Inferences on Odds Ratios, Relative Risks, and Risk Differences Based on Standard Regression Programs

Statistical analyses of the joint effects of several factors (covariates) on the risk of disease, death, or other dichotomous outcomes, are frequently based on a model that relates the effect of the covariates to some function of the probability of the outcome. The odds ratio, relative risk, and the difference in risks are among the simplest candidates for the outcome function. Each can be specified as a special case of the generalized linear model, but their use has been limited to researchers with access to specialized computer programs that are not yet generally available in standard computer packages. The purpose of this communication is to describe how to implement the maximum likelihood estimation procedures and hypothesis testing associated with the generalized linear model using any computer program that can perform weighted least squares analyses. The procedure is applied specifically to models for relative risks, risk differences, and odds ratios. The techniques are illustrated with SAS and SPSSx programs for data sets previously presented.