Sample Size Determination Under Non-proportional Hazards

The proportional hazards assumption rarely holds in clinical trials of cancer immunotherapy. Specifically, delayed separation of the Kaplan-Meier survival curves and long-term survival have been observed. Routine practice in designing a randomized controlled two-arm clinical trial with a time-to-event endpoint assumes proportional hazards. If this assumption is violated, traditional methods could inaccurately estimate statistical power and study duration. This article addresses how to determine the sample size in the presence of nonproportional hazards (NPH) due to delayed separation, diminishing effects, etc. Simulations were performed to illustrate the relationship between power and the number of patients/events for different types of nonproportional hazards. Novel efficient algorithms are proposed to optimize the selection of a cost-effective sample size.