survival analysis1 Every achievement originates from the seed of determination.

survival analysis 2 Survival Analysis Nonparametric Methods for Comparing Survival Distributions

survival analysis 3 Abbreviated Outline How to formally compare 2 or more survival distributions using hypothesis tests These tests look at weighted differences between the observed and expected hazard rates, allowing us to put more emphasis on certain parts of the curves

survival analysis 4 Hypotheses

survival analysis 5 Notation

survival analysis 6 Test Statistics

survival analysis 7 Test Statistics

survival analysis 8 Test Statistics

survival analysis 9 Test Statistics

survival analysis 10 Test Statistics

survival analysis 11 Test Statistics Reject Ho if U is too large.

survival analysis 12 Log-rank Test Constant weight function: Treat all observed failure times equally. It has optimum power to detect alternatives where the hazard rates in the M populations are proportional to each other

survival analysis 13 Proportional Hazard Assumption An underline assumption of many methods Suppose there are 2 groups of survival data. Then h 1 (u)=c*h 2 (u) where h i (u) is the hazard function of group i and c is a constant

survival analysis 14 Wilcoxon Test Survival time t (j) is weighted by n j, the number of individuals at risk at time t (j). This test is less sensitive than the log- rank test to deviation of the observed to the expected in the tail of the distribution of survival times.

survival analysis 15 Example: 6-MP To compare the survival distributions of the placebo group and the 6-MP group using the log-rank test Test of Equality over Strata Pr > Test Chi-Square DF Chi-Square Log-Rank <.0001 Wilcoxon Log(LR) <.0001

survival analysis 16 Stratified Tests Previously, we assumed that the various groups of individuals under comparison are homogeneous with respect to other factors which may affect survival time One way of detecting differences in survival between groups, while accounting for the effects of other factors is to stratify.

survival analysis 17 Stratified Tests When the number of strata is large, a test typically has low power to detect treatment differences.

survival analysis 18 Stratified Tests Hypothesis:

survival analysis 19 Stratified Tests

survival analysis 20

survival analysis 21 Example: 6-MP The patients are stratified according to remission status (partial or complete). Consider a test of Ho of no treatment effect, adjusting for the patient’s remission status. The stratified log-rank test (chisq=17.9 and p-value = 2.28x10^-5) indicates that the distribution of survival times is significantly different between 6-MP and placebo groups.