Bayesian Versus Frequentist Hypotheses Testing in Clinical Trials with Dichotomous and Countable Outcomes

In the problem of hypothesis testing, a question of practical importance is: When do Bayesian and frequentist methodologies suggest similar solutions? Substantial progress has been made for one-sided hypotheses on the parameters of continuous distributions. In this article, we study the problem of testing one-side hypotheses in binomial and Poisson trials, using Bayesian models with conjugate priors. By correctly choosing prior parameters, we can make the posterior probability smaller than, equal to, or larger than the frequentist p-value. The results are illustrated through simulation modeling and analysis of data from clinical trials.