M&M: A maximum duration design with the Maxcombo test for a group sequential trial of an immunotherapy with a random delayed treatment effect

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.