Statistical power for a long-term survival trial with a time-dependent treatment effect

A time-dependent treatment effect is often observed in cancer clinical trials with survival endpoints, especially in long-term studies. This article evaluates the statistical power of the log-rank test when change point(s) in treatment effect are given. Following the work of Schoenfeld, we derive the asymptotic properties of the log-rank test statistics with time-dependent step-function alternatives. We show that the statistical power for such an alternative hypothesis is determined by the distribution of the number of events for given time intervals. Then, the relationship between the statistical power and the sample size, accrual, and minimum follow-up period can be established. Aided by the examples of two prostate cancer trials conducted by the Radiation Therapy Oncology Group, we demonstrate the changes in statistical power under various alternative hypotheses such as prolonged lag time and a declining treatment effect in long-term studies. Having examined the loss in statistical power by the interim analyses under the alternative hypothesis with a lag time, we recommend that the lower sequential boundary not be used in a long-term survival clinical trial. Control Clin Trials 2000;21:561-573