Matching methods for causal inference: A review and a look forward

By Elizabeth A. Stuart. 2010

5,245 citations recorded by the source corpus.

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970’s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine, and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods–or developing methods related to matching–do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

Subfields: Statistics and Probability

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Citations in the corpus

All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, methodology): “The resulting estimate is analogous to exact matching procedures commonly used in causal inference, which are known to work best when the covariates are discrete and low dimensional, in order for exact matches to be common (Stuart, 2010).”
Identifying Statistical Bias in Dataset Replication (2020, background): “In causal inference terms, statistic matching is an instance of covariate balancing (Stuart, 2010; Imai & Ratkovic, 2013).”
The Selective Labels Problem: Evaluating Algorithmic Predictions in the Presence of Unobservables (2017, methodology): “(2) non-parametric methods such as propensity score matching, nearest-neighbor matching, which do not explicitly model the relationship between observed features, treatments, and outcomes [4, 15, 35, 36, 41].”
Automated versus Do-It-Yourself Methods for Causal Inference: Lessons Learned from a Data Analysis Competition (2017, background): “…modeling of the assignment mechanism was largely ignored until the past decade, particularly in the context of propensity score estimation, because it was seen by many primarily as a means to an end for achieving good balance (Lee, Lessler and Stuart, 2010; Westreich, Lessler and Funk, 2010).”
Imposing Minimax and Quantile Constraints on Optimal Matching in Observational Studies (2017, background): “For discussion of optimal matching in observational studies, see Rosenbaum (1989, 2010, Part II), Hansen and Klopfer (2006), Hansen (2007), Stuart (2010), Lu et al. (2011), Yang et al. (2012), Zubizarreta (2012), and Pimentel et al. (2015), and see CONTACT Paul R. Rosenbaum…”
Covariate balancing propensity score by tailored loss functions (2016, background): “Over the next three decades, numerous methods based on the propensity score have been proposed, most notably propensity score matching (e.g. Rosenbaum and Rubin, 1985, Abadie and Imbens, 2006), propensity score subclassification (e.g. Rosenbaum and Rubin, 1984), and inverse probability weighting (e.”
Generalized Optimal Matching Methods for Causal Inference (2016, background): “In causal inference, matching is the pursuit of comparability between samples that di↵er in systematic ways due to selection (often self-selection) by way of subsampling or re-weighting the samples [1].”
Text and Causal Inference: A Review of Using Text to Remove Confounding from Causal Estimates (2020, background): “, age, gender, occupation), then estimating effect size within each stratum (Stuart, 2010).”
Impact of participation in extra-curricular activities during college on graduate employability: an empirical study of graduates of Taiwanese business schools (2014, methodology): “Matching is intended to replicate randomised experiments using observational data (Greevy et al. 2004; Stuart 2010).”
Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System (2014, methodology): “Common matching methods attempt to achieve covariate balance indirectly, by finding treated and control units that are close on a summary measure of the covariates such as the Mahalanobis distance or the propensity score (see Stuart 2010; Lu et al. 2011 for reviews).”
Balance diagnostics after propensity score matching. (2019, methodology): “By using the same standard deviation before and after matching, the change in balance is independent of the change in mean difference, rather than being conflated with an accompanying change in standard deviation (10).”
Large-scale physical activity data reveal worldwide activity inequality (2017, methodology): “We also computed the correlation between obesity and activity inequality for specific age groups in our dataset — [10,20), [20,30), [30,40), [40,50) and [50,100), again using only subjects with a reported age.”
Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes (2017, methodology): “hat subject, i.e. T(x) = E h Y (1) i −Y (0) i Xi = x i . (1) The central goal of this paper is to eﬃciently estimate the function T(x) from an observational dataset, e.g. a retrospective cohort study [26, 34] or a hospital’s electronic health record [15]. Since our primary motivation for addressing ”
Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements (2018, background): “Under the assumption of unconfoundedness, propensity score matching and weighting methods aim to balance observed covariates across different values of a treatment variable [e.g., Imbens (2004), Ho et al. (2007), Stuart (2010)].”
Housing and Employment Insecurity among the Working Poor (2016, background): “…Felony .726 .568 Number of other adults .090 .156 Less than high school 1.068† .568 High school/GED .797 .518 Some college .547 .515 Age .131 .090 Age squared .002 .001 Months since move .020*** .006 Constant 5.066*** 1.682 N 624 Pseudo R2 .095 †p< .10 *p< .05 **p< .01 ***p< .001 (two-tailed tests)”