Improved maximum likelihood estimator in relative risk regression

Relative risk allows to parametrize in a simple and interpretable way the effect of a group of explanatory variables on a binary response of interest. Despite its ease of interpretation, statistical inference on this parameter is often challenging and limited to specific experimental designs. Starting from a previous work in the field, we propose the use of two estimating procedures for the cases in which there are many explanatory variables, but the interest is mainly focused on the effect of a binary risk factor. These methods, aiming at mean and median bias reduction of the maximum likelihood estimator, rely on a systematic correction of the likelihood estimating equation. We show through a simulation study and an application that the proposed methods perform better than ordinary maximum likelihood.