Applications of Bayesian methods to arthritis research

Bayesian methods are used to compare two independent proportions which arise in arthritis research problems. Some new prior distributions are considered as well as ones previously presented. The specific problem we investigate is the comparison of two proportions where each proportion represents the proportion of a population which shows improvement as the result of a treatment. A Morgernstern-type bivariate distribution is used to represent the bivariate prior distribution of the two proportions, p₁ and p₂. This distribution allows p ₁ and p₂ to be correlated. The joint posterior distribution of p1 and p2, and the univariate posterior distribution of p = p1 − p ₂ are derived. Bayes factors are computed and used to evaluate the evidence against the hypotheses of no difference in the two proportions. We also investigate how the choice of the correlations for the priors impacts on the resulting posterior probabilities and Bayes factors. Simulation studies are used to investigate the Bayesian methods and the classical methods. The definition of patient improvement proposed by the committee of the American College of Rheumatology (ACR) requires obtaining values of seven variables in rheumatoid arthritis (RA) clinical trials. In some studies, all seven variables are not available. We also investigate how this lack of complete information affects the probabilities of patient improvement and propose adjustment in the choice of prior distributions for p₁ and p ₂ to account for this.