Bayesian Hypothesis Assessment in Two-arm Trials Using Relative Belief Ratios

Abstract: This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either for or against a hypothesis. In addition to the relative belief ratio, we also compute a measure of the strength of this evidence as a calibration of the relative belief ratio. Furthermore, we make use of the relative belief ratio as a measure of evidence, to assess whether a given prior induces bias either for or against a hypothesis. Prior elicitation, model checking and checking for prior-data conflict procedures are developed to ensure that the choices of model and prior made are relevant to the specific application. We highlight the applicability of the approach and illustrate the proposed method by applying it to a data set obtained from a two-arm clinical trial.