Sequential decision rules for 2-arm clinical trials: a Bayesian perspective

Practical employment of Bayesian trial designs has been 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 1 error rate. This represents an internally inconsistent hybrid methodology, where important advantages from applying the Bayesian principles are lost. In particular, all pre-planned interim looks have an inflating multiplicity effect on Type 1 error rate. To present an alternative approach, we consider the prototype case of a 2-arm superiority trial with binary outcomes. The design is adaptive, using error tolerance criteria based on sequentially updated posterior probabilities, to conclude efficacy of the experimental treatment or futility of the trial. In the proposed approach, the regulators are assumed to have the main responsibility in defining criteria for the error control against false conclusions of efficacy, whereas the trial investigators will have a natural role in determining the criteria for concluding futility and thereby stopping the trial. It is suggested that the control of Type 1 error rate be replaced by the control of a criterion called regulators' False Discovery Probability (rFDP), the term corresponding directly to the probability interpretation of this criterion. Importantly, the sequential error control during the data analysis based on posterior probabilities will satisfy the rFDP criterion automatically, so that no separate computations are needed for such a purpose. 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. The proposed approach can lower the ultimately unnecessary barriers from the practical application of Bayesian trial designs.