Group Sequential Design Under Non-proportional Hazards: Methodologies and Examples

Non-proportional hazards (NPH) are often observed in clinical trials with time-to-event endpoints. A common example is a long-term clinical trial with a delayed treatment effect in immunotherapy for cancer. When designing clinical trials with time-to-event endpoints, it can be crucial to consider NPH scenarios to gain a complete understanding of design operating characteristics. In this chapter, we focus on group sequential design for three NPH methods: the extsnsion of logrank test to approximate the distribution of the logrank test under NPH, the weighted logrank test, and the MaxCombo test. For each of these approaches, we provide both their analytic forms and examples. To facilitate statisticians in designing and comparing group sequential designs under NPH, we have implemented the group sequential design methodology in the gsDesign2 R package at https://cran.r-project.org/web/packages/gsDesign2/ .