New approaches for testing non-inferiority for three-arm trials with Poisson distributed outcomes

With the availability of limited resources, innovation for improved statistical method for the design and analysis of randomized controlled trials (RCTs) is of paramount importance for newer and better treatment discovery for any therapeutic area. Although clinical efficacy is almost always the primary evaluating criteria to measure any beneficial effect of a treatment, there are several important other factors (e.g., side effects, cost burden, less debilitating, less intensive, etc.), which can permit some less efficacious treatment options favorable to a subgroup of patients. This leads to non-inferiority (NI) testing. The objective of NI trial is to show that an experimental treatment is not worse than an active reference treatment by more than a pre-specified margin. Traditional NI trials do not include a placebo arm for ethical reason; however, this necessitates stringent and often unverifiable assumptions. On the other hand, three-arm NI trials consisting of placebo, reference, and experimental treatment, can simultaneously test the superiority of the reference over placebo and NI of experimental treatment over the reference. In this article, we proposed both novel Frequentist and Bayesian procedures for testing NI in the three-arm trial with Poisson distributed count outcome. RCTs with count data as the primary outcome are quite common in various disease areas such as lesion count in cancer trials, relapses in multiple sclerosis, dermatology, neurology, cardiovascular research, adverse event count, etc. We first propose an improved Frequentist approach, which is then followed by it's Bayesian version. Bayesian methods have natural advantage in any active-control trials, including NI trial when substantial historical information is available for placebo and established reference treatment. In addition, we discuss sample size calculation and draw an interesting connection between the two paradigms.