1. Survival Analysis Rick Chappell, Ph.D. Professor,
Department of Biostatistics and Medical Informatics
University of Wisconsin School of Medicine & Public Health
BMI 542 – Week 6, Lecture 1
(slides adapted in part from D. DeMets’) 2

2. Survival Analysis Terminology
Concerned about time to some event
Event is often death
Event may also be, for example
1. Cause-specific death
2. Recurrence of tumor or death,
whichever comes first
3. Death or some non-fatal event
4. Release from hospital; marriage; divorce; job tenure; job acquisition …

3. Survival Rates at Yearly Intervals
YEARS
At 5 years, survival rates the same
Survival experience in Group A appears more favorable, considering 1 year, 2 year, 3 year and 4 year rates together

4. Beta-Blocker Heart Attack Trial
LIFE-TABLE CUMULATIVE MORTALITY CURVE

5. Survival Analysis 1. Estimation of survival curves
2. Comparison of survival curves
Estimation
Simple Case
All patients entered at the same “time” and followed for the same length of time
Survival curve is estimated at various time points by (number of deaths)/(number of patients)
As intervals become smaller and number of patients larger, a smoother survival curve may be plotted
Typical Clinical Trial Setting

6. Staggered Entry
T years 1
T years 2
Subject
T years 3
T years 4 T 2T
Time Since Start of Trial (T years)
Each patient has T years of follow-up
Time for follow-up taking place may be different for each patient

7. • * * Subject o Administrative 1 Right Censoring 2 Failure 3
Loss to Follow-up * 4
Failure T 2T
Time Since Start of Trial (T years)
Failure time is time from entry until the time of the event
Right Censoring means vital status of patient is not known beyond that point

8. * • * Subject Administrative Censoring 1 o 2 Failure 3 Censoring
Loss to Follow-up 4 *
Failure T
Follow-up Time (T years)

9. Clinical Trial with Common Termination Date
Subject 1 o 2 * 3 • 4 • o 5 • * • • 6 7 • • 8 • * 9 • o o 10 • o * 11 • o o T 2T
Follow-up Time (T years)
Trial
Terminated

10. Kaplan-Meier Estimate (JASA, 1958) – see “KM.mechanics” pdf
Assumptions
1. "Exact" time of event is known
Failure = uncensored event
Loss = censored event
Failures are independent of Losses! See KMBias.ppt
2. For a "tie", failure always before loss (minor)
3. Divide follow-up time into intervals such that
a. Each event defines left side of an interval
b. No interval has both deaths & losses

11. 2. Comparison of Two Survival Curves
Assume that we now have a treatment group and a control group and we wish to make a comparison between their survival experience
How do we do so in a way which builds upon the Kaplan-Meier estimator?
Point-wise at a “landmark” time using Greenwood.
Medians?
Mantel-Haenszel (log rank) test, with equal weighting;
Peto-Prentice (Gehan) test, with earlier events upweighted & later ones downweighted.