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Lifetime data analysis

Professor Jane L Hutton,Department of Statistics,

The University of Warwick

December 2008

Professor Jane L Hutton,Department of Statistics, The University of Warwick


8/6/2019 Lifetime 2


Examples

Aluminium smelting :Alumina liqueed in steel-lined cell. Cell replacedwhen carbon lining cracks. Record days of serviceuntil cell replacement.

Australian Prime Ministers :Months in office of Australian Prime Minister.

Leukaemia patients :Survival time in weeks of two groups of leukaemiapatients. The groups are AG+ and AG-, andwhite blood cell count is known. (Feigl andZelen).



8/6/2019 Lifetime 2


Examples

Electrical insulating uid :Investigate time to breakdon for insulating uid.Relate to high voltage level, and then ‘normal’voltage level.

Brain tumours and Epilepsy :Which drug reduces the number of seizures inchildren? Does the same drug work in adults?

Cerebral Palsy :What affects long will my child live?



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Aluminium smelting

Failure time for reduction cells in aluminium smelting, in days:1540,1415,660,999,1193,1006,869,1035, 797, 296, 775, 1424,1169, 1500, 728, 670, 841Sort into increasing order:296 660 670 728 775 797 841 869 999 1005 1035 1169 11931415 1424 1500 1540Five number summary:

Minimum Lower Median Upper MaximumQuartile Quartile

296.0 775.0 999.0 1193.0 1540.0



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time for reduction cells in aluminium s

Days400 600 800 1000 1200 1400

0 . 8

0 . 9

1 . 0

1 . 1

1 . 2



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Distribution of failure time for reduction cells in aluminium smelting

Days

E s

t i m a

t e d s u r v

i v a l f u n c t i o n

0 500 1000 1500

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0



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Leukaemia patients

Survival of leukaemia patients

Weeks

E s t i m a

t e d s u r v i v a

l f u n c t i o n

0 50 100 150

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

AG -AG +



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Survival of leukaemia patients

Weeks

E s

t i m a

t e d s u r v

i v a l

f u n c

t i o n

0 50 100 150

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

AG -AG +



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Electrical insulating uid

Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis

8/6/2019 Lifetime 2


Breakdown time by voltage level

Breakdown time (minutes)0 20 40 60 80 100 120

2 6

2 8

3 0

3 2

3 4

3 6

3 8

2

2

4


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Breakdown by voltage level; log plot

Voltage level(kV)

B r e a

k d o w n

t i m e

( l o g m

i n u

t e s

)

26 28 30 32 34 36 38

- 2

0

2

4

6

8


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Breakdown time by voltage level

Minutes

E s

t i m a

t e d s u r v

i v a l f u n c t i o n

0 20 40 60 80 100 120

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

kV=28

kV=30

kV=32

kV=34kV=36

kV=38


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Brain tumours and Epilepsy


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Survival of people with brain tumours

Time to death (months)

E s

t i m a

t e d s u r v i v a

l

0 20 40 60 80

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0


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Survival of people with brain tumours F

Time to death (years)

E s

t i m a

t e d s u r v i v a

l

0 2 4 6

0 . 0

5

0 . 1

0

0 . 5

0

1 . 0

0


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Survival of people with brain tumours R

Time to death (years)

E s

t i m a

t e d s u r v i v a

l

0 2 4 6

0 . 0

5

0 . 1

0

0 . 5

0

1 . 0

0


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8/6/2019 Lifetime 2


Age in years

P r e

d i c t e d s u r v

i v a l

f u n c

t i o n

0 10 20 30 40

0 . 4

0 . 6

0 . 8

1 . 0

Predicted survival from age two years

Severe motor, cognitive & visual disabilities, normal bw

normal bw: birthweight > 2500g

low bw: birthweight <= 2500g

Severe motor, cognitive & visual disabilities, low bw

Severe motor & cognitive disabilities, normal bw

Severe motor & cognitive disabilities, low bw

Severe motor disabilities, low bw

Severe motor disabilities, normal bw

Only severe ambulatory disability, normal bw

Only severe ambulatory disability, low bw

No severe disabilities, low bw


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8/6/2019 Lifetime 2


Course outline

IntroductionMain denitions and formulaeNon-parametric survival analysis

◮ Kaplan-Meier estimate◮ Actuarial estimate◮ Log-rank test

Parametric survival analysis◮ Survival functions◮ Likelihood methods◮ Diagnostic plots

Regression models for survival data◮ Accelerated life models◮ Proportional hazards models


lifetime 2

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