Monte Carlo error in the Bayesian estimation of risk ratios using log-binomial regression models: an efficient MCMC method

In cohort studies binary outcomes are very often analyzed by logistic regression. However, it is well-known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log-binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log-binomial model is difficult due to the constraints that must be imposed on these coefficients. Bayesian methods allow a straightforward approach for log-binomial regression models, produce smaller mean squared errors and the posterior inferences can be obtained using the software WinBUGS. However, the Markov chain Monte Carlo (MCMC) methods implemented in WinBUGS can lead to a high Monte Carlo error. To avoid this drawback we propose an MCMC algorithm that uses a reparameterization based on a Poisson approximation and has been designed to efficiently explore the constrained parameter space.