Optimal two-stage log-rank test for randomized phase II clinical trials

Randomized controlled clinical trials are conducted to determine whether a new treatment is safe and efficacious compared to a standard therapy. We consider randomized clinical trials with right censored time to event endpoint, called survival time here. The two-sample log-rank test is popularly used to test if the experimental therapy has a longer survival distribution than the control therapy or not. We consider an early stopping for futility only or for both futility and efficacy. For planning such clinical trials, this article presents two-stage designs that are optimal in the sense that either the maximal sample size or the expected sample size when the experimental therapy is futile or superior is minimized under the given type I and II error rates. Optimal designs for a range of design parameters are tabulated and evaluated using simulations.