Bayesian decision theoretic two‐stage design in phase II clinical trials with survival endpoint

In this paper, we consider two-stage designs with failure-time endpoints in single-arm phase II trials. We propose designs in which stopping rules are constructed by comparing the Bayes risk of stopping at stage I with the expected Bayes risk of continuing to stage II using both the observed data in stage I and the predicted survival data in stage II. Terminal decision rules are constructed by comparing the posterior expected loss of a rejection decision versus an acceptance decision. Simple threshold loss functions are applied to time-to-event data modeled either parametrically or nonparametrically, and the cost parameters in the loss structure are calibrated to obtain desired type I error and power. We ran simulation studies to evaluate design properties including types I and II errors, probability of early stopping, expected sample size, and expected trial duration and compared them with the Simon two-stage designs and a design, which is an extension of the Simon's designs with time-to-event endpoints. An example based on a recently conducted phase II sarcoma trial illustrates the method.