Bayesian approach for assessing noninferiority in a three-arm trial with binary endpoint

With the recent advancement in many therapeutic areas, quest for better and enhanced treatment options is ever increasing. While the "efficacy" metric plays the most important role in this development, emphasis on other important clinical factors such as less intensive side effects, lower toxicity, ease of delivery, and other less debilitating factors may result in the selection of treatment options, which may not beat current established treatment option in terms efficacy, yet prove to be desirable for subgroups of patients. The resultant clinical trial by means of which one establishes such slightly less efficacious treatment is known as noninferiority (NI) trial. Noninferiority trials often involve an active established comparator arm, along with a placebo and an experimental treatment arm, resulting into a 3-arm trial. Most of the past developments in a 3-arm NI trial consider defining a prespecified fraction of unknown effect size of reference drug, i.e., without directly specifying a fixed NI margin. However, in some recent developments, more direct approach is being considered with prespecified fixed margin, albeit in the frequentist setup. In this article, we consider Bayesian implementation of such trial when primary outcome of interest is binary. Bayesian paradigm is important, as it provides a path to integrate historical trials and current trial information via sequential learning. We use several approximation-based and 2 exact fully Bayesian methods to evaluate the feasibility of the proposed approach. Finally, a clinical trial example is reanalyzed to demonstrate the benefit of the proposed approach.