A general framework for constraint approaches to adjusted risk differences

The risk difference is an intelligible measure for comparing disease incidence in two exposure or treatment groups. Despite its convenience in interpretation, it is less prevalent in epidemiological and clinical areas where regression models are required in order to adjust for confounding. One major barrier to its popularity is that standard linear binomial or Poisson regression models can provide estimated probabilities out of the range of (0,1), resulting in possible convergence issues. For estimating adjusted risk differences, we propose a general framework covering various constraint approaches based on binomial and Poisson regression models. The proposed methods span the areas of ordinary least squares, maximum likelihood estimation, and Bayesian inference. Compared to existing approaches, our methods prevent estimates and confidence intervals of predicted probabilities from falling out of the valid range. Through extensive simulation studies, we demonstrate that the proposed methods solve the issue of having estimates or confidence limits of predicted probabilities out of (0,1), while offering performance comparable to its alternative in terms of the bias, variability, and coverage rates in point and interval estimation of the risk difference. An application study is performed using data from the Prospective Registry Evaluating Myocardial Infarction: Event and Recovery (PREMIER) study.