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

Authors

  • Lawrence C. Kleinman,

    1. Department of Health Policy, Mount Sinai School of Medicine, Box 1077, New York, NY 10029,
    2. Quality Matters Inc., Allentown, PA,
    3. Department of Society, Health and Human Development, Harvard School of Public Health, Boston, MA,
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    • Address correspondence to Lawrence C. Kleinman, M.D., M.P.H., Associate Professor of Health Policy and Pediatrics, Vice Chair for Research and Education, Department of Health Policy, Mount Sinai School of Medicine, Box 1077, New York, NY 10029; e-mail: lawrence.kleinman@mssm.edu. Dr. Kleinman is President and CEO, Quality Matters Inc., Allentown, PA, and also Adjunct Associate Professor, Department of Society, Health and Human Development, Harvard School of Public Health, Boston, MA. Edward C. Norton, Ph.D., is a professor in the Department of Health Management and Policy, School of Public Health, and a professor in the Department of Economics, University of Michigan, Ann Arbor, MI.

  • Edward C. Norton

    1. Department of Health Management and Policy, School of Public Health,
    2. Department of Economics, University of Michigan, Ann Arbor, MI
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Abstract

Objective. 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.

Study Design. 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 Collection. Data sets produced using Monte Carlo simulations.

Principal Findings. 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.

Conclusions. 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.

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