Estimation of relative risk and prevalence ratio

Relative risks (RRs) and prevalence ratios (PRs) are measures of association that are more intuitively interpretable than odds ratios (ORs). Many health science studies report OR estimates, however, even when their designs permit and study questions target RRs and/or PRs. This is, partially, attributable to the popularity and technical advantage (i.e. no restriction on the parameter space) of logistic regression for estimating ORs. To improve this practice, several biostatistical approaches for estimating RR/PR, adjusting for potential confounders, have been proposed. In this paper, we consider two RR/PR estimating methods: (1) the modification of log-binomial regression with the COPY method; and (2) an inverse-probability-of-treatment-weighted (IPTW) log-binomial regression we newly propose. For the COPY method, we rigorously establish the existence and uniqueness of the maximum-likelihood estimator, provided certain degeneracies in the data do not occur. Moreover, the global maximum of the COPY-modified likelihood is shown to occur at an interior point of the restricted parameter space. This result explains why the COPY method avoids convergence problems of log-binomial models frequently. For the IPTW estimator, we show that its simple procedure results in standardized estimates of RR/PR, and discuss its potential challenges, extensions, and an improvement through propensity-score-based grouping of observations. Furthermore, we compare the performances of four RR/PR estimation methods, including the COPY method and IPTW log-binomial regression, on simulated data. We demonstrate a lack of robustness of the COPY method against misspecification of the true relationship between binary outcome and explanatory variables, and show robustness of the IPTW approach in this regard.