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8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 1/20
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
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 2/20
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).
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 3/20
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?
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 4/20
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
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 5/20
time for reduction cells in aluminium s
Days400 600 800 1000 1200 1400
0 . 8
0 . 9
1 . 0
1 . 1
1 . 2
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 6/20
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
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 7/20
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 +
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 8/20
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 +
Professor Jane L Hutton,Department of Statistics, The University of Warwick
Lifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 9/20
Electrical insulating uid
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 10/20
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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 11/20
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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 12/20
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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
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Brain tumours and Epilepsy
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
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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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
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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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 16/20
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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
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8/6/2019 Lifetime 2
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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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 19/20
8/6/2019 Lifetime 2
http://slidepdf.com/reader/full/lifetime-2 20/20
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
Professor Jane L Hutton,Department of Statistics, The University of WarwickLifetime data analysis