Improved and computationally stable estimation of relative risk regression with one binary exposure

In medical statistics, when the effect of a binary risk factor on a binary response is of interest, relative risk is often the preferred measure due to its direct interpretation. However, statistical inference on this quantity is not as straightforward as for other measures of association, especially when further explanatory variables have to be taken into account. Starting from a review of available methods for inference on relative risk, this paper deals with small and moderate sample size settings for which we show that classical approaches can be problematic. For this reason, we propose the use of improved estimation procedures, aiming at mean or median bias reduction of the maximum likelihood estimator. In particular, these methods are developed for a new alternative specification of a model recently proposed by Richardson et al, where higher computational stability of the estimation methods is achieved. A real-data example and extensive simulation studies show that the proposed methods perform remarkably better than the standard ones.