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.

Doubly robust estimation combines a form of outcome regression with a model for the exposure (i.e., the propensity score) to estimate the causal effect of an exposure on an outcome. When used individually to estimate a causal effect, both outcome regression and propensity score methods are unbiased only if the statistical model is correctly specified. The doubly robust estimator combines these 2 approaches such that only 1 of the 2 models need be correctly specified to obtain an unbiased effect estimator. In this introduction to doubly robust estimators, the authors present a conceptual overview of doubly robust estimation, a simple worked example, results from a simulation study examining performance of estimated and bootstrapped standard errors, and a discussion of the potential advantages and limitations of this method. The supplementary material for this paper, which is posted on the Journal's Web site (http://aje.oupjournals.org/), includes a demonstration of the doubly robust property (Web Appendix 1) and a description of a SAS macro (SAS Institute, Inc., Cary, North Carolina) for doubly robust estimation, available for download at http://www.unc.edu/~mfunk/dr/.

Publication of results based on propensity score methods has increased dramatically, but there is little evidence that these methods yield substantially different estimates compared with conventional multivariable methods.

Better understanding of biases related to selective prescribing of, and adherence to, preventive treatments has led to improvements in the design and analysis of pharmacoepidemiologic studies. One influential development has been the “active comparator, new user” study design, which seeks to emulate the design of a head-to-head randomized controlled trial. In this review, we first discuss biases that may affect pharmacoepidemiologic studies and describe their direction and magnitude in a variety of settings. We then present the historical foundations of the active comparator, new user study design and explain how this design conceptually mitigates biases leading to a paradigm shift in pharmacoepidemiology. We offer practical guidance on the implementation of the study design using administrative databases. Finally, we provide an empirical example in which the active comparator, new user study design addresses biases that have previously impeded pharmacoepidemiologic studies.

No abstract

Use of propensity scores to identify and control for confounding in observational studies that relate medications to outcomes has increased substantially in recent years. However, it remains unclear whether, and if so when, use of propensity scores provides estimates of drug effects that are less biased than those obtained from conventional multivariate models. In the great majority of published studies that have used both approaches, estimated effects from propensity score and regression methods have been similar. Simulation studies further suggest comparable performance of the two approaches in many settings. We discuss five reasons that favour use of propensity scores: the value of focus on indications for drug use; optimal matching strategies from alternative designs; improved control of confounding with scarce outcomes; ability to identify interactions between propensity of treatment and drug effects on outcomes; and correction for unobserved confounders via propensity score calibration. We describe alternative approaches to estimate and implement propensity scores and the limitations of the C-statistic for evaluation. Use of propensity scores will not correct biases from unmeasured confounders, but can aid in understanding determinants of drug use and lead to improved estimates of drug effects in some settings.Use of propensity scores in pharmacoepidemiologic studies has increased substantially over the past few years, yet evidence is lacking that this approach will systematically give better estimates of drug effects than those obtained from conventional regression approaches. If one compares the distributions of variables included in a propensity score between users of a drug and non-users matched on the propensity score, the balance of these distributions between groups will frequently be better than if drug allocation were randomized (Joffe & Rosembaum 1999). However, randomization tends to balance the unmeasured confounders, whereas matching on the propensity score often will not.Thus, propensity score methods and conventional multivariate methods (Drake 1993) have similar inability to control unmeasured confounding. In this context, this article considers whether increased use of propensity scores is warranted. We begin with definitions, a review of the properties of the propensity score, and a description of its increasing use. We summarize available empirical comparisons and simulation studies of drug effects estimated by the propensity score versus conventional regression methods. We mention specific circumstances when use of propensity scores

Frailty, a poorly measured confounder in older patients, can promote treatment in some situations and discourage it in others. This can create unmeasured confounding and lead to nonuniform treatment effects over the propensity score (PS). The authors compared bias and mean squared error for various PS implementations under PS trimming, thereby excluding persons treated contrary to prediction. Cohort studies were simulated with a binary treatment T as a function of 8 covariates X. Two of the covariates were assumed to be unmeasured strong risk factors for the outcome and present in persons treated contrary to prediction. The outcome Y was simulated as a Poisson function of T and all X's. In analyses based on measured covariates only, the range of PS's was trimmed asymmetrically according to the percentile of PS in treated patients at the lower end and in untreated patients at the upper end. PS trimming reduced bias due to unmeasured confounders and mean squared error in most scenarios assessed. Treatment effect estimates based on PS range restrictions do not correspond to a causal parameter but may be less biased by such unmeasured confounding. Increasing validity based on PS trimming may be a unique advantage of PS's over conventional outcome models.

Epidemiologic studies are increasingly used to investigate the safety and effectiveness of medical products and interventions. Appropriate adjustment for confounding in such studies is challenging because exposure is determined by a complex interaction of patient, physician, and healthcare system factors. The challenges of confounding control are particularly acute in studies using healthcare utilization databases where information on many potential confounding factors is lacking and the meaning of variables is often unclear. We discuss advantages and disadvantages of different approaches to confounder control in healthcare databases. In settings where considerable uncertainty surrounds the data or the causal mechanisms underlying the treatment assignment and outcome process, we suggest that researchers report a panel of results under various specifications of statistical models. Such reporting allows the reader to assess the sensitivity of the results to model assumptions that are often not supported by strong subject-matter knowledge.