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American Journal of Epidemiology Advance Access originally published online on April 19, 2006
American Journal of Epidemiology 2006 163(12):1149-1156; doi:10.1093/aje/kwj149
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American Journal of Epidemiology Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.

Practice of Epidemiology

Variable Selection for Propensity Score Models

M. Alan Brookhart1, Sebastian Schneeweiss1, Kenneth J. Rothman1,2, Robert J. Glynn1,3, Jerry Avorn1 and Til Stürmer1,3

1 Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA
2 Departments of Epidemiology and Medicine, Boston University Medical Center, Boston, MA
3 Division of Preventive Medicine, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA

Correspondence to Dr. M. Alan Brookhart, Division of Pharmacoepidemiology and Pharmacoeconomics, Brigham and Women's Hospital and Harvard Medical School, 1620 Tremont Street, Suite 3030, Boston, MA 02120 (e-mail: abrookhart{at}rics.bwh.harvard.edu).

Despite the growing popularity of propensity score (PS) methods in epidemiology, relatively little has been written in the epidemiologic literature about the problem of variable selection for PS models. The authors present the results of two simulation studies designed to help epidemiologists gain insight into the variable selection problem in a PS analysis. The simulation studies illustrate how the choice of variables that are included in a PS model can affect the bias, variance, and mean squared error of an estimated exposure effect. The results suggest that variables that are unrelated to the exposure but related to the outcome should always be included in a PS model. The inclusion of these variables will decrease the variance of an estimated exposure effect without increasing bias. In contrast, including variables that are related to the exposure but not to the outcome will increase the variance of the estimated exposure effect without decreasing bias. In very small studies, the inclusion of variables that are strongly related to the exposure but only weakly related to the outcome can be detrimental to an estimate in a mean squared error sense. The addition of these variables removes only a small amount of bias but can increase the variance of the estimated exposure effect. These simulation studies and other analytical results suggest that standard model-building tools designed to create good predictive models of the exposure will not always lead to optimal PS models, particularly in small studies.

confounding factors (epidemiology); effect modifiers (epidemiology); models, statistical; propensity score; regression analysis; simulation; subset selection; variable selection

Abbreviations: MSE, mean squared error; PS, propensity score


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