What's the Risk? A Simple Approach for Estimating Adjusted Risk Measures from Nonlinear Models Including Logistic Regression

Abstract

To develop and validate a general method (called regression risk analysis) to estimate adjusted risk measures from logistic and other nonlinear multiple regression models. We show how to estimate standard errors for these estimates. These measures could supplant various approximations (e.g., adjusted odds ratio [AOR]) that may diverge, especially when outcomes are common. Regression risk analysis estimates were compared with internal standards as well as with Mantel-Haenszel estimates, Poisson and log-binomial regressions, and a widely used (but flawed) equation to calculate adjusted risk ratios (ARR) from AOR. Data sets produced using Monte Carlo simulations. Regression risk analysis accurately estimates ARR and differences directly from multiple regression models, even when confounders are continuous, distributions are skewed, outcomes are common, and effect size is large. It is statistically sound and intuitive, and has properties favoring it over other methods in many cases. Regression risk analysis should be the new standard for presenting findings from multiple regression analysis of dichotomous outcomes for cross-sectional, cohort, and population-based case-control studies, particularly when outcomes are common or effect size is large.