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Designs for Oncology MTD Finding

Yevgen TymofyeyevMERCK & Co., Inc

September 12, 2008

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Acknowledgement

Linda Sun Keaven Anderson Jason Clark Chen Cong Lisa Lupinacci Yang Song

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Outline Objectives of Phase I Oncology Trials Considered designs:

3+3 Design, Group Designs, Cumulative Cohort Design Modified Ji Bayesian Design Continual Reassessment Method (CRM) Misc. techniques

Isotonic regression Simon’s acceleration

Some design comparison and recommendations

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Phase I Oncology Trials

Cancer cells are cells with uncontrolled growth.

Most oncology drugs are somewhat toxic to kill tumor cells or to control the growth.

Therefore, Phase I oncology trials start with cancer patients directly, instead of healthy subjects like in other therapeutic areas.

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Objectives of Phase I Oncology Trials The general belief of oncologists is that the more

toxic a regiment is, the more efficacious. For all designs we assume monotonic dose-toxicity relation

The primary objective of Phase I oncology studies is to find the maximum tolerated dose (MTD).

MTD – highest dose where Dose Limiting Toxicity (DLT) rate is acceptable.

MTD will be carried to Phase II trials for proof of concept evaluation in terms of efficacy.

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Traditional 3+3 Design

This is an adaptive design, since we allocate patients according to what we have learned during the study. Start from the lowest dose level Adapt every cohort of 3 patients Dose escalate until unacceptable toxicity rate

Variants of design include “A+B”, accelerated titration design, etc.

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Dose 3 patients

DLTs?

Dose is Not Safe (de-escal-

ate)

Dose Is Safe(escalate)

Dose 3 more patients

TotalDLTs?

>2/3

1/3

0/3

>2/6

=1/6

Traditional 3+3 Design

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Comments on Traditional 3+3 Design Pros:

Simple and intuitive algorithm Easy to implement and monitor Model free: don’t have to assume dose response curve

Cons: Target DLT rate for MTD is about 20% (unclear) The safety and tolerability of the final dose is only tested

with a maximum of 6 patients Require to observe toxicity outcome in the current cohort

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A+B designs

Lin and Shin (2001) 3+3 is a special case, when A=B=3 Applicable for targeting wide range DLT Require to observe toxicity outcome in the

current cohort (longer study duration and problem with lost to follow-up)

Ivanova (2006) provides rules on how to construct A+B designs and group up-and- down designs

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Group Up-and-Down Designs

Wetherill (1963); Gezmu and Flournoy (2006) Subjects are treated in cohorts of size s X(dj) – number of toxicities observed in the last

cohort at dose j, j=1,…,K Design denoted by UD(s,cL,cU), cL and cU are set in a

way to “target” given Γ, i.e MTD 0 ≤ cL ≤ cU ≤ s

The next cohort is assigned to (i) dose dj+1 if X(dj) ≤ cL

(ii) dose dj-1 if X(dj) ≥ cU

(iii) dose dj if cL <X(dj)< cU

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Cumulative Cohorts Design (CCD) for Dose Finding Ivanova, Flournoy, Chung (2005) Treatment allocation rule is similar to the group up-

and-down designs Let q = X(dj)/ N(dj), where N(dj) –sample size on

dose dj If q ≤ Γ- Δ , increase dose If q ≥ Γ+Δ , decrease dose If Γ- Δ ≤ q ≤ Γ+Δ, repeat dose

Note: For a given Γ,the same Δ is recommended for all N(dj).

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CCD (cont.)

Treatment allocation rule based on not only the most resent cohort of subjects (as for A+B and group-up-down designs) but rather on all cumulative information at the current dose

Simple and have good operating characteristics; “Time to event” (TITE) modification of CCD is

available to use in studies where the follow-up response time is long (similar to TITE CRM)

Performance results form the literature CCD ~ CRM CCD is often more preferable than group designs

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Modified Ji Bayesian Design

To address the issues with traditional 3+3 design, Merck oncology group started to use a two-stage Bayesian adaptive design which modifies Ji’s (2007) design.

Stage 1: Dose Escalation Mimic 3+3 design

Stage 2: Dose Confirmation Adaptively allocating patients around the potential MTD

dose to confirm the safety and tolerability of the final selected dose

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An Example of Modified Ji Design MTD: the target DLT rate is 20% The maximum sample size is 50

This number is largely determined by budget/resource

Stage 1: Dose Escalation Follow the scheme of 3+3 design Until 2 out of 3 patients or 2 out of 6 patients

experience DLTs at a given dose

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An Example of Modified Ji Design (Cont’) Stage 2: Dose Confirmation

Start to allocate patients continuously (or in cohorts) at the dose right below the highest tested dose.

Once each enrolled patient DLT information is available, use the monitoring table provided to determine whether to put the next patient to the next higher dose, or the next lower dose, or the same dose. The monitoring table is determined by Bayesian statistics

This Stage ends when Either there is a dose with 3 or fewer patients out of 14 having DLT Or all 50 patients have been enrolled

Final analysis: Pooled Adjacent Violator Algorithm (PAVA), ref. Robertson at. al.

(1988), to select the dose which has DLT rate most close to the target rate.

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An Example of Modified Ji Design (Cont’)Number of patients treated at current dose

Number of

toxicities

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 E E E E E E E E E E E E 1 S S S E E E E E E E E E 2 DU D D D S S S S E E E E 3 DU DU DU DU D D D D S S S S 4 DU DU DU DU DU DU D D D D D 5 DU DU DU DU DU DU DU DU DU D 6 DU DU DU DU DU DU DU DU DU 7 DU DU DU DU DU DU DU DU 8 DU DU DU DU DU DU DU 9 DU DU DU DU DU DU 10 DU DU DU DU DU 11 DU DU DU DU 12 DU DU DU 13 DU DU 14 DU

E = Escalate to the next higher dose S = Stay at the current dose D = De-escalate to the next lower dose U = The current dose is unacceptably toxic

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Bayesian Statistics Used in modified Ji Design Put non-informative prior to DLT rate of each dose

Beta (1, 1) for all doses That is, this design is also model free and doesn’t have to

assume dose response curve Once patient toxicity information becomes available,

update the posterior distribution of DLT rate of the testing dose Allocate the next patient according to how the posterior

distribution relates to the target DLT rate.

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Illustration of Ji’s Algorithm

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Ji Design Decision Rules

Current tried dose is i; pT- target toxicity prob. of MTD Posterior probability of the intervals at dose i

qD = P (pi-pT > K1 σi | data) qS = P (-K2 σi ≤ pi-pT ≤ K1 σi | data) qE= P (pi-pT < - K2 σi | data) σi is the posterior std. dev. of pi

Compute J=I( P (pi+1>pT | data ) > ξ) Choose max { qD, qS, qE(1-J) } which results in

D – “De-escalate” S – “Stay” E – “Escalate”

Parameters K1, K2, ξ, are prior parameters can be adjusted according to study specifics

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Comments on the modified Ji Bayesian Design Pros:

Keep all the pros of 3+3 design: model free, easy to implement and monitor, dose-escalation is transparent to physicians

Address issues of 3+3 design: the final dose can be selected with greater confidence/assurance.

Cons: Can’t handle partial information. Time-to-event

CRM, TITE-CCD may be applicable

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Continual Reassessment Method (CRM), simple version Bayesian parametric model

E.g., Probability of toxicity at dose k, ψk = (ak ) θ

θ – parameter with non - informative prior (a1, …, am ) – fixed pre-specified values

Typical example: (.05, .1, .2, .3, .5, .7 )

Rules applied after each new response(s) : Update posterior for θ, hence update ψk for all dose levels

k=1,…,m Allocate next patient (s) to the dose suggested to be the

closes to MTD reconciling constrains Check for early stopping criteria

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Example of CRM run

1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

Dose

Re

spo

nse

0/1 0/1

2/17

4/91/2

True modelTargetEstimated prob. of tox.Observed ResponseSelected MTD

Simulation Dose Allocation, n=30

Dose

Nu

mb

er

Su

bje

cts

1 2 3 4 5 6

01

5

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Example of potential CRM problems, DLT target = 0.30 Dose 1 2 3 4 5 6 7 8 9

N 3 4 5 4 — — 2 — —

# DLT 0 0 0 0 — — 2 — —

(A) Posterior summaries

ak 0.01 0.015 0.02 0.025 0.03 0.04 0.05 0.1 0.17

ψk 0.069 0.085 0.01 0.11 0.12 0.144 0.163 0.242 0.33

(B) Posterior summaries (equidistant ak)

ak 0.063 0.125 0.188 0.25 0.313 0.375 0.438 0.5 0.563

ψk 0.024 0.054 0.09 0.13 0.176 0.226 0.281 0.341 0.405

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Early Stopping for CRM

Zohar and Chevret (2001) Stopping criteria

All doses are unacceptable toxic All doses are of unacceptably low toxicity The current dose is expected to be the best

estimate of the MTD Suitability on the dose scale Suitability on the response probability scale

Based on point estimated Based on precision in estimates

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Evaluation of modified Ji design and competing designs What are the operating characteristics of the

modified Ji design? accuracy speed safety

Do we need the first , “3+3”, design stage? How does the design compare to other

competing designs?

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Versions of the Modified Ji Design The following rules are

very similar: Two stage design Skipping the 3+3 stage

and working with the table when response from subjects is analyzed in cohorts of size 3

Number of patients at current dose 

Nu

mb

er o

f tox

icitie

s

  1 2 3 4 5 6

0 S E E E E E

1 DU D S S S E

2   DU DU D D D

3     DU DU DU DU

4       DU DU DU

Table for MTD= 20%

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Versions of the Modified Ji Design (Cont.)

Put “S” in the grey entries of the table.

Number of patients at current dose 

Nu

mb

er o

f tox

icitie

s

  1 2 3 4 5 6

0 S E E E E E

1 DU D S S S E

2   DU DU D D D

3     DU DU DU DU

4       DU DU DU

Table for MTD= 20%

Equivalently, each newly tested dose starts with 3 patients, and then cohort size of 1

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Simon’s Acceleration

Purpose: design a trial so that fewer patients are treated at sub-therapeutic dose levels

Method: only one patient per cohort until one patient experienced dose-limiting toxic effects after that switch to 3+3 approach for further escalation

Extension: (3 stage design) accelerated escalation → (3+3) → confirmation

Performance from simulations: As expected, good when target dose is in the high dose range (good

dose finding and short study duration) Poor when target dose is in the low dose range (poor

dose finding, larger number of DLTs)

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Isotonic Regression

Robertson at. el (1988) Nonparametric (robust) shape

constrained fit (least square error fit subject to order restriction)

“Borrow” strength cross doses Typically isotonic regression

improve probability of right selection of the target dose

Better describe dose-toxicity relation

Performed when trial is finished 1 2 3 4 5 6 7

0.0

0.1

0.2

0.3

0.4

Dose

Pro

babi

lity

of T

oxic

ity

observed proportionsisotonic fit

Example

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Isotonic regression

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Estimation Bias of Isotonic Regression

1 2 3 4 5

-3-2

-10

12

3

Dose

Iso

ton

ic E

stim

ate

True response

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Criteria for Design Evaluation Total number of observed DLTs Probability of the correct selection of the target dose

(accuracy) Expected total sample size Distribution of subjects to dose levels Other things to look at

Design flexibility Tuning parameters Cohort size Stopping rules

Simplicity (implementation and study conduct)

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Design Name Design Descriptionn at MTD

Max N

1 Traditional 3+3Once we see 2/6, the next lower dose is claimed to be the target dose

6 N/A

2Original Ji design with cohort size 1

Dose adaptation according to the monitoring table from the beginning of the study

14 50

3 Two-stage modified JiStage 1: dose escalation, 3+3Stage 2: dose confirmation, cohort sz 1

14 50

4

Modified Ji's design(cohort size 1 after the first 3 pts) or modified table entries for n=1,2

No stages, each newly tested dose starts with 3 patients, and then cohort size of 1 14 50

5Three-stage modified Ji(Objective: allocate fewer

pts in lower doses)

Stage 1: dose escalation, cohort sz 1 (Simon's accelerated titration)Stage 2: dose escalation, (3+3)Stage 3: dose confirmation, cohort sz 1

14 50

6 CRMOne param. Bayesian model, with early stopping for dose misspec.

14 40

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Dose-Response Profiles

Dose

To

xici

ty

0.0

0.2

0.4

0.6

0.8

Scenario 1

1 2 3 4 5 6

Scenario 2 Scenario 3

Scenario 4 Scenario 5

0.0

0.2

0.4

0.6

0.8

Scenario 6

0.0

0.2

0.4

0.6

0.8

Scenario 7 Scenario 8 Scenario 9

1 2 3 4 5 6

Scenario 10 Scenario 11

1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

Scenario 12

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Simulation results ( , , ): Accuracy, Speed, Safety

Target dose (scenario #)

Performance of Design

3+3Original Ji

w/ chrt sz=1

Modif. Ji 2 stage

Ji w/ 3 sub. at new

dose

Simon’s + 2 stage

CRM

middle dose(s) w/ moderate spacing

(1-4)

LHH

LAA

ALA

ALA

AHL

HHL

middle dose(s) – closer spacing

(11)

LH (18)H (.13)

LA (25)A (.16)

HL (31)A (.16)

HL (32)A (.16)

AA (26)L (.19)

HH (23)L (.20)

The highest dose or higher than all

(5,6)

HH (20)N / A

LA (24)N / A

A - HL (30)N / A

HL (31)N / A

HH (21)N / A

HH(20)N / A

Lower than all doses (7)

L (.70)H (5.7)

H (0.44)

H (.93)H (5.4)H(0.43)

A (.90)L (8.3)

H (0.42)

A (.91)L (7.7)

H (0.43)

A (.92)L (10)

A (0.48)

H (.95)H (6.0)L (0.78)

Multiple doses with toxicity =

0.2, (9,10)

N / AH (14,13)H (0.18)

N / AA (24,15)A (0.17)

N / AL (27,20)A (0.19)

N / AL (28,22)A (0.19)

N / AL (26,20)L (0.23)

N / AA(24,21)L (0.24)

“H” = High, “A”= Average, “L”= Low

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Conclusions

CCD and Ji design have similar methodology but were not compared directly here

The modified Ji design and its versions improve the 3+3 design (confirm the MTD is tolerable by using moderate number of patients)

The modified Ji design in general performed well in our simulation studies in terms of finding MTD and safety

One parameter CRM tends to provide better (but comparable to Ji design) estimation of MTD BUT is criticized for exposing subjects to highly toxic doses and dependency on parameter tuning. CRM remains a sound alternative design and two parameter version will be investigated in the future.

Modified Ji design is easy to implement as dose assignments for new patients are readily determined in the monitoring table which is created and validated before study beginning.

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References

Durham, S.D., Flournoy, N. Random walks for quantile estimation. Statistical Decision Theory and Related Topics V, Berger, J. and Gupta, S., eds. Springer-Verlag, New York 1994 467-476.

Gezmu, M., Flournoy, N. Group up-and-down designs for dose fundings. J. Statist. Plann. Inference 2006 136:1749-1764

Ivanova, A., Flournoy, N., Chung, Y. Cumulative cohort design for dose finding. Journal of Statistical Planning and Inference (2007)

Ivanova, A. Escalation, up-and-down and A+B designs for dose-finding trials. Statistics in Medicine 2006 25:3668-3678

Ji, Y., Li, Y., Bekele, N. Dose-finding in phase I clinical trials based on toxicity probability intervals. Clinical Trials 2007 4:235-244

Lin, Y., Shih, W.J. Statistical properties of the traditional algorithm-based designs for phase I cancer clinical trials. Biostatistics 2001 2:203-215.

O'Quigley, J., Pepe, M., Fisher L. Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics 1990 46:33 - 48.

Wetherill, G.B. Sequential estimation of quantal respose curves. J. Roy. Statist. Soc. 1963 B 25: 1-48

Zohar, S., Chevret, S. The continual reassessment method: comparison of Bayesian stopping rules for dose-ranging studies. Statistics in Medicine 2001 20 2827-2843

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Recommended Literature

Chevret, S. ed. Statistical Methods for Dose Finding. 2006. John Wiley.

Ting, N. ed. Dose Finding in Drug Development. Springer-Verlag. 2006 New-York.