A Bayesian decision-theoretic dose-finding trial

We describe the use of a successful combination of Bayesian inference and decision theory in a clinical trial design. The trial involves three important decisions, adaptive dose allocation, optimal stopping of the trial, and the optimal terminal decision upon stopping. For all three decisions we use a formal Bayesian decision-theoretic approach. The application demonstrates how Bayesian posterior inference and decision-theoretic approaches combine to provide a coherent solution in a complex application. The main challenges are the need for a flexible probability model for the unknown dose–response curve, a delayed response, the sequential nature of the stopping decision, and the complex considerations involved in the terminal decision. The main methodological features of the proposed solution are the use of decision theory to achieve optimal learning about the unknown dose–response curve, an innovative grid-based approximation method to implement backward induction for the sequential stopping decision, and a utility function for the terminal decision that is based on a posterior predictive description of a future confirmatory trial.