Cited by 702Advanced Causal Inference TechniquesOptimal Experimental Design MethodsStatistical Methods in Clinical Trials

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Comparison of Multivariate Matching Methods: Structures, Distances, and Algorithms

Gu, Xing Sam, Rosenbaum, Paul R.·1993·Journal of Computational and Graphical Statistics

DOI 10.1080/10618600.1993.10474623

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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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Background
Drug-Eluting or Bare-Metal Stenting in Patients With Diabetes Mellitus: Results From the Massachusetts Data Analysis Center Registry
Garg, P., Normand, S., Silbaugh, T. S., Wolf, R., Zelevinsky, K., Lovett, A. F., Varma, M. R., Zhou, Z., & Mauri, L. (2008) · Circulation · doi:10.1161/circulationaha.108.820159 · Cited by 135
Applying Propensity Score Methods in Medical Research: Pitfalls and Prospects
Luo, Z.-H., Gardiner, J., & Bradley, C. (2010) · Medical Care Research and Review · doi:10.1177/1077558710361486 · Cited by 134
“First, although not universally accepted, some researchers (Heckman, Ichimura, Smith, & Todd, 1998) have advocated choosing nonexperimental comparison samples as close to the experimental sample as possible before estimating PSs, for example, restricting the comparison sample to be in the same age groups or geographic…”
Method
Estimating the effect of treatment on binary outcomes using full matching on the propensity score
Austin, P. C., & Stuart, E. A. (2015) · Statistical Methods in Medical Research · doi:10.1177/0962280215601134 · Cited by 130
“Alternative matching methods include many-to-one matching and variable ratio matching.(7,8) A rarely-used alternative matching method is full matching.”
Method
Persistence on Therapy and Propensity Matched Outcome Comparison of Two Subcutaneous Interferon Beta 1a Dosages for Multiple Sclerosis
Kalincik, T., Spelman, T., Trojano, M., Duquette, P., Izquierdo, G., Grammond, P., Lugaresi, A., Hupperts, R., Cristiano, E., van Pesch, V., et al. (2013) · PLoS ONE · doi:10.1371/journal.pone.0063480 · Cited by 128
A practical guide to propensity score analysis for applied clinical research
Lee, J., & Little, T. D. (2017) · Behaviour Research and Therapy · doi:10.1016/j.brat.2017.01.005 · Cited by 149
Applying Propensity Score Methods in Clinical Research in Neurology
Austin, P., Xinyu, A., Vyas, M., & Kapral, M. (2021) · Neurology · doi:10.1212/wnl.0000000000012777 · Cited by 123
“These include fixed ratio M:1 matching, variable ratio matching, and full matching (10-15).”
Background
Assessing the Effectiveness of a College Freshman Seminar Using Propensity Score Adjustments
Clark, M. H., & Cundiff, N. L. (2011) · Research in Higher Education · doi:10.1007/s11162-010-9208-x · Cited by 99
“In most cases, propensity scores reduce bias as well as traditional covariate adjustments, however, some studies have shown that propensity scores are more effective in reducing bias than other methods ( Gu and Rosenbaum 1993; Shah et al. 2005; Stu ¨rmer et al. 2006).”
Result
Association of Playing High School Football With Cognition and Mental Health Later in Life
Deshpande, S. K., Hasegawa, R. B., Rabinowitz, A. R., Whyte, J., Roan, C., Tabatabaei, A., Baiocchi, M., Karlawish, J. H., Master, C. L., & Small, D. S. (2017) · JAMA Neurology · doi:10.1001/jamaneurol.2017.1317 · Cited by 146
“However, theydeterminedparticipation in contact sports by querying only medical records, potentiallyunderestimating the true rateofparticipation and leading to information bias.(12) Without population-level samples, it is difficult to estimate the base rate of long-term dysfunction among professional football players,…”
Association of Single vs. Dual Chamber ICDs with Mortality, Readmissions and Complications among Patients Receiving an ICD for Primary Prevention
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
“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.”
Left ventricular thrombus and subsequent thromboembolism, comparison of anticoagulation, surgical removal, and antiplatelet agents.
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
Matching and Propensity Scores
Steiner, P. M., & Cook, D. (2013) · Oxford University Press eBooks · doi:10.1093/oxfordhb/9780199934874.013.0013 · Cited by 96
“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).”
BackgroundMethod
Endovascular 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
A Note on Optimal Matching With Variable Controls Using the Assignment Algorithm
Ming, K., & Rosenbaum, P. R. (2001) · Journal of Computational and Graphical Statistics · doi:10.1198/106186001317114938 · Cited by 102
“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-citation
A Martingale Representation for Matching Estimators
Abadie, A., & Imbens, G. W. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.682537 · Cited by 82
“(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.”
Background
Optimal 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 115
“Gu and Rosenbaum examined the performance of different matching algorithms [3].”
BackgroundMethod
Optimal 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
Piloting electronic medical record–based early detection of inpatient deterioration in community hospitals
Escobar, G. J., Turk, B. J., Ragins, A. I., Ha, J., Hoberman, B., LeVine, S. M., Ballesca, M. A., Liu, V. X., & Kipnis, P. (2016) · Journal of Hospital Medicine · doi:10.1002/jhm.2652 · Cited by 98
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 119
“Nearestneighbors are typically identified based on distance measures, but there are no a priori rules for the selection of a distance measure [34].”
Background
Are 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
“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.”
Method
Estimating and using propensity score in presence of missing background data: an application to assess the impact of childbearing on wellbeing
Mattei, A. (2009) · Stat. Methods Appl. · doi:10.1007/s10260-007-0086-0 · Cited by 95
“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).”
Background
Impact of Improved Rice Technology (NERICA varieties) on Income and Poverty among Rice Farming Households in Nigeria: A Local Average Treatment Effect (LATE) Approach
Nguezet, P., Diagne, A., Okoruwa, V., & Ojehomon, V. (2011) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.155535 · Cited by 95
Declaring and Diagnosing Research Designs
Blair, G., Cooper, J., Coppock, A., & Humphreys, M. (2019) · American Political Science Review · doi:10.1017/s0003055419000194 · Cited by 112
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
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”
Method
Attributing 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
“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).”
Method
Adjusting for unmeasured spatial confounding with distance adjusted propensity score matching
Papadogeorgou, G., Choirat, C., & Zigler, C. M. (2018) · Biostatistics · doi:10.1093/biostatistics/kxx074 · Cited by 69
“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
DOI: 10.1080/10618600.1993.10474623
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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Comparison of Multivariate Matching Methods: Structures, Distances, and Algorithms

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