1 Introduction to medical survival analysis John Pearson Biostatistics consultant University of Otago Canterbury 7 October 2008

2 Objectives Describe survival data Define survival analysis terms Compare survival of groups Describe study design Acknowledgement: Thanks to Colm Fahy for providing the example data.

3 Omissions Not covered: – most methodology issues –mathematical justification See –Collett: Modelling Survival Data in Medical Research –Hosmer & Lemeshow: Applied Survival Analysis –Many other good texts.

4 Example: Metastatic Parotid SCC Disease risk factors: – >50 yo –Male –Exposure to sun –Caucasian ancestry 61 patients operated on since 1990 Audit done 1/6/8 14 patients died from SCCMP, 20 died from other causes, 1 couldn’t be found

5 Example: Patient data Only 7 patients shown. Dates have been confidentialized.

6 Example: Patient data

7

8 Example: Survival Data

9 Date formats and manipulation can cause headaches. Check what happens when your software subtracts dates to get survival time.

10 Example: Survival Data censored Missing data

11 Example: Survival Data censored Missing data censored

12 Example: Survival Data censored Missing data censored Censored data is explicitly addressed by survival analysis, using simple linear regression is not recommended. Options: 1.SPSS 2.SAS 3.R 4.Other software

13 Example: Survival Data censored Missing data censored Missing data can have a large effect on results, requires careful management. Options: 1.Omit 2.Impute 3.Model

14 What is survival analysis Time to event data –Continuous –Right skewed, ≥0, not normal –Censored –Analyse risk (hazard function) Examples –Time to death –Time to onset/relapse of disease –Length of stay in hospital

15 What is survival analysis Time to event data –Continuous –Right skewed, ≥0, not normal –Censored –Analyse risk (hazard function) Examples –Time to death –Time to onset/relapse of disease –Length of stay in hospital

16 Censoring Right censoring Left censoring Interval censoring Censoring is also categorised by 1.Fixed study length 2.Fixed number of events 3.Random entry to study

17 Censoring Right censoring –observed survival time is less than actual –Study ends before event Left censoring Interval censoring

18 Censoring Right censoring Left censoring –Time to relapse –Time to event is less than observed t < 3 Interval censoring Surgery 0 Recurrence 3 month exam t

19 Censoring Right censoring Left censoring Interval censoring –Time to relapse – 3 < t < 6 Surgery 0 Free of disease 3 month exam t Recurrence 6 month exam

20 Censoring Independent censoring Survival time is independent of censoring process. A censored patient is representative of those at risk at censoring time. The methods described here assume independent censoring

21 Censoring Independent censoring Survival time is independent of censoring process. Informative censoring Patients removed from study if condition deteriorates.

22 Censoring example How are the SCCMP patients censored?

23 Censoring example How are the SCCMP patients censored? Enter study on surgery date Last known status is at audit Random right censoring.

24 Survival function The survival function S(t) is the probability of surviving longer than time t. S(t) = P(T>t) Where T is the survival time.

25 Hazard function The hazard function λ(t) is the probability of dying “at” time t. Also called the instantaneous failure rate and force of mortality. Usually plotted is the cumulative hazard function, that is the accumulated hazard until time t.

26 Survival function For censored data the survival function can only be estimated.

27 Survival function Life table estimates WHO, StatsNZ

28 Survival function Kaplan Meier estimates

29 Survival function Kaplan Meier estimates 1. Order data by time to event (death) 2. Number at risk of event is number surviving less number censored. 3. Estimate of probability of surviving to next event 4. Multiply probabilities to estimate survival

30 Kaplan Meier plot

31 Kaplan Meier plot SCCMP Standard errors and 95% CI’s calculated by most software (SPSS, R, SAS) Usually use Greenwood’s or Tsiatis’ formula, software dependent.

32 Cumulative Hazard SCCMP

33 Summary statistics 1.Median survival: time when S(t) = 0.5 Must have enough data 2.Mean survival: area under the survival curve 3.5 year survival is survival rate at 5 years

34 Kaplan Meier estimate KM and lifetables are non-parametric methods: no assumptions are made about the distribution on the survival times. Typical distributions are exponential and Weibull. More powerful but can be sensitive to getting the distribution right.

35 Disease specific survival

36 Comparing 2 groups Log rank test Computed in SPSS, SAS, R Most popular –(Bland Altman BMJ 2004;328:1073 (1 May) Limitations –No estimate of size –Unlikely to detect a difference when risk is not consistent

37 Immuno compromised

38 Immuno compromised

39 Immuno compromised

40 Immuno compromised

41 Age group Call: survdiff(formula = Surv(mths,Status == "DOD") ~ ICOMP) N Observed Expected (O-E)^2/E (O-E)^2/V Age75=< Age75= Chisq= 0.6 on 1 degrees of freedom, p= 0.455

42 Facial Nerve Log rank p value: 0.09

43 Multiple independent variables Cox proportional hazards model Most common model Linear model for the log of the hazard ratio Baseline hazard unspecified

44 SCCMP example CPH model: Survival ~ Preserved + Age + ICOMP Preserved and ICOMP categorical Age continuous Plot survival for patients with each of /Y/N/partial nerve preservation adjusted for age and immuno compromised status

45 SCCMP example - SPSS Analyze > Survival > Cox Regression COXREG Months /STATUS=Status('DEAD') /PATTERN BY Preserved /CONTRAST (Preserved)=Indicator /CONTRAST (ICOMP)=Indicator(1) /METHOD=ENTER Preserved Age ICOMP /PLOT SURVIVAL /SAVE=PRESID XBETA /PRINT=CI(95) CORR SUMMARY BASELINE /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

46 SCCMP example - SPSS Patients with their facial nerve preserved have 12.6 times less hazard ratio, (95% CI 2-70). Preserving the facial nerve significantly reduces patients risk, (p value <0.001 CPH model).

47 SCCMP CPH model Adjusted for age and immuno compromised patients

48 Next Steps: Check proportional hazards assumption –Residual plots for groups Time dependent covariates More complex models we also didn’t do power calculations

49 Summary Survival analysis accounts for censoring in time to event data Log rank test: difference in survival between 2 groups Cox proportional hazard model More complex/powerful models available SPSS, R, SAS, Stata