Sample size determination and evaluation for two-stage adaptive designs of single arm clinical trials based on median event time test

Clinical trials play a critical role in drug development which involves a series of phases and requires a significant amount of time and effort. Efficient clinical trial designs are necessary to investigate a new drug. Investigators strongly desire to use the time-to-event endpoint as the primary endpoint for Phase II studies, which evaluates the therapeutic efficacy of the new drug, with the hypothesis that the new drug improves the median survival time. The one-sample log-rank test has been used for single-arm Phase II trials, but it generally requires more samples. Recently, the median event time test was proposed to provide a simple, straightforward decision rule, which compares the observed median survival time for the new drug with the threshold, which is determined through the numerical search. We improve the computation of the method for the two-stage design of single-arm clinical trials based on the median event time test. By utilizing the large sample theory of order statistics, we provide the explicit formulas to calculate the sample size for the first and second stages and propose the testing procedure. The performance of the proposed method is evaluated through simulations and a trial example.