Relative Risk Regression for Binary Outcomes: Methods and Recommendations

Relative risks are often considered preferable to odds ratios for quantifying the association between a predictor and a binary outcome. Relative risk regression is an alternative to logistic regression where the parameters are relative risks rather than odds ratios. It uses a log link binomial generalised linear model, or log-binomial model, which requires parameter constraints to prevent probabilities from exceeding 1. This leads to numerical problems with standard approaches for finding the maximum likelihood estimate (MLE), such as Fisher scoring, and has motivated various non-MLE approaches. In this paper we discuss the roles of the MLE and its main competitors for relative risk regression. It is argued that reliable alternatives to Fisher scoring mean that numerical issues are no longer a motivation for non-MLE methods. Nonetheless, non-MLE methods may be worthwhile for other reasons and we evaluate this possibility for alternatives within a class of quasi-likelihood methods. The MLE obtained using a reliable computational method is recommended, but this approach requires bootstrapping when estimates are on the parameter space boundary. If convenience is paramount, then quasi-likelihood estimation can be a good alternative, although parameter constraints may be violated. Sensitivity to model misspecification and outliers is also discussed along with recommendations and priorities for future research.