Sample size calculation for the one-sample log-rank test

Abstract

An improved method of sample size calculation for the one-sample log-rank test is provided. The one-sample log-rank test may be the method of choice if the survival curve of a single treatment group is to be compared with that of a historic control. Such settings arise, for example, in clinical phase-II trials if the response to a new treatment is measured by a survival endpoint. Present sample size formulas for the one-sample log-rank test are based on the number of events to be observed, that is, in order to achieve approximately a desired power for allocated significance level and effect the trial is stopped as soon as a certain critical number of events are reached. We propose a new stopping criterion to be followed. Both approaches are shown to be asymptotically equivalent. For small sample size, though, a simulation study indicates that the new criterion might be preferred when planning a corresponding trial. In our simulations, the trial is usually underpowered, and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used, whereas a trial based on the new stopping criterion maintains power with the type-I error rate still controlled.

Keywords: one-sample log-rank test; phase-II trial; power calculation; sample size.