1. Lecture 3
Survival analysis

2. The slang Current life table Cohort life table
What is the life time now?
Cohort life table
What is the life time of this group?

3. Problem
Do patients survive longer after treatment A than after treatment B?
Possible solutions:
ANOVA on mean survival time?
ANOVA on median survival time?
Survival analysis
Aka. Actuarial / life table analysis

4. The example

5. Person-year of observation
In total: days ~ 41.4y
11 patients died: 11/41.4y = y-1
26.6 death/100y
1000 patients in 1 y or
100 patients in 10y

6. Mortality rates 11 of 25 patients died 11/25 = 44%
When is the analysis done?

7. 1-year survival rate 6 patients dies the first year
25 patients started
24%

8. 1-year survival rate 3 patients less than 1 year 6/(25-3) = 27%
24% -27%

9. Actuarial / life table anelysis
Patients on dialysis
180 day pariods

10. Actuarial / life table anelysis
Ni number of patients starting a given period

11. Actuarial / life table anelysis
Wi number of patients that have not yet been in the study long enough to finish this period

12. Actuarial / life table anelysis
Number exposed to risk:
ni – wi/2
Assuming that patients withdraw in the middle of the period on average.

13. Actuarial / life table anelysis
di : Number of patients that died

14. Actuarial / life table anelysis
qi = di/(ni – wi/2)
Proportion of patients terminating in the period

15. Actuarial / life table anelysis
pi = 1 - qi
Proportion of patients surviving

16. Actuarial / life table anelysis
Si = pi pi-1 ...pi-N
Cumulative proportion of surviving
Conditional probability

17. Survival curves
How long will a dialysis patient survive?

18. A few concerns Withdrawals are assumed to happen at time midpoints
Kaplan Meiers method will fix this
The probability of surviving a period is treated as if it is independent of survival of other periods.

19. Kaplan-Meier product limit method
Changes in the survival curve are calculated when an event occurs
Withdrawals are ignored as events

20. Kaplan-Meier
Simple example with only 4 ”death-events”.

21. Confidence of survival curves
Standard Error (SE)
Assumed to be normally distributed
95% confidence is 1.96*SE

22. Confidence interval of the Kaplan-Meier method

23. The Kaplan-Meier method

24. Actuarial and Kaplan-Meier Survival curves
0.6117
Kaplan-Meier
0.6154

25. Comparing survival curves

26. Comparing survival curves
Two principle methods
Logrank statistics
Mantel Haenszel chi-square statistics

27. Logrank statistics

28. Logrank statistics

29. Hazard ratio

30. Mantel Haenszel chi-square statistics

31. Mantel Haenszel chi-square statistics

32. Hazard function