In this talk, I will present a Bayesian approach to the problem of comparing two independent binomial proportions and its application to the design and analysis of proof-of-concept clinical trials.
First, I will discuss numerical integration methods to compute exact posterior distribution functions, probability densities, and quantiles of the risk difference, relative risk, and odds ratio. These numerical methods are building blocks for applying exact Bayesian analysis in practice. Exact probability calculations provide improved accuracy compared to normal approximations and are computationally more efficient than simulation-based approaches, especially when these calculations have to be invoked repeatedly as part of another simulation study.
Second, I will show applicability of exact Bayesian calculations in the context of a proof-of-concept clinical trial in ophthalmology. A single-stage design and a two-stage adaptive design based on posterior predictive probability of achieving proof-of-concept based on dual criteria of statistical significance and clinical relevance will be presented. A two-stage design allows early stopping for either futility or efficacy, thereby providing a higher level of cost-efficiency than a single-stage design. A take-home message is that exact Bayesian methods provide an elegant and efficient way to facilitate design and analysis of proof-of-concept studies.
Sverdlov O, Ryeznik Y, Wu S. (2015). Exact Bayesian inference comparing binomial proportions, with application to proof-of-concept clinical trials. Therapeutic Innovation and Regulatory Science 49(1), 163-174.