  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 is crucial to consider NPH scenarios to
gain a complete understanding of design operating characteristics. In this
paper, we focus on group sequential design for three NPH methods: the average
hazard ratio, the weighted logrank test, and the MaxCombo combination test. For
each of these approaches, we provide analytic forms of design characteristics
that facilitate sample size calculation and bound derivation for group
sequential designs. Examples are provided to illustrate the proposed methods.
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/.
