The asymptotic properties of nonparametric tests for comparing survival distributions

Abstract

The asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary, and possibly unequal, right censoring. The test statistics include equivalents to the log rank statistic, the modified Wilcoxon statistic and the class of rank invariant test procedures introduced by Peto & Peto. When there are equal censoring distributions and the hazard functions are proportional the sample size formula for the F test used to compare exponential samples is shown to be valid for the log rank test. In certain situations the power of the log rank test falls as the amount of censoring decreases.