Comparison of Multivariate Matching Methods: Structures, Distances, and Algorithms
Abstract
A comparison and evaluation is made of recent proposals for multivariate matched sampling in observational studies, where the following three questions are answered: (1) Algorithms: In current statistical practice, matched samples are formed using “nearest available” matching, a greedy algorithm. Greedy matching does not minimize the total distance within matched pairs, though good algorithms exist for optimal matching that do minimize the total distance. How much better is optimal matching than greedy matching? We find that optimal matching is sometimes noticeably better than greedy matching in the sense of producing closely matched pairs, sometimes only marginally better, but it is no better than greedy matching in the sense of producing balanced matched samples. (2) Structures: In common practice, treated units are matched to one control, called pair matching or 1–1 matching, or treated units are matched to two controls, called 1–2 matching, and so on. It is known, however, that the optimal structure is a full matching in which a treated unit may have one or more controls or a control may have one or more treated units. Optimal 1 — k matching is compared to optimal full matching, finding that optimal full matching is often much better. (3) Distances: Matching involves defining a distance between covariate vectors, and several such distances exist. Three recent proposals are compared. Practical advice is summarized in a final section.
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“Full matching (Gu & Rosenbaum, 1993; Hansen, 2004; Rosenbaum, 1991) involves forming matched sets consisting of either one treated subject and at least one untreated subject or one untreated subject and at least one treated subject.”
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“Alternative matching methods include many-to-one matching and variable ratio matching.(7,8) A rarely-used alternative matching method is full matching.”
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ResultAssociation of Playing High School Football With Cognition and Mental Health Later in Life
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Peterson, P. N., Varosy, P., Heidenreich, P., Wang, Y.-F., Dewland, T. A., Curtis, J., Go, A., Greenlee, R., Magid, D., Normand, S., et al. (2013) · Journal of the American Medical Association (JAMA) · doi:10.1001/jama.2013.4982 · Cited by 119 · see citing works
“This matching interval has been shown to eliminate approximately 90% of the bias in observed confounders.(11) The success of matching was evaluated by examining standardized differences in the observed patient and clinician characteristics between singleand dual-chamber treatment groups.”
Lee, J., Park, J. J., Jung, H.-W., Cho, Y.-S., Oh, I., Yoon, C., Suh, J., Chun, E., Choi, S.-I., Youn, T., et al. (2013) · Journal of atherosclerosis and thrombosis · doi:10.5551/jat.13540 · Cited by 118 · see citing works
Matching and Propensity Scores
Steiner, P. M., & Cook, D. (2013) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780199934874.013.0013 · Cited by 114 · see citing works
“Though optimal matching performs on average better, there is no guarantee that it does better than greedy matching for a given dataset (Gu & Rosbenbaum, 1993).”
BackgroundMethodEndovascular vs . Open Repair of Abdominal Aortic Aneurysms in the Medicare Population
Schermerhorn, M., O'Malley, A., Jhaveri, A., Cotterill, P., Pomposelli, F., & Landon, B. (2008) · New England Journal of Medicine · doi:10.1056/nejmoa0707348 · Cited by 114 · see citing works
A Note on Optimal Matching With Variable Controls Using the Assignment Algorithm
Ming, K., & Rosenbaum, P. (2001) · Journal of Computational and Graphical Statistics · doi:10.1198/106186001317114938 · Cited by 111 · see citing works
“Ming and Rosenbaum (2000) showed that matching with a variable number of controls can remove substantially more bias than matching with a fixed number of controls; see also Rosenbaum (1991b) for related theory and Gu and Rosenbaum (1993) for a related simulation. Matching is typically implemented by defining a distanc…”
BackgroundInfluentialSelf-citationA Martingale Representation for Matching Estimators
Abadie, A., & Imbens, G. (2012) · Social Science Research Network · doi:10.1080/01621459.2012.682537 · Cited by 109 · see citing works
“(2) Many other matching schemes are possible (see, e.g., Gu and Rosenbaum 1993; Rosenbaum 2002; Hansen 2004; Iacus, King, and Porro 2009; Diamond and Sekhon 2010), and the results in this article are of broad generality.”
BackgroundOptimal full matching for survival outcomes: A method that merits more widespread use
Austin, P. C., & Stuart, E. A. (2015) · Statistics in Medicine · doi:10.1002/sim.6602 · Cited by 106 · see citing works
“Gu and Rosenbaum examined the performance of different matching algorithms [3].”
BackgroundMethodOptimal a priori balance in the design of controlled experiments
Kallus, N. (2013) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12240 · Cited by 105 · see citing works
Escobar, G., Turk, B. J., Ragins, A. I., Ha, J., Hoberman, B., Levine, S., Ballesca, M. A., Liu, V. X., & Kipnis, P. (2016) · Journal of Hospital Medicine · doi:10.1002/jhm.2652 · Cited by 102 · see citing works
Post-Crackdown Effectiveness of Field-Based Forest Law Enforcement in the Brazilian Amazon
Börner, J., Kis-Katos, K., Hargrave, J., & König, K. (2015) · PLoS ONE · doi:10.1371/journal.pone.0121544 · Cited by 98 · see citing works
“Nearestneighbors are typically identified based on distance measures, but there are no a priori rules for the selection of a distance measure [34].”
BackgroundAre Violent Delinquents Worth Treating? A Cost–Benefit Analysis
Caldwell, M., Vitacco, M., & Rybroek, G. V. V. (2006) · Journal of Research in Crime and Delinquency · doi:10.1177/0022427805280053 · Cited by 96 · see citing works
“Several studies (Dehejia and Wahba 1999; Drake 1993; Gu and Rosenbaum 1993; Imai, 2002) have found that the propensity score method produces estimates of casual effects that are more reliable than other commonly used methods.”
MethodMattei, A. (2009) · Stat. Methods Appl. · doi:10.1007/s10260-007-0086-0 · Cited by 95 · see citing works
“Much work has been done in the case where covariates are fully observed (e.g., Gu and Rosenbaum, 1993; Rubin and Thomas, 1992a, 1992b, 1996).”
BackgroundNguezet, P., Diagne, A., Okoruwa, V., & Ojehomon, V. (2011) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.155535 · Cited by 95 · see citing works
Declaring and Diagnosing Research Designs
Blair, G., Cooper, J., Coppock, A., & Humphreys, M. (2019) · American Political Science Review · doi:10.1017/s0003055419000194 · Cited by 94 · see citing works
Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology
Rubin, D., & Waterman, R. P. (2006) · Statistical Science · doi:10.1214/088342306000000259 · Cited by 94 · see citing works
Overall survival advantage with partial nephrectomy: A bias of observational data?
Shuch, B., Hanley, J. M., Lai, J. C., Vourganti, S., Kim, S. P., Setodji, C. M., Dick, A. W., Chow, W., & Saigal, C. (2013) · Cancer · doi:10.1002/cncr.28141 · Cited by 92
“Both these techniques have been compared, and both produce well-balanced matched samples.(17) Original Article”
MethodAttributing Effects to a Cluster-Randomized Get-Out-the-Vote Campaign
Hansen, B. B., & Bowers, J. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.ap06589 · Cited by 90 · see citing works
“Full matching’s improvement upon older forms of matching was documented with simulation studies by Gu and Rosenbaum (1993), and with actual data by Hansen (2004, §2).”
MethodAdjusting for unmeasured spatial confounding with distance adjusted propensity score matching
Papadogeorgou, G., Choirat, C., & Zigler, C. (2016) · Biostatistics · doi:10.1093/biostatistics/kxx074 · Cited by 89 · see citing works
“Gu and Rosenbaum [1993] found that optimal is better than greedy matching in returning balanced matched pairs, but returned similarly balanced matched data sets.”
Background
- Authors
- Gu, X. S., & Rosenbaum, P. R.
- Affiliations
- C.S. First Boston Hong Kong, Ltd.
- University of Pennsylvania (US)
- ORCID
- Rosenbaum, Paul R.
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 1993-12
- Volume
- 2
- Issue
- 4
- Pages
- 405-420
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2030614017
- Cited by
- 702
- References
- 0
- Citations by year
- 2026: 20 · 2025: 29 · 2024: 27 · 2023: 32 · 2022: 35 · 2021: 41 · 2020: 46 · 2019: 37 · 2018: 51 · 2017: 36 · 2016: 36 · 2015: 40 · 2014: 36 · 2013: 35 · 2012: 27
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Computational and Graphical Statistics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- optimal matching, greedy matching, pair matching, covariate balance, distance measures, observational studies
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