Every achievement originates from the seed of determination

Every achievement originates from the seed of determination. survival analysis 1

Survival Analysis Nonparametric Methods for Comparing Survival Distributions 2 survival analysis

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 ¢ 3 survival analysis

Hypotheses 4 survival analysis

Notation 5 survival analysis

Test Statistics 6 survival analysis

Test Statistics 7 survival analysis

Test Statistics 8 survival analysis

Test Statistics 9 survival analysis

Test Statistics 10 survival analysis

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

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 ¢ 12 survival analysis

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 hi(u) is the hazard function of group i and c is a constant 13 survival analysis

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

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 15 Test Chi-Square DF Pr > Chi-Square Log-Rank Wilcoxon -2 Log(LR) 16. 7929 13. 4579 16. 4852 1 1 1 <. 0001 0. 0002 <. 0001 survival analysis

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. ¢ 16 survival analysis

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

Stratified Tests ¢ 18 Hypothesis: survival analysis

Stratified Tests 19 survival analysis

20 survival analysis

Example: 6 -MP ¢ ¢ ¢ 21 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. 28 x 10^-5) indicates that the distribution of survival times is significantly different between 6 -MP and placebo groups. survival analysis