Semiparametric bayesian testing procedure for noninferiority trials with binary endpoints

A semiparametric testing approach based on the Bayes factor is developed for non-inferiority trials with binary endpoints. The proposed method is shown to work for a broad class of hypotheses by accommodating a variety of dissimilarity measures between two binomial parameters. Two of the unique features of the proposed testing procedure include: (i) construction of a flexible class of conjugate priors using a mixture of beta densities to maintain approximate equality of prior probabilities of the competing hypotheses; and (ii) automatic determination of the cutoff value of the Bayes factor to facilitate the decision making process. In contrast to the use of Jeffreys's rule of thumb, two forms of total weighted average error criteria are used to determine the cutoff value. Through several simulation studies it is demonstrated that the proposed Bayesian procedure has competitive frequentist properties of controlling type I error as compared to the default frequentist test and meanwhile the proposed criterion improves the statistical power, especially in small samples. The method is further illustrated using the data from a streptococcal pharyngitis clinical trial.