In cohort studies with common outcomes, the odds ratio estimated from a logistic regression analysis is often interpreted as an indirect estimate of the risk ratio. In such settings, the odds ratio will be farther from the null than the risk ratio. Direct and unbiased estimates of the risk ratio may be obtained from a log binomial model fit by maximum likelihood. When the maximum likelihood log binomial model fails to converge (as is common) or provides predicted probability estimates or upper confidence limits greater than 1.0, various approaches have been suggested, but each has drawbacks, as we describe. We propose a novel Bayesian approach for the estimation of the risk ratio from the log binomial model that addresses drawbacks of existing approaches. Posterior computation can be accomplished easily using the WinBUGs code provided.