Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log-binomial regression models

Abstract

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 in the estimation of risk ratios than the frequentist methods, and the posterior inferences can be obtained using the softwareWinBUGS. However,Markov chainMonte Carlo (MCMC) methods implemented inWinBUGS can lead to largeMonte Carlo errors in the approximations to the posterior inferences since they produce correlated simulations and the accuracy of the approximations are inversely related to this correlation. To reduce correlation and to improve accuracy, we propose a reparameterization based on a Poisson model and a sampling algorithm coded in R.