Sample Size and Power of Survival Trials in Group Sequential Design With Delayed Treatment Effect

Abstract

ABSTRACTIn study designs for randomized clinical trials with a survival endpoint, the log-rank test is commonly used with the treatment effect under a proportional hazards assumption. Recently, treatment effects in cancer immunotherapy trials have exhibited a delayed effect pattern with late separation of survival curves, raising challenges to the use of conventional study design hypotheses and analysis. In particular, when a trial with interim analyses is designed using a group sequential method, the expected treatment effect from a log-rank test statistic varies across analysis times and differs from the parameter specified under the alternative hypothesis. In this article, we present statistical analytical work that formulates a design including interim analyses with a survival endpoint under a delayed treatment effect alternative. Closed-form solutions are provided for calculating power and sample size over varying study/follow-up times for the group sequential, delayed treatment effect design. The analytical work is also presented graphically and simulations are conducted for validation.