Abstract

Propensity score methods are increasingly being used to estimate the effects of treatments on health outcomes using observational data. There are four methods for using the propensity score to estimate treatment effects: covariate adjustment using the propensity score, stratification on the propensity score, propensity-score matching, and inverse probability of treatment weighting (IPTW) using the propensity score. When outcomes are binary, the effect of treatment on the outcome can be described using odds ratios, relative risks, risk differences, or the number needed to treat. Several clinical commentators suggested that risk differences and numbers needed to treat are more meaningful for clinical decision making than are odds ratios or relative risks. However, there is a paucity of information about the relative performance of the different propensity-score methods for estimating risk differences. We conducted a series of Monte Carlo simulations to examine this issue. We examined bias, variance estimation, coverage of confidence intervals, mean-squared error (MSE), and type I error rates. A doubly robust version of IPTW had superior performance compared with the other propensity-score methods. It resulted in unbiased estimation of risk differences, treatment effects with the lowest standard errors, confidence intervals with the correct coverage rates, and correct type I error rates. Stratification, matching on the propensity score, and covariate adjustment using the propensity score resulted in minor to modest bias in estimating risk differences. Estimators based on IPTW had lower MSE compared with other propensity-score methods. Differences between IPTW and propensity-score matching may reflect that these two methods estimate the average treatment effect and the average treatment effect for the treated, respectively. Copyright © 2010 John Wiley & Sons, Ltd.

Highlights

  • In randomized controlled trials, the effect of treatment on dichotomous outcomes can be reported using a variety of measures of treatment effect: the odds ratio, the relative risk, the absolute risk reduction, and the number needed to treat (NNT)

  • Matching on the propensity score resulted in estimated risk differences that were modestly biased away from the null treatment effect: the estimates displayed a greater absolute risk reduction compared with the true absolute risk reduction

  • Propensity-score matching resulted in a 95 per cent confidence interval that was 13 per cent wider than that of the doubly robust method with the fully specified outcomes regression model

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Summary

Introduction

The effect of treatment on dichotomous outcomes can be reported using a variety of measures of treatment effect: the odds ratio, the relative risk (and the associated relative risk reduction), the absolute risk reduction, and the number needed to treat (NNT) (the reciprocal of the absolute risk reduction). In the face of these proposals, some medical journals require that the NNT be reported for any randomized controlled trial with a dichotomous outcome [5]. Common to all these recommendations is the agreement that limited aInstitute for Clinical Evaluative Sciences, Toronto, ON, Canada bDepartment of Health Management, Policy and Evaluation, University of Toronto, ON, Canada ∗Correspondence to: Peter C.

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