Assessment of risks by predicting counterfactuals.

Risk assessment is fundamental to most epidemiological and biomedical investigations. In this article, risks are assessed in terms of risk difference and risk ratio by predicting counterfactual outcomes. Models considered for binary outcomes are probit, logistic, and extreme-value regressions. New confidence intervals for the effect measures are proposed using the method of variance estimates recovery, and evaluated by a simulation study. A SAS macro is provided for the calculations. A risk ratio obtained using counterfactuals is also compared in the simulation with that directly estimated from the modified Poisson model to answer a recent concern about the validity of the latter approach. Two examples are used to illustrate the methods.