An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies
TL;DR: The propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects, and different causal average treatment effects and their relationship with propensity score analyses are described.
Abstract: The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.
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TL;DR: This document contains the checklist and explanatory and elaboration information to enhance the use of theRECORD checklist, and examples of good reporting for each RECORD checklist item are also included herein.
Abstract: Routinely collected health data, obtained for administrative and clinical purposes without specific a priori research goals, are increasingly used for research. The rapid evolution and availability of these data have revealed issues not addressed by existing reporting guidelines, such as Strengthening the Reporting of Observational Studies in Epidemiology (STROBE). The REporting of studies Conducted using Observational Routinely collected health Data (RECORD) statement was created to fill these gaps. RECORD was created as an extension to the STROBE statement to address reporting items specific to observational studies using routinely collected health data. RECORD consists of a checklist of 13 items related to the title, abstract, introduction, methods, results, and discussion section of articles, and other information required for inclusion in such research reports. This document contains the checklist and explanatory and elaboration information to enhance the use of the checklist. Examples of good reporting for each RECORD checklist item are also included herein. This document, as well as the accompanying website and message board (http://www.record-statement.org), will enhance the implementation and understanding of RECORD. Through implementation of RECORD, authors, journals editors, and peer reviewers can encourage transparency of research reporting.
2,644 citations
TL;DR: A suite of quantitative and qualitative methods are described that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample to contribute towards an evolving concept of ‘best practice’ when using IPTW to estimate causal treatment effects using observational data.
Abstract: The propensity score is defined as a subject's probability of treatment selection, conditional on observed baseline covariates. Weighting subjects by the inverse probability of treatment received creates a synthetic sample in which treatment assignment is independent of measured baseline covariates. Inverse probability of treatment weighting (IPTW) using the propensity score allows one to obtain unbiased estimates of average treatment effects. However, these estimates are only valid if there are no residual systematic differences in observed baseline characteristics between treated and control subjects in the sample weighted by the estimated inverse probability of treatment. We report on a systematic literature review, in which we found that the use of IPTW has increased rapidly in recent years, but that in the most recent year, a majority of studies did not formally examine whether weighting balanced measured covariates between treatment groups. We then proceed to describe a suite of quantitative and qualitative methods that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample. The quantitative methods use the weighted standardized difference to compare means, prevalences, higher-order moments, and interactions. The qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and control subjects in the weighted sample. Finally, we illustrate the application of these methods in an empirical case study. We propose a formal set of balance diagnostics that contribute towards an evolving concept of 'best practice' when using IPTW to estimate causal treatment effects using observational data.
2,602 citations
Cites background from "An Introduction to Propensity Score..."
...The propensity score is defined as the probability of treatment assignment conditional on measured baseline covariates [1–3]....
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TL;DR: In this article, the authors provided robust estimates of incidence rates and relative risks of neurological and psychiatric diagnoses in patients in the 6 months following a COVID-19 diagnosis, using data obtained from the TriNetX electronic health records network (with over 81 million patients).
1,162 citations
TL;DR: Two different propensity score methods (matching and inverse probability of treatment weighting) can be used to estimate the measures of effect that are frequently reported in randomized controlled trials with time‐to‐event outcomes: marginal survival curves and marginal hazard ratios.
Abstract: Propensity score methods are increasingly being used to estimate causal treatment effects in observational studies. In medical and epidemiological studies, outcomes are frequently time-to-event in nature. Propensity-score methods are often applied incorrectly when estimating the effect of treatment on time-to-event outcomes. This article describes how two different propensity score methods (matching and inverse probability of treatment weighting) can be used to estimate the measures of effect that are frequently reported in randomized controlled trials: (i) marginal survival curves, which describe survival in the population if all subjects were treated or if all subjects were untreated; and (ii) marginal hazard ratios. The use of these propensity score methods allows one to replicate the measures of effect that are commonly reported in randomized controlled trials with time-to-event outcomes: both absolute and relative reductions in the probability of an event occurring can be determined. We also provide guidance on variable selection for the propensity score model, highlight methods for assessing the balance of baseline covariates between treated and untreated subjects, and describe the implementation of a sensitivity analysis to assess the effect of unmeasured confounding variables on the estimated treatment effect when outcomes are time-to-event in nature. The methods in the paper are illustrated by estimating the effect of discharge statin prescribing on the risk of death in a sample of patients hospitalized with acute myocardial infarction. In this tutorial article, we describe and illustrate all the steps necessary to conduct a comprehensive analysis of the effect of treatment on time-to-event outcomes. © 2013 The authors. Statistics in Medicine published by John Wiley & Sons, Ltd.
1,065 citations
Cites methods from "An Introduction to Propensity Score..."
...Four different propensity score methods are used for reducing the effects of confounding when estimating the effects of treatment on outcomes: propensity score matching, stratification on the propensity score, inverse probability of treatment weighting (IPTW) using the propensity score, and covariate adjustment using the propensity score [19–21]....
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TL;DR: Survivors of COVID-19 appear to be at increased risk of psychiatric sequelae, and a psychiatric diagnosis might be an independent risk factor for COIDs, according to a preliminary study using data from 69 million patients.
986 citations
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TL;DR: The authors discusses the central role of propensity scores and balancing scores in the analysis of observational studies and shows that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates.
Abstract: : The results of observational studies are often disputed because of nonrandom treatment assignment. For example, patients at greater risk may be overrepresented in some treatment group. This paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies. The propensity score is the (estimated) conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching, multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations, and visual representation of multivariate adjustment by a two-dimensional plot. (Author)
23,744 citations
TL;DR: A discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation is presented in this paper, where the objective is to specify the benefits of randomization in estimating causal effects of treatments.
Abstract: A discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation is presented. The objective is to specify the benefits of randomization in estimating causal effects of treatments. The basic conclusion is that randomization should be employed whenever possible but that the use of carefully controlled nonrandomized data to estimate causal effects is a reasonable and necessary procedure in many cases. Recent psychological and educational literature has included extensive criticism of the use of nonrandomized studies to estimate causal effects of treatments (e.g., Campbell & Erlebacher, 1970). The implication in much of this literature is that only properly randomized experiments can lead to useful estimates of causal effects. If taken as applying to all fields of study, this position is untenable. Since the extensive use of randomized experiments is limited to the last half century,8 and in fact is not used in much scientific investigation today,4 one is led to the conclusion that most scientific "truths" have been established without using randomized experiments. In addition, most of us successfully determine the causal effects of many of our everyday actions, even interpersonal behaviors, without the benefit of randomization. Even if the position that causal effects of treatments can only be well established from randomized experiments is taken as applying only to the social sciences in which
8,377 citations
"An Introduction to Propensity Score..." refers methods in this paper
...I first describe the potential outcomes framework, which has also been described as the Rubin Causal Model (Rubin, 1974)....
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...Because propensity score methods allow one to mimic some of the characteristics of an RCT in the context of an observational study, I begin this article by describ- framework, which has also been described as the Rubin Causal Model (Rubin, 1974)....
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TL;DR: Findings indicate that low EPV can lead to major problems, and the regression coefficients were biased in both positive and negative directions, and paradoxical associations (significance in the wrong direction) were increased.
6,490 citations
Additional excerpts
...When outcomes are either binary or time-to-event in nature, prior research has suggested that at least 10 events should be observed for every covariate that is entered into a regression model ( Peduzzi, Concato, Feinstein, & Holford, 1995 ; Peduzzi, Concato, Kemper, Holford, & Feinstein, 1996 )....
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TL;DR: This article used multivariate matching methods in an observational study of the effects of prenatal exposure to barbiturates on subsequent psychological development, using the propensity score as a distinct matching variable.
Abstract: Matched sampling is a method for selecting units from a large reservoir of potential controls to produce a control group of modest size that is similar to a treated group with respect to the distribution of observed covariates. We illustrate the use of multivariate matching methods in an observational study of the effects of prenatal exposure to barbiturates on subsequent psychological development. A key idea is the use of the propensity score as a distinct matching variable.
5,633 citations
"An Introduction to Propensity Score..." refers background or methods in this paper
...There are two primary methods for this: nearest neighbor matching and nearest neighbor matching within a specified caliper distance (Rosenbaum & Rubin, 1985)....
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...Building on the prior work of Cochran and Rubin on matching on a single normally distributed confounding variable, Rosenbaum and Rubin (1985) suggested that similar reduction in bias can be achieved by matching on the logit of the propensity score using caliper widths similar to those described by…...
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...Propensity score matching entails forming matched sets of treated and untreated subjects who share a similar value of the propensity score (Rosenbaum & Rubin, 1983a, 1985)....
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TL;DR: The propensity score, defined as the conditional probability of being treated given the covariates, can be used to balance the variance of covariates in the two groups, and therefore reduce bias as mentioned in this paper.
Abstract: In observational studies, investigators have no control over the treatment assignment. The treated and non-treated (that is, control) groups may have large differences on their observed covariates, and these differences can lead to biased estimates of treatment effects. Even traditional covariance analysis adjustments may be inadequate to eliminate this bias. The propensity score, defined as the conditional probability of being treated given the covariates, can be used to balance the covariates in the two groups, and therefore reduce this bias. In order to estimate the propensity score, one must model the distribution of the treatment indicator variable given the observed covariates. Once estimated the propensity score can be used to reduce bias through matching, stratification (subclassification), regression adjustment, or some combination of all three. In this tutorial we discuss the uses of propensity score methods for bias reduction, give references to the literature and illustrate the uses through applied examples.
4,948 citations