A Bayesian adaptive phase III design for multi-arm trials with time-to-event endpoint for nonproportional hazards utilizing the generalized gamma distribution

In case of trials with time-to-event endpoints, sample size calculations are well-studied under the assumption of proportional hazards or when the endpoint of interest follows an exponential distribution. When prior evidence suggests otherwise, using traditional approaches may lead to inefficiently designed and underpowered studies. In such situations, a recently introduced frequentist approach proposes a sample size calculation for a fixed two-arm trial based on the accelerated failure time model thereby allowing nonproportional hazards and can be utilized for any distribution from the generalized gamma family. Advances in the field of clinical trials research have focused on the need for adaptive phase III designs with complex features, however, existing methods in literature have ignored the nonproportional hazards scenario. In this article, we propose a Bayesian adaptive design for a multi-arm phase III trial with nonproportional hazards allowing many complex features such as incorporation of prior knowledge of early phase studies, arms dropping, and response adaptive randomization. We extend the frequentist approach utilizing a generalized gamma distribution to a Bayesian setting while simultaneously addressing one of the key limitations of the frequentist approach. Extensive simulations are performed to study the operation characteristics of the proposed design using two examples representing real-life applications.