Bayesian single‐arm phase II trial designs with time‐to‐event endpoints

For the cancer clinical trials with immunotherapy and molecularly targeted therapy, time‐to‐event endpoint is often a desired endpoint. In this paper, we present an event‐driven approach for Bayesian one‐stage and two‐stage single‐arm phase II trial designs. Two versions of Bayesian one‐stage designs were proposed with executable algorithms and meanwhile, we also develop theoretical relationships between the frequentist and Bayesian designs. These findings help investigators who want to design a trial using Bayesian approach have an explicit understanding of how the frequentist properties can be achieved. Moreover, the proposed Bayesian designs using the exact posterior distributions accommodate the single‐arm phase II trials with small sample sizes. We also proposed an optimal two‐stage approach, which can be regarded as an extension of Simon's two‐stage design with the time‐to‐event endpoint. Comprehensive simulations were conducted to explore the frequentist properties of the proposed Bayesian designs and an R package BayesDesign can be assessed via R CRAN for convenient use of the proposed methods.