Group sequential design for time-to-event outcome with non-proportional hazards using the concept of relative time utilizing two different Weibull distributions

A group sequential design allows investigators to sequentially monitor efficacy and safety as part of interim testing in phase III trials. Literature is well developed in the case of continuous and binary outcomes, however, in case of trials with a time-to-event outcome, popular methods of sample size calculation often assume proportional hazards. In situations where the proportional hazards assumption is inappropriate as indicated by historical data, these popular methods are very restrictive. In this paper, a novel simulation-based group sequential design is proposed for a two-arm randomized phase III clinical trial with a survival endpoint for the non-proportional hazards scenario. By assuming that the survival times for each treatment arm follow two different Weibull distributions, the proposed method utilizes the concept of Relative Time to calculate the efficacy and safety boundaries at selected interim testing points. The test statistic used to generate these boundaries is asymptotically normal, allowing p-value calculation at each boundary. Many design features specific to time-to-event data can be incorporated with ease. Additionally, the proposed method allows the flexibility of having the accelerated failure time model and the proportional hazards model as constrained special cases. Real life applications are discussed demonstrating the practicality of the proposed method.