Stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure

Senn, S., Graf, E. and Caputo, A. (2007) Stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure. Statistics in Medicine, 26(30), pp. 5529-5544. (doi: 10.1002/sim.3133)

Abstract

Stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure. A more traditional alternative technique is the direct adjustment for confounding in regression models. This paper discusses fundamental differences between the two approaches, with a focus on linear regression and propensity score stratification, and identifies points to be considered for an adequate comparison. The treatment estimators are examined for unbiasedness and efficiency. This is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models. We demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model, even if it is built on coarser covariate strata than the linear model. As a consequence the coarsening property of the propensity score—adjustment for a one-dimensional confounder instead of a high-dimensional covariate—may be viewed as a way to implement a pre-specified, richly parametrized linear model. We conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

• Item Type: Articles
• Keywords: confounding; propensity score; Gauss–Markov theorem; linear models; conditional independence
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Senn, Professor Stephen
• Authors: Senn, S., Graf, E., and Caputo, A.
• Subjects: R Medicine > RA Public aspects of medicine; Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Statistics in Medicine
• Publisher: John Wiley
• ISSN: 1097-0258