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

TL;DR

This paper introduces a Bayesian method using relative belief ratios for evaluating equivalence and non-inferiority hypotheses in two-arm clinical trials, emphasizing evidence calibration, bias assessment, and prior-data conflict checks.

Contribution

It develops a comprehensive Bayesian framework with new measures for evidence, bias detection, and prior validation tailored for two-arm trial hypothesis testing.

Findings

Effective evidence calibration using relative belief ratios

Method for detecting prior-induced bias

Application demonstrated on real clinical trial data

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.