A Novel Bayesian Testing Approach to Assess Non-Inferiority

Non-inferiority (NI) clinical trials have gained immense popularity within the last decades, especially in cancer and cardiovascular studies. These trials are designed to establish the non-inferiority of a new experimental treatment as compared to the existing active control. In other words, NI trials are required to demonstrate that the efficacy of an experimental treatment is not unacceptably worse than that of an active control by more than a pre-specified small margin. We consider three-arm NI trials that have been widely acknowledged as the Gold Standard. Three-arm NI trials aim to simultaneously establish both NI and the assay sensitivity (AS). Hence, the analysis of three-arm NI trials involves multiple hypothesis testing. The existing literature on the Bayesian modeling of three-arm NI trials suggests implementing a test procedure based on the joint posterior probability of the NI and AS hypotheses. This joint testing of NI with AS resembles the framework of intersection-union (IU) testing, which may result in a very conservative test. In this article we propose a novel Bayesian testing based on an isotonic transformation in conjunction with Bayes factors. Bayes factors for assessing NI with AS are computed based on Gibbs Sampling. The performance of the proposed testing is evaluated through simulated data sets under varying scenarios. Empirical results show that the proposed Bayesian method gives better control in terms of Type-I error rates, and more powers than existing Bayesian tests. The usefulness of our test is illustrated by synthetic data from the Mildly Asthmatic Study.