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Databases used in pharmacoepidemiological studies often include records of prescribed medications and encounters with medical care providers, from which one can construct surrogate measures for both drug exposure and covariates that are potential confounders. It is often possible to track day-by-day changes in these variables. However, while this information can be critical for study success, its volume can pose challenges for statistical analysis.
A propensity score (PS) is analogous to the disease risk score in that it combines a large number of possible confounders into a single variable (the score). The exposure propensity score (EPS) is the conditional probability of exposure to a treatment given observed covariates. In a cohort study, matching or stratifying treated and comparison subjects on EPS tends to balance all of the observed covariates. However, unlike random assignment of treatments, the propensity score may not balance unobserved covariates. Invited Commentary: Propensity Scores (Am J Epidemiol 1999;150:327–33) reviews the uses and limitations of propensity scores and provide a brief outline of the associated statistical theory. The authors present results of adjustment by matching or stratification on the propensity score.
High-dimensional Propensity Score Adjustment in Studies of Treatment Effects Using Healthcare Claims Data (Epidemiol 2009; 20(4):512-22) discusses the high dimensional propensity score (hd-PS) model approach. It attempts to empirically identify large numbers of potential confounders in healthcare databases and, by doing so, to extract more information on confounders and proxies. Covariate selection in high-dimensional propensity score analyses of treatment effects in small samples (Am J Epidemiol 2011;173:1404-13) evaluates the relative performance of hd-PS in smaller samples. Confounding adjustment via a semi-automated high-dimensional propensity score algorithm: an application to electronic medical records (Pharmacoepidemiol Drug Saf 2012;20:849-57) evaluates the use of hd-PS in a primary care electronic medical record database. In addition, the article Using high-dimensional propensity score to automate confounding control in a distributed medical product safety surveillance system (Pharmacoepidemiol Drug Saf 2012;21(S1):41-9) summarises the application of this method for automating confounding control in sequential cohort studies as applied to safety monitoring systems using healthcare databases and also discusses the strengths and limitations of hd-PS.
Most cohort studies match patients 1:1 on the propensity score. Increasing the matching ratio may increase precision but also bias. One-to-many propensity score matching in cohort studies (Pharmacoepidemiol Drug Saf. 2012;21(S2):69-80) tests several methods for 1:n propensity score matching in simulation and empirical studies and recommends using a variable ratio that increases precision at a small cost of bias. Matching by propensity score in cohort studies with three treatment groups (Epidemiology 2013;24(3):401-9) develops and tests a 1:1:1 propensity score matching approach offering a way to compare three treatment options.
The use of several measures of balance for developing an optimal propensity score model is described in Measuring balance and model selection in propensity score methods (Pharmacoepidemiol Drug Saf 2011;20:1115-29) and further evaluated in Propensity score balance measures in pharmacoepidemiology: a simulation study (Pharmacoepidemiol Drug Saf 2014; Epub 2014 Jan 29). In most situations, the standardised difference performs best and is easy to calculate (see Balance measures for propensity score methods: a clinical example on beta-agonist use and the risk of myocardial infarction (Pharmacoepidemiol Drug Saf 2011;20(11):1130-7) and Reporting of covariate selection and balance assessment in propensity score analysis is suboptimal: a systematic review (J Clin Epidemiol. 2015;68(2):112-21)). Metrics for covariate balance in cohort studies of causal effects (Stat Med 2013;33:1685-99) shows in a simulation study that the c-statistics of the PS model after matching and the general weighted difference perform as well as the standardized difference and are preferred when an overall summary measure of balance is requested.
Performance of propensity score calibration – a simulation study (Am J Epidemiol 2007;165(10):1110-8) introduces ‘propensity score calibration’ (PSC). This technique combines propensity score matching methods with measurement error regression models to address confounding by variables unobserved in the main study. This is done by using additional covariate measurements observed in a validation study, which is often a subset of the main study.
Treatment effects in the presence of unmeasured confounding: dealing with observations in the tails of the propensity score distribution--a simulation study (Am J Epidemiol. 2010; 1;172(7):843–54) demonstrates how “trimming” of the propensity score eliminates subjects who are treated contrary to prediction and their exposed/unexposed counterparts, thereby reducing bias by unmeasured confounders.
Although in most situations propensity score models, with the exception of hd-PS, do not have any advantages over conventional multivariate modelling in terms of adjustment for identified confounders, several other benefits may be derived. Propensity score methods may help to gain insight into determinants of treatment including age, frailty and comorbidity and to identify individuals treated against expectation. A statistical advantage of PS analyses is that if exposure is not infrequent it is possible to adjust for a large number of covariates even if outcomes are rare, a situation often encountered in drug safety research. Furthermore, assessment of the PS distribution may reveal non-positivity.
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