Sample size determination for comparing more than two survival distributions

We examine the asymptotic properties of the Tarone and Ware and Harrington and Fleming classes of test statistics under alternative hypotheses when there are comparisons between more than two survival distributions in the presence of arbitrary right censoring. When we assume equal censoring distributions across treatment groups and proportional hazards, we derive the sample size formula for testing the equality of k ⩾ 2 survival distributions using the logrank test. This work extends Schoenfeld's derivation for comparing two survival distributions and also generalizes the results of Makuch and Simon. We also derive the sample size formula for testing monotone dose-response using Tarone's trend test. We then investigate the practicality of the formula in various situations by presenting empirical power with use of Monte Carlo simulations. In addition, with stratification present, we derive the sample size formula for the stratified logrank test, which is an extension of Palta and Amini.