Bayesian Approach for Assessing Non-inferiority in Three-arm Trials for Risk Ratio and Odds Ratio

In this paper we consider three-arm non-inferiority (NI) trial that includes an experimental, a reference, and a placebo arm. While for binary outcomes the risk difference (RD) is the most common and well explored functional form for testing efficacy (or effectiveness), recent FDA guideline suggested other measures such as relative risk (RR) and odds ratio (OR) on the basis of which NI of an experimental treatment can be claimed. However, developing test based on these different functions of binary outcomes are challenging since the construction and interpretation of NI margin for such functions are not trivial extensions of RD based approach. Recently, we have proposed Frequentist approaches for testing NI for these functionals. In this article we further develop Bayesian approaches for testing NI based on effect retention approach for RR and OR. Bayesian paradigm provides a natural path to integrate historical trials' information, as well as it allows the usage of patients'/clinicians' opinions as prior information via sequential learning. In addition we discuss, in detail, the sample size/power calculation which could be readily used while designing such trials in practice.