Uniformly most powerful Bayesian interval design for phase I dose-finding trials

Interval designs have recently attracted much attention in phase I clinical trials because of their simplicity and desirable finite-sample performance. However, existing interval designs typically cannot converge to the optimal dose level since their intervals do not shrink to the target toxicity probability as the sample size increases. The uniformly most powerful Bayesian test (UMPBT) is an objective Bayesian hypothesis testing procedure, which results in the largest probability that the Bayes factor against null hypothesis exceeds the evidence threshold for all possible values of the data generating parameter. On the basis of the rejection region of UMPBT, we develop the uniformly most powerful Bayesian interval (UMPBI) design for phase I dose-finding trials. The proposed UMPBI design enjoys convergence properties because the induced interval indeed shrinks to the toxicity target and the recommended dose converges to the true maximum tolerated dose as the sample size increases. Moreover, it possesses an optimality property that the probability of incorrect decisions is minimized. We conduct simulation studies to demonstrate the competitive finite-sample operating characteristics of the UMPBI in comparison with other existing interval designs. As an illustration, we apply the UMPBI design to a panitumumab and standard gemcitabine-based chemoradiation combination trial.