Phase II clinical trials with time-to-event endpoints: optimal two-stage designs with one-sample log-rank test

Phase II clinical trials are often conducted to determine whether a new treatment is sufficiently promising to warrant a major controlled clinical evaluation against a standard therapy. We consider single-arm phase II clinical trials with right censored survival time responses where the ordinary one-sample logrank test is commonly used for testing the treatment efficacy. For planning such clinical trials, this paper presents two-stage designs that are optimal in the sense that the expected sample size is minimized if the new regimen has low efficacy subject to constraints of the type I and type II errors. Two-stage designs, which minimize the maximal sample size, are also determined. Optimal and minimax designs for a range of design parameters are tabulated along with examples.