Kaplan-Meier Survival Analysis: Techniques and Interpretation

1. Kaplan-Meier survival curves and the log rank test Dr Douwe Postmus (d.postmus@umcg.nl)

2. Content • What makes the analysis of time-to-event data special? • Kaplan-Meier estimator of the survival curve • Log rank test to compare the survival curves between two or more groups

3. Example • Population: patients admitted to the hospital with symptoms of heart failure (HF) • Outcome: time from hospital discharge to HF hospitalization or death from any cause • Parameter of interest: survival curve S(t) • Proportion of patients with an event time larger than t

4. Survival curve for the population • Survival curve S(t): proportion of patients in the population with an event time larger than t • 1-year survival: S(1)=0.72 • 2-year survival: S(2)=0.56 • 3-year survival: S(3)=0.45 • 4-year survival: S(4)=0.37 • 5-year survival: S(5)=0.30 • S(t) is generally unknown and needs to be estimated from the data

5. Random sample of n=1000 • Estimated survival based on the event times in the sample • 1-year survival: 708 / 100 = 0.71 • 2-year survival: 542 / 100 = 0.54 • 3-year survival: 445 / 100 = 0.45 • 4-year survival: 370 / 100 = 0.37 • 5-year survival: 300 / 100 = 0.30

6. Actual versus estimated survival

7. Right censoring • Administrative censoring: the event is observed only if it occurs prior to some pre-specified time • Studies with a fixed follow-up time (e.g., maximum of 2 years per patient) • Studies with a fixed duration (e.g., 5 years between start and end of study) • Loss to follow-up: subjects who drop out from the study before it is terminated

8. Graphically Start of study End of study x o o censored o x x event x o

9. Random sample (n=1000) with right-censored observations

10. How toestimatethe 1-year survival? • For the 578 patients whose event times were observed we know that • 296 survived for more than 1 year • 282 experienced the event within the first year • For the 442 patients whose event times were censored we know that • 332 survived for more than 1 year • 90 either experienced the event within the first year or survived for more than one year

11. 1-year survival: lowerandupperbounds • Lower bound: count the 90 patients who either experienced the event within the first year or survived for more than one year as if they experienced the event • Upper bound: count the 90 patients who either experienced the event within the first year or survived for more than one year as if they survived

12. Graphically

13. Estimationbased on conditionalprobabilities Hazard: probability of experiencing the event within the interval conditional on being alive at the start of the interval

14. Actual versus estimated survival

15. Kaplan-Meier estimator • Survival curve estimated based on conditional probabilities • Takes all the unique event and censoring times and sorts them in ascending order (from low to high) • Uses the periods between the sorted event and censoring times as the intervals

16. KM survival curve for the example (time in days instead of years)

17. Actual versus estimated survival

19. Creating KM survival curves in SPSS

20. Creating KM survival curves in SPSS

21. KM survival curves forthethreegroups

22. Log rank test

23. Limitations of thelog rank test • The log rank test canbeusedtocomparethe survival curves of two or more groups • Stratification can be used to adjust for the effect of a second categorical covariate • Treatment effect adjusted for gender (i.e., separate survival curves for male and female patients) • Examples of research questionsforwhichthelog rank test cannotbeused • Is ageassociatedwiththe time to HF hospitalization or deathfromanycause? • Treatment effect adjustedforseveralcovariates

24. Next lecture

25. contact: d.postmus@umcg.nl