinical Trials and Observational Studies Marubini E

Valsecchi MG ISBN 0471939870

Biostatistics in Clinical Trials Redmond C Colton T ISBN 0471822116

Statistical Methods for Clinical Trials Norleans MX ISBN 0824704673

Sample size estimates---------------------------------------------------------------------------------------------

Handbook of Sample Size Guidelines for Clinical Trials Shuster JJ ISBN 0849335426

How Many Subjects Statistical Power Analysis in Research Kraemer HCh Thiemann S

ISBN 0803929498

Sample Size Tables for Clinical Studies Machin D Campbell M Fayers P Pinol A

ISBN 0865428700

Data management -----------------------------------------------------------------------------------------------------

Management of Data in Clinical Trials McFadden E ISBN 047130316X

4

Basic terminology

5

6

7

Randomization

Methodology and process of random (or pseudorandom)

assignment of subjects to two or more treatment arms

When was randomization used for the first time

in clinical research

8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis

Interim analysis is analysis of the data at one or more time

points prior to the official close of the study with the

intention of possibly terminating the study early

OBrien-Flemming

interim monitoring

boundaries for the

primary endpoint are

based on

predetermined

number of planned

interim analysis with

overall type error of

a=005

Interim analysis

10

1 is generally not recommended to be used in clinical trials

2 is recommended to be used in clinical trials if proper rules

are respected

3 affects study power but not probability of false positive

result

4 is not recommended to be used in triple-blind clinical trials

5 is recommended only for multicentric clinical trials

6 is recommended for clinical trials with 500 and more

subjects

7 is not used in clinical trials with overall survival as primary

endpoint

11

12

ITT and PP analysis

Intention-to-treat (ITT) analysis is based on data of all

randomized subjects regardless of

- fulfilling of inclusion criteria

- taking medicine in accordance to randomization code

- compliance with study protocol

- premature withdrawal from study

Per-protocol (PP) analysis is based only on data of subjects

compliant to study protocol

Study population that reflects the best situation

in clinical practice is

13

1 per protocol population

2 safety set

3 randomized set

4 intent to treat population

14

15

Parallel design

Entry

R A N D O M I Z A T I O N

Arm 1

Arm 2

Arm n

Subjects are randomized to receive one of the tested treatments

and use only this treatment during the whole experiment

16

Cross-over design

All subjects are exposed to all treatments tested in experiment

Randomization is performed only to assign different sequences

of treatments applied

Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2

The best design for clinical trial is

17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential

6 depends on individual study settings (pathology study

duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6

PID 1PID 2PID 3PID 4

Visits

VA

S P

ain

No missing values in longitudial study

20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21

LOCF Bias in data display

22

23

Hypotheses in clinical trials

Better

Equivalence testing

Superiority testing

Non-inferiority testing

24

Meta-analysis

Meta-analysis refers to the analysis of analyseshellip the

statistical analysis of a large collection of analysis results

from individual studies for the purpose of integrating the

findings (Glass 1976 p3)

Meta-analysis techniques are needed because only

summary statistics are typically available in the literature

Problems with meta-analysis

- bdquopublication biasldquo (bdquofunnel shapeldquo)

- multiple results from one population

- heterogeneous assessment of efficiency and safety in different

studies

25

Meta-analysis general approach

26

Economical analysis in clinical trials

Basic classification of economical analysis

bdquoCost-minimizationldquo analyses (CMA)

bdquoCost-effectivenessldquo analyses (CEA)

bdquoCost-utilityldquo analyses (CUA)

bdquoCost-benefitldquo analyses (CBA)

The main objective of pharmacoeconomical analyses in clinical

trials is to compare two or more treatments from the view of

costs and benefits

27

QALY

28

QALY

QALYs are used in

29

1 cost-minimization analysis

2 survival analysis

3 cost-effectiveness analysis

4 oncology trials

5 cost-utility analysis

6 cost-benefit analysis

30

Multivariate statistical methods

ndash Methods of common evaluation of the effect of several factors

(type of treatment stage of disease genetic factors markers

etc) on the treatment efficiency and safety

ndash In clinical trials are typically not used for primary endpoint

analysis

ndash Are used mainly on exploratory purposes

ndash Could be used to verify whether different distribution of

prognostic factors in treatment arms could affect the

differences in outcomes between treatment arms

31

Subgroup analyses

ndash Analyses of efficiency orand safety on subgroup of subjects

defined by specific entry criteria (eg sex age)

ndash Advantages Potential of finding subgroup of patients with

significantly betterworse outcomes ndash targeting of treatment

ndash Disadvantages Increase of risk of false positive results

ndash When performing subgroup analyses respecting of guidelines

for such analysis is required (prospectively defined subgroups

etc)

32

Hazard ratio Risk ratio Example of study

33

Hazard ratio Risk ratio Calculation

34

Hazard ratio Odds ratio Calculation

35

Absolute and relative risk reduction NNT

Absolute risk reduction (ARR)

The difference between the control grouprsquos event rate (CER

eg 10) and the experimental grouprsquos event rate (EER eg

eg 20) ARR = 10

Relative risk reduction (RRR)

The percent reduction in events in the treated group

compared to the control group event rate For the example

above 10 20 = 05 = 50

Number needed to treat (NNT)

The number of patients that must be treated to prevent one

adverse outcome or for one patient to benefit The NNT is

the inverse of the ARR NNT = 1ARR

36

Multiplicity testing or repeated measurements

The use of many significance tests in a single study eg

many subgroup analyses the use of many testing methods

analysis of many variables and serial measurements (time

course) of the same variable can increase the probability of

obtaining false-positive results Care should therefore be

exercised in the study design and in the interpretation of P

values in such a situation

37

Multiplicity testing or repeated measurements solution

1) Look for other simpler endpoints

The best approach for avoiding multiplicity of testing is to use one or

only a few statistics instead of multiple ones wherever possible

2) Give a conservative interpretation and do not use the term

`significant

Another approach is to indicate exact P values and to interpret each

result conservatively without the term `significant or `not significant

3) Controlling the level of significance

A simple ad hoc method is to use the Bonferroni correction The idea

behind this is that if one were conducting n significance tests then to

obtain an overall type I error rate of [alpha] one would only declare any

one of them `significant if the P value were smaller than [alpha] n for

example the significance level is set at 001 for 5 subgroup analyses

38

Classification of clinical trials

39

PROCESS OF NEW DRUG DEVELOPMENT

Clinical trials Phase IV

10-15

YEARS

Klinickeacute studie Faacuteze I Faacuteze II Faacuteze III

Registration and approval from regulatory authorities

Laboratory experiments

Preclinical testing

Clinical trials Phase I Phase II Phase III

40

bdquoPHASE 1ldquo clinical trials

Objectives

Assessment of basic product pharmacokinetic parameters in humans

Estimation of the maximal tolerated dose MTD (cytostatics etc)

Evaluation of Adverse Events (AE)

Dose finding study

Ideal design enable exact evaluation of the ldquodose ndash responserdquo curve

Because of ethical reasons adaptive designs are used dosage for

subsequent subject is based on the response of previous subject

The first dose used is based on results of preclinical testing (animal

testing)

Study subjects

12-20

Mostly healthy volunteers

Not vulnerable subjects

Design

41

3 subjects initial dose

Adverse events

NOT present

bdquoPHASE 1ldquo ndash example of subjectsrsquo enrollment 1

Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42

1 subject initial dose

Adverse events

NOT present

End of study

Another subject lower dose YES

NO

AE not present in 2 subjects

AE present in 2 subjects

Another subject higher dose

NO

YES


Another subject lower dose

YES

NO


43

Studie bdquo FAacuteZE 2ldquo bdquoPHASE 2ldquo clinical trials

20 ndash 200

Number of study subjects

fixed

enrollment by groups

sequential (including evaluation of response of each subject continuously)

Objectives

Study subjects

Design

Verification of the treatment effectiveness

Evaluation of tolerance and safety

Decision whether Phase III trials will be performed

Randomization is rare

Experiments with one arm

Treatment effectiveness and safety is compared to known products

or placebo

44

Comparison of the effectiveness and safety of the test product with placebo

or other type of control (active treatment control)

Getting data for regulatory authorities

ldquoCost ndash effectivenessrdquo analyses

Objectives

Study subjects

Design

Parallel

bdquoCross ndash overldquo

Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45

Comparison of cross-over vs parallel design

ADVANTAGES

bull elimination of between-subject variability of symptoms

bull no need for large samples

bull fewer ethical problems

bull subjects are able to express their preference for one of the compounds being given

DISADVANTAGES

bull carryover effect

bull time effect due to spontaneously evolving symptoms

46

Descriptive studies (analysis of existing databases)

bdquoCross - sectionalldquo studies (analysis of structured sample of patients)

bdquoCase - controlldquo studies (retrospective studies with selected paired

control groups)

Cohort studies (retrospective or prospective comparison of selected

cohort with control group)

Objectives

Design

Verification of product characteristics in bdquoreal settingsldquo

Detailed analyses of adverse events

Evaluation of QoL

Changes in dosage

bdquoCost-effectivenessldquo studies


Safety is usually assessed

47

1 only in Phase I trials

2 only in Phase II trials

3 only in Phase III trials

4 only in Phase IV trials

5 only in Phase I and Phase II trials

6 only in Phase I and Phase III trials

7 in Phase I ndash IV trials

48

Study designs

1048713 Prevalence surveys

1048713 Case-series

1048713 Surveillance data

1048713 Analyses of routinely

collected data (registries

mortality data etc)

Descriptive studies - designed to describe occurrence of

disease by time place and person

Analytic studies - designed to examine etiology and

causal associations

Experimental

(intervention studies) - Investigator intentionally alters one or

more factors to study the effects of so

doing

Non-experimental

(observational studies) - Does not involve intervention

investigator observes without intervention

other than to record count and analyze results

1048713 Cohort

(retrospective and

prospective)

1048713 Case-control

1048713 Cross-sectional

1048713 Ecological

Uncontrolled trials - experimental trials without control or

comparison groups (eg phase III

clinical trials)

Controlled trials - trials with control groups (eg

phase III trials)

- controlled trials can be clinical

trials (unit of randomization is an

individual) or community trials

(unit of randomization is a

community or cluster)

Randomized (RCTs) - interventions allocated randomly (all

participants or clusters have the same

chance of being allocated to each of the

study groups)

Quasi-randomized - allocation done using schemes such

as according to date of birth (odd or

even) number of the hospital record

date at which they are invited to

participate in the study (odd or even) or

alternatively into the different study

groups

Non-randomized - allocation to different groups done

arbitrarily (without any underlying

random process)

Classification of experiments

49

Fundamentals of biostatistics

for clinical trials

50

51

Questions bdquoYesNoldquo

Types of data in clinical trials

How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52

Types of analyses in clinical trials

Descriptive analyses

RESULTS

Representative sampling

variability

Hypotheses testing

RESULTS

Selection of subjects

RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53

Descriptive statistics

MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54

Central statistics computation possible variable distributions

x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0

X Concentration of marker in blood sample

55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

Median = 50 quantile

MAX ndash MIN = range

Modus = the most frequent value


56

Descriptive statistics Interval estimates

Sample populations

Target

population Interval width is determined

by

a) Sample size

b) variability

c) Required accuracy

j(x)

-3s +3s micro

Distribution of x in

target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58

How to define hypothesis in clinical trial

Null hypothesis H0

Alternative hypothesis H1

usually ldquono differencerdquo or what is NOT supposed in target

population

usually ldquoexist differencerdquo or what IS supposed to be true

in target population

59

Possible errors in hypothesis testing

H1 (difference exists) H0 (no difference)

Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK

True situation in population C

o

n

c

l

u

s

i

o

n Type I error - relative frequency (probability) of rejection of H0

if the same clinical trial is repeated many times and in reality

(in population) H0 is true

Type II error - relative frequency (probability) of failing to

reject H0 if the same clinical trial is repeated many times and

in reality (in population) H0 is false

Power - relative frequency (probability) of rejection of H0 (and

accepting H1) if in reality (in population) H0 is false

60

Type I error is interpreted as the probability of rejecting

the null hypothesis H0 if this hypothesis is true

Error of the false-positive result

Mostly is a set to level of 5

P lt 005helliphelliphellipwe reject the null hypothesis

P gt= 005helliphelliphellipwe accept the null hypothesis

Type I error (a) ndash interpretation

Negative result of the study (Pgt005) needs to be

interpreted in the context of the clinical significant

difference and sample size (study power)

61

Type II error is the probability of not-rejecting the

null hypothesis H0 if this hypothesis is not true

Error of the false-negative result

Mostly is set to level of 10-20

Power of the statistical test is 1-

The power of statistical test is the probability

of proving difference in experiment if the

difference really exists in reality

Type II error (b) ndash interpretation

62

a level of significance

- have to be chosen before the statistical test is performed

This is the probability of incorrectly rejecting the null hypothesis when it is

actually true

Traditional values of a are 005 001 or 0001

p-value level of significance

- could be approximately interpreted as the probability that the

observed result is due to chance alone if H0 hypothesis is true

p-value is calculated after the statistical test if p-value is less than

a =gt the null hypothesis is rejected

Statistical conclusion is based only on predefined a level

(conclusion is affected only by fact if p-value is less or higher

than predefined a level)

Concept of p-value

Variability of data could be characterized by

63

1 mean

2 median

3 modus

4 standard deviation

5 geometric mean

64

Praktickeacute aspekty analyacutezy dat v KHL 65

Application of survival analysis

bdquoReliability studiesldquo in industry

bdquoLifetime dataldquo in clinical research - bdquoOverall Survival (OS)ldquo

- bdquoTime to Progression (TTP)ldquo

- bdquoTime to Treatment Failure (TTF)ldquo

- bdquoDuration of Responseldquo

- bdquoRelapse Free Survivalldquo

- others


Most common usage of survival analysis in clinical research

Description of survival in one group of patients

and estimation of survival parameters (eg

median survival)

comparison of survival in two or more group

of patinets with different type of treatment

Multivariate analysis of prognostic factors and

its impact on survival


Example of survival data

Data of patients with angina pectoris in study with 15 years of follow-up

(Mayo Clinic Gehan 1969)

Survival time

[years]

Number of patients known to

survive at beginning of interval

Number of patients lost to

follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30


Example of censored data in clinical trial

Model clinical trial

Number of patients4 pts

Primary endpointOverall Survival (OS)

Accrual Period12 months

Minimal follow-up24 months


Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn

Patient 2 Lost to follow up

Accrual Follow up



Follow-up

0 12 months 36 months 24 months

Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W

D=death L-lost to follow-up W-withdrawn

Follow up



Study objective

Analysis of the effect of maintenance therapy on prolongation

of time to relaps in patients with acute lymphoblastic

leukemia

Study design

After CR patients were randomised into two arms

- Placebo

- 6-mercaptopurine (6-MP)

Primary endpoint

Time to Progression (TTP)

Kaplan-Meier curve Example


Study outcomes

A total of 42 patients randomised (11)

Placebo 21 of 21 patients with relapse

6-MP 12 of 21 without relapse ath the study end

Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35

(censored observations)


Possible evaluation of study results

1 Comparison of mean or median of time to relapse

- not possible not available in censored patients

Need for another method of analysis

Survival analysis

2 Comparison of relapse rates in both groups

(100 for placebo 43 for 6-MP)

- no information on prolongation of time to relapse

- in censored patients it is possible that relapse will

occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^

p(X) = conditional survival probability of X months ^

p is calculated for each time interval separately ^

p in different time intervals are independent ^

Basic principle of Kaplan-meier curve


Conditional survival probability of 1 month after diagnosis

p(1) = Number of patients enetering study ndash number of pts died during 1 month

Number of patients enetering study ^

p(6) = Number of pts bdquoat riskldquo in 6 month ndash number of pts died during 6 month

Number of pts bdquoat riskldquo in 6 month


^

Cumulative survival probability 12 months after diagnosis

P(12) = p(1) x p(2) x p(3) helliphelliphellip x p(12) ^ ^ ^ ^



Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability

t(j) dj nj pj=(nj-dj)nj P(t)

1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000

Calculation of survival in Placebo arm


Survival in Placebo arm

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448

Calculation of survival in arm with 6-MP


Survival in 6-MP arm

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP


Comparison of survival in treatment arms

0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

2

Information sources

3







ISBN 047113404X










ISBN 0803929498


ISBN 0865428700

Data management -----------------------------------------------------------------------------------------------------


4

Basic terminology

5

6

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

3







ISBN 047113404X










ISBN 0803929498


ISBN 0865428700

Data management -----------------------------------------------------------------------------------------------------


4

Basic terminology

5

6

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

4

Basic terminology

5

6

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

5

6

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

6

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

7

Randomization





8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP



8

1 447 BC

2 1447

3 1878

4 1924

5 1946

6 2008

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

9

Interim analysis




OBrien-Flemming

interim monitoring

boundaries for the


based on

predetermined

number of planned



a=005

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

Interim analysis

10



are respected


result




subjects


endpoint

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

11

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

12

ITT and PP analysis











13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP



13


2 safety set

3 randomized set


14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

14

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

15

Parallel design

Entry


Arm 1

Arm 2

Arm n



16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

16

Cross-over design




Entry


Sequence 1

Sequence 2

W A S H

O U T

Drug

Placebo Drug

Placebo

Period

1 2


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


17

1 parallel groups

2 cross-over

3 triple triangle

4 exponential

5 sequential


duration etc)

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

18

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

19

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain


20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

20

LOCF principle

6

7

8

9

10

11

12

13

0 1 2 3 4 5 6


Visits

VA

S P

ain

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

21


22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

22

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

23


Better

Equivalence testing

Superiority testing


24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

24

Meta-analysis











studies

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

25


26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

26









costs and benefits

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

27

QALY

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

28

QALY

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

QALYs are used in

29


2 survival analysis


4 oncology trials



30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

30






analysis





31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

31

Subgroup analyses








etc)

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

32


33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

33


34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

34


35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

35





eg 20) ARR = 10




above 10 20 = 05 = 50





36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

36









37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

37






`significant









38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

38


39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

39



10-15

YEARS




Preclinical testing


40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

40


Objectives




Dose finding study





testing)

Study subjects

12-20



Design

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

41


Adverse events

NOT present


Another 3 subjects

higher dose

YES

NO

Another 3 subjects

Initial dose

AE at most

in 1 subject

End of study

NO

Another 3 subjects

higher dose

YES

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

42


Adverse events

NOT present

End of study


NO




NO

YES



YES

NO


43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

43


20 ndash 200


fixed



Objectives

Study subjects

Design







or placebo

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

44





Objectives

Study subjects

Design

Parallel


Factorial

Randomization

100 ndash 1 000

number of subjects

fixed




45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

45


ADVANTAGES





DISADVANTAGES



46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

46




control groups)



Objectives

Design



Evaluation of QoL

Changes in dosage




47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


47








48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

48

Study designs


1048713 Case-series




mortality data etc)




causal associations

Experimental



doing

Non-experimental




1048713 Cohort

(retrospective and

prospective)



1048713 Ecological



clinical trials)


phase III trials)









study groups)







groups



random process)


49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

49


for clinical trials

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

50

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

51



How many

times

How much

Higher lower

Is equal

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

52



RESULTS


variability

Hypotheses testing

RESULTS


RANDOMIZATION

Measurement of

parameter X

Variability of X

in arm A

variability of X

in arm B

Arm A Arm B

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

53


MEAN

MEDIAN

MODUS

Continuous data

Interval data

Ordinal data

Binary data

Continuous

data

Discrete

data

Statistics

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

54


x

y(x)

0 x

y(x)

0

x

y(x)

0 x

y(x)

0


55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

55

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x

f(x)

x

MIN Median MAX

Z

quantile

Median Y

quantile

x

x





56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

56


Sample populations

Target


by

a) Sample size

b) variability


j(x)

-3s +3s micro


target population

j(x)

Sample of n=10 for

estimation of mean

j(x)

Sample of n=100 for

estimation of mean

micro micro

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

57

Hypotheses testing

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

58


Null hypothesis H0



population



59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

59



Reject H0

(difference exists)

OK

Power (1- )

Type I error

a error

Do not reject H0

(no difference)

Type II error

error

OK


o

n

c

l

u

s

i

o









60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

60











61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

61










62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

62




actually true










Concept of p-value


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


63

1 mean

2 median

3 modus


5 geometric mean

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP

64









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP









- others





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP





median survival)









Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP





Survival time

[years]




follow up

0-1 2418 0

1-2 1962 39

2-3 1697 22

3-4 1523 23

4-5 1329 24

5-6 1170 107

6-7 938 133

7-8 722 102

8-9 546 68

9-10 427 64

10-11 321 45

11-12 233 53

12-13 146 33

13-14 95 27

14-15 59 23

15-16 30









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP









Calendar time 01012000 01012001 31122002 01012002

Patient 1 Death

Patient 3 Deat

h

Patient 4 Withdrawn


Accrual Follow up



Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


Follow-up


Patient 1

Patient 2

Patient 3

Patient 4

D

L

D

W


Follow up



Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


Study objective



leukemia

Study design


- Placebo


Primary endpoint




Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


Study outcomes




Time in weeks

Placebo 1 1 2 2 3 4 4 5 5 8 8 8 8 11 1 1 12

12

15 17 22 23

6-MP 6 6 6 6 7 9 10 10 11 13 16 17 19

20 22 23 25 32 32 34 35







Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP






Survival analysis





occur in follow-up


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP


Time [months]

1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 M 11 M 12

M

^ p(1) p(2)

p(3) p(4)

p(5) p(6)

p(7) p(8)

p(9) p(10)

p(11) p(12)

^ ^

^ ^

^ ^

^ ^

^ ^

^












^





Time to

progressi

on

Number of

censored

Number of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo


Time to

progressi

on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

6-MP



0 5 10 15 20 25 30 35 40

Time

00

01

02

03

04

05

06

07

08

09

10

Cum

ula

tive P

roportio

n S

urv

ivin

g

Placebo

6-MP








^





Time to

progressi

on

Number of

censored

Number of

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Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




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bdquoat riskldquo

Conditionalsurvival

probability

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probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




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censored

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bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


1 0 2 21 1921=0905 0905

2 0 2 19 1719=0895 0905 x 0895 = 0810

3 0 1 17 1617=0941 0810 x 0941 = 0762

4 0 2 16 1416=0875 0762 x 0875 = 0667

5 0 2 14 1214=0857 0667 x 0857 = 0571

8 0 4 12 812=0667 0571 x 0667 = 0381

11 0 2 8 68=0750 0381 x 0750 = 0286

12 0 2 6 46=0667 0286 x 0667 = 0191

15 0 1 4 34=0750 0191 x 0750 = 0143

17 0 1 3 23=0667 0143 x 0667 = 0095

22 0 1 2 12=0500 0095 x 0500 = 0048

23 0 1 1 01=0000 0048 x 0000 = 0000




0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Time to

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on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

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of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




0

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Time to

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on

Number of

censored

Number

of

relapses

Number of pts

bdquoat riskldquo

Conditionalsurvival

probability

Cumulative survival

probability


6 1 3 21 1821=0857 0857

7 0 1 17 1617=0941 0857 x 0941 = 0807

9 1 0 16

10 1 1 15 1415=0933 0807 x 0933 = 0753

11 1 0 13

13 0 1 12 1112=0917 0753 x 0917 = 0690

16 0 1 11 1011=0909 0690 x 0909 = 0628

17 1 0 10

19 1 0 9

20 1 0 8

22 0 1 7 67=0857 0628 x 0857 = 0538

23 0 1 6 56=0833 0538 x 0833 = 0448




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statistics in clinical trials: how to interpret published data … · 2014-04-16 · 30...

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