Is control of type I error rate needed in Bayesian clinical trial designs?

Abstract: Practical employment of Bayesian trial designs is still rare. Even if accepted in principle, the regulators have commonly required that such designs be calibrated according to an upper bound for the frequentist type I error rate. This represents an internally inconsistent hybrid methodology, where important advantages from following the Bayesian principles are lost. In particular, all preplanned interim looks have an inflating multiplicity effect on type I error rate. To present an alternative approach, we consider the prototype case of a 2-arm superiority trial with dichotomous outcomes. The design is adaptive, using error control based on sequentially updated posterior probabilities, to conclude efficacy of the experimental treatment or futility of the trial. As gatekeepers for a proposed design, the regulators have the main responsibility in determining the parameters of the control of false positives, whereas the trial sponsors and investigators will have a natural role in specifying the criteria for stopping the trial due to futility. It is suggested that the traditional frequentist operating characteristics in the design, type I and type II error rates, be replaced, respectively, by Bayesian criteria called False Discovery Probability (FDP) and False Futility Probability (FFP), both terms corresponding directly to their probability interpretations. Importantly, the sequential error control during the data analysis based on posterior probabilities will satisfy these numerical criteria automatically, without need of preliminary computations before the trial is started. The method contains the option of applying a decision rule for terminating the trial early if the predicted costs from continuing would exceed the corresponding gains.