Exact Bayesian Inference Comparing Binomial Proportions, With Application to Proof-of-Concept Clinical Trials

The authors revisit the problem of exact Bayesian inference comparing two independent binomial proportions. Numerical integration in R is used to compute exact posterior distribution functions, probability densities, and quantiles of the risk difference, relative risk, and odds ratio. An application of the methodology is given in the context of randomized comparative proof-of-concept clinical trials that are driven by evaluation of quantitative criteria combining statistical significance and clinical relevance. A two-stage adaptive design based on predictive probability of success is proposed and its operating characteristics are studied via Monte Carlo simulation. The authors conclude that exact Bayesian methods provide an elegant and efficient way to facilitate design and analysis of proof-of-concept studies.