Abstract
The propensity score is a subject's probability of treatment, conditional on observed baseline covariates. Conditional on the true propensity score, treated and untreated subjects have similar distributions of observed baseline covariates. Propensity-score matching is a popular method of using the propensity score in the medical literature. Using this approach, matched sets of treated and untreated subjects with similar values of the propensity score are formed. Inferences about treatment effect made using propensity-score matching are valid only if, in the matched sample, treated and untreated subjects have similar distributions of measured baseline covariates. In this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified: comparing means and prevalences of baseline characteristics using standardized differences; ratios comparing the variance of continuous covariates between treated and untreated subjects; comparison of higher order moments and interactions; five-number summaries; and graphical methods such as quantile–quantile plots, side-by-side boxplots, and non-parametric density plots for comparing the distribution of baseline covariates between treatment groups. We describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero, thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified. We highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity-score model. In particular, methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative. Copyright © 2009 John Wiley & Sons, Ltd.
Highlights
Researchers are increasingly using observational studies to estimate the effects of treatments and exposures on health outcomes
Our set of three Monte Carlo simulations demonstrated that observing balance on the means of covariates does not imply that the propensity-score model has been correctly specified
Greater bias was observed when matching on the mis-specified propensity score compared with when matching on the correctly specified propensity score despite the fact that balance in the means of covariates was observed
Summary
Researchers are increasingly using observational studies to estimate the effects of treatments and exposures on health outcomes. Non-randomized studies of the effect of treatment on outcomes can be subject to treatment-selection bias in which treated subjects differ systematically from untreated subjects. Propensity-score methods are being used with increasing frequency to estimate treatment effects using observational data. The propensity score is defined as the probability of treatment assignment conditional on measured baseline covariates [1, 2]. Rosenbaum and Rubin demonstrated a key property of the propensity score: conditional on the true propensity score, treatment status is independent of measured baseline covariates [1]. In other words, treated and untreated subjects with the same propensity score will have similar distributions of observed baseline covariates
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