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Handout24 - Lecture 24 1 Summarizing comparisons of...

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Lecture 24 1. Summarizing comparisons of survivor functions from Proc Lifetest 2. Proportional hazards regression: Proc PHreg 3. Graphical checks of proportional hazards assumption 4. Testing whether hazards are proportional 5. Time-varying explanatory variables 1 Summarizing tests comparing survivor functions When a test finds a significant difference between survivor curves, it does not tell us when they differ. Three common approaches to summarizing comparison of two groups A and B : 1. If curves are consistently separated, report overall result. If ˆ S A is consistently lower than ˆ S B , then group A suffered more early events and had a smaller percent surviving at any given time. Report results of log-rank test. During the two years after treatment, the proportion surviving was significantly higher in group B (log-rank test, p = .0378). 2

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2. Select a percent surviving, and report times when each group reached it. Common choice is 50% surviving, the median survival time. Quartile Estimates Point 95% Confidence Interval Percent Estimate [Lower Upper) Group A 75 1.58795 1.27036 . 50 0.69541 0.52841 1.32512 25 0.39425 0.20260 0.53388 Group B 75 2.39836 1.55784 3.47981 50 1.38535 1.04860 1.85079 25 0.95277 0.68446 1.06229 Median survival in group A was 0.7 years (95% CI: 0.5–1.3 years), while in group B median survival was 1.4 years, twice as long (95% CI: 1.0–1.9 years). 3 3. Select a time and report percent in each group surviving at that time. Percent surviving (and confidence interval) beyond a particular time comes from the Proc Lifetest listing of ˆ S ( t ). Stratum 1: group = A Survival Standard Number Number years Survival Failure Error Failed Left 0.00000 1.0000 0 0 0 45 . . . . 0.86242 0.4444 0.5556 0.0741 25 20 1.09788 0.4222 0.5778 0.0736 26 19 After one year of treatment, estimated proportion surviving in group A was 44% ± 7%, but in group B the estimated proportion surviving was 68% ± 7%. 4
Hazard function hazard function h ( t ) = f ( t ) S ( t ) = chance of an event at time t percent alive at time t Hazard h(t) is time-specific event rate. Survivor function S ( t ) = percent still at risk (alive) at time t . Hazard function h ( t ) = chance of event at time t for the subset of people at risk.

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