Bayesian models as a unified approach to estimate relative risk (or prevalence ratio) in binary and polytomous outcomes

Abstract

Background: Disadvantages have already been pointed out on the use of odds ratio (OR) as a measure of association for designs such as cohort and cross sectional studies, for which relative risk (RR) or prevalence ratio (PR) are preferable. The model that directly estimates RR or PR and correctly specifies the distribution of the outcome as binomial is the log-binomial model, however, convergence problems occur very often. Robust Poisson regression also estimates these measures but it can produce probabilities greater than 1. Results: In this paper, the use of Bayesian approach to solve the problem of convergence of the log-binomial model is illustrated. Furthermore, the method is extended to incorporate dependent data, as in cluster clinical trials and studies with multilevel design, and also to analyse polytomous outcomes. Comparisons between methods are made by analysing four data sets. Conclusions: In all cases analysed, it was observed that Bayesian methods are capable of estimating the measures of interest, always within the correct parametric space of probabilities.