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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Fullerton, B., Pöhlmann, B., Krohn, R., Adams, J., Gerlach, F. M., & Erler, A. (2016) · Health Services Research · doi:10.1111/1475-6773.12452 · Cited by 25
Oral Bisphosphonates and Upper Gastrointestinal Cancer Risks in Asians with Osteoporosis: A Nested Case-Control Study Using National Retrospective Cohort Sample Data from Korea
Jung, S.-Y., Sohn, H., Park, E.-J., Suh, H. S., Park, J.-W., & Kwon, J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0150531 · Cited by 20
“For matching, the greedy method was used to identify these controls[25].”
Method
Bias Due to Sample Selection in Propensity Score Matching for a Supportive Housing Program Evaluation in New York City
Lim, S., Marcus, S., Singh, T., Harris, T., & Seligson, A. L. (2014) · PLoS ONE · doi:10.1371/journal.pone.0109112 · Cited by 20
“N:N), which is more efficient in balancing covariates than matching restricted to one-to-one pairs [5,7].”
Background
Comparative outcomes of leukotriene receptor antagonists and long-acting β-agonists as add-on therapy in asthmatic patients: a population-based study.
Sadatsafavi, M., Lynd, L., Marra, C., Bedouch, P., & Fitzgerald, M. (2013) · Journal of Allergy and Clinical Immunology · doi:10.1016/j.jaci.2013.02.007 · Cited by 20
Economic Effects of Investment Support of Adding Value to Food Products
Mezera, J., & Špička, J. (2013) · doi:10.22004/ag.econ.148102 · Cited by 20
“Gu and Rosenbaum (1993) compared the imbalance of Mahalanobis distance metrics versus the propensity score difference in optimal 1:1 matching for numbers of covariates (P) between 2 and 20 and control/ treatment subject ratios between 2 and 6.”
Background
Economic Impacts of Regional Approaches to Rural Development: Initial Evidence on the Delta Regional AuthorityPreprint
Pender, J., & Reeder, R. (2010) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.262240 · Cited by 20
Constructing Matched Sets and Strata
Rosenbaum, P. (1995) · Springer series in statistics · doi:10.1007/978-1-4757-2443-1_9 · Cited by 20
Self-citation
Impacts of disability on poverty: Quasi-experimental evidence from landmine amputees in Cambodia
Takasaki, Y. (2020) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2020.09.027 · Cited by 23
On the link between rail transit and spatial income segregation
Nilsson, I., & Delmelle, E. (2020) · Applied Geography · doi:10.1016/j.apgeog.2020.102364 · Cited by 19
Matching methods in precision oncology: An introduction and illustrative example
Weymann, D., Laskin, J., Jones, S. J. M., Lim, H., Renouf, D., Roscoe, R., Schrader, K., Sun, S., Yip, S., Marra, M., et al. (2020) · Molecular Genetics & Genomic Medicine · doi:10.1002/mgg3.1554 · Cited by 19
“Compared to nearest neighbor matching, optimal matching produces more closely matched pairs but does not improve overall balance across matched cohorts (Austin, 2014; Gu & Rosenbaum, 1993).”
Background
Inclusion of multiple high‐risk histopathological criteria improves the prediction of adjuvant chemotherapy efficacy in lung adenocarcinoma
Sereno, M., He, Z., Smith, C., Baena, J., Das, M., Hastings, R., Rake, G., Fennell, D., Nakas, A., Moore, D., et al. (2020) · Histopathology · doi:10.1111/his.14301 · Cited by 19
Investigating Causal DIF via Propensity Score Methods.
Liu, Y., Zumbo, B., Gustafson, P., Huang, Y., Kroc, E., & Wu, A. (2016) · Scholarworks (University of Massachusetts Amherst) · doi:10.7275/ewqz-n963 · Cited by 19
“For example, Gu and Rosenbaum (1993) conducted a simulation study, Marcus (2000) applied it to the evaluation of the Head Start compensatory education program, and Hansen and Klopfer (2006) extended the full optimal matching using optmatch R package (Hansen, 2004; Hansen, Fredrickson, Buckner, Errickson, & Solenberger…”
Method
Does knee replacement surgery for osteoarthritis improve survival? The jury is still out
Misra, D., Lu, N., Felson, D., Choi, H. K., Seeger, J., Einhorn, T., Neogi, T., & Zhang, Y.-Q. (2016) · Annals of the Rheumatic Diseases · doi:10.1136/annrheumdis-2016-209167 · Cited by 19
The Search for Causal Inferences: Using Propensity Scores Post Hoc to Reduce Estimation Error With Nonexperimental Research
Tumlinson, S. E., Sass, D. A., & Cano, S. M. (2014) · Journal of Pediatric Psychology · doi:10.1093/jpepsy/jst143 · Cited by 19
“Interested readers can consult Guo and Fraser (2010) and references cited therein for more information regarding variations of matching algorithms, sensitivity analyses, and other issues related to PSM.”
Background
The externalities of crime: The effect of criminal involvement of parents on the educational attainment of their children
Rud, I., van Klaveren, C., Groot, W. N. J., & van den Brink, H. M. (2013) · Economics of Education Review · doi:10.1016/j.econedurev.2013.11.006 · Cited by 21
“Additionally, Mahalanobis matching is considered as a reliable approach when the vector of matching characteristics is not highly dimensional (Gu and Rosenbaum 1993; Rubin and Thomas 2000).”
A Comparison of Long-Term Mortality for Off-Pump and On-Pump Coronary Artery Bypass Graft Surgery
Wu, C., Camacho, F. T., Culliford, A., Gold, J., Wechsler, A., Higgins, R., Lahey, S., Smith, C. R., Jordan, D., & Hannan, E. (2012) · Circulation. Cardiovascular Quality and Outcomes · doi:10.1161/circoutcomes.111.963124 · Cited by 19
Investigating the effect of school-wide positive behavioral interventions and supports on student learning and behavioral problems in elementary and middle schools
Ryoo, J., Hong, S., Bart, W., Shin, J., & Bradshaw, C. P. (2018) · Psychology in the Schools · doi:10.1002/pits.22134 · Cited by 18
Financial Difficulty Effects on Depressive Symptoms Among Dementia Patient Caregivers
Nam, I. (2016) · Community mental health journal · doi:10.1007/s10597-016-0033-3 · Cited by 18
“Matched pairs were removed from the pool, then the second caregiver with financial difficulty was connected to the nearest remaining caregiver without any financial difficulty, and so on (Gu and Rosenbaum 1993).”
Background
Secular changes in body dimensions of Royal Australian Air Force aircrew (1971–2005)
Tomkinson, G., Clark, A. J., & Blanchonette, P. (2010) · Ergonomics · doi:10.1080/00140139.2010.489967 · Cited by 18
“Using a greedy matching procedure (Gu and Rosenbaum 1993), subjects in the 1971 and 2005 datasets were matched one-for-one for decimal age, yielding 220 matched pairs.”
Method
Association of maternal heavy metal exposure during pregnancy with isolated cleft lip and palate in offspring: Japan Environment and Children’s Study (JECS) cohort study
Takeuchi, M., Yoshida, S., Kawakami, C., Kawakami, K., & Ito, S. (2022) · PLoS ONE · doi:10.1371/journal.pone.0265648 · Cited by 17
Beta-Blockers, Tachycardia and Survival Following Sepsis- An Observational Cohort Study.
Guz, D., Buchritz, S., Guz, A., Ikan, A., Babich, T., Daitch, V., Gafter-Gvili, A., Leibovici, L., & Avni, T. (2021) · Clinical Infectious Diseases · doi:10.1093/cid/ciab034 · Cited by 17
Clinical characteristics associated with depression or anxiety among patients presenting for knee surgery.
La, A., Nadarajah, V., Jauregui, J. J., Shield, W. P., Medina, S. H., Dubina, A. G., Meredith, S. J., Packer, J. D., & Henn, R. F. (2020) · Journal of Clinical Orthopaedics and Trauma · doi:10.1016/j.jcot.2019.08.009 · Cited by 17
Evaluating Propensity Score Methods in a Quasi-Experimental Study of the Impact of Menu-Labeling
Mayne, S. L., Lee, B. K., & Auchincloss, A. H. (2015) · PLoS ONE · doi:10.1371/journal.pone.0144962 · Cited by 17
“Full matching also makes use of all available data (does not drop any individuals from the analysis), and has been found to perform better than k:1 matching in simulated and real data.[19, 32] Our finding that constrained full matching resulted in an overall reduction in standardized bias is consistent with a prior st…”
Result
Acceleration in elementary school: Using propensity score matching to estimate the effects on academic achievement.
Kretschmann, J., Vock, M., & Lüdtke, O. (2014) · Journal of Educational Psychology · doi:10.1037/a0036631 · Cited by 22
Assessing the association between the use of NRT for smoking reduction and attempts to quit smoking using propensity score matching
Beard, E., Aveyard, P. N., Brown, J., & West, R. (2012) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2012.05.039 · Cited by 14
“In some cases, the requirement of xact matches often leads to many individuals not being matched, hich can result in larger bias than if the matches are inexact but ore individuals remain in the analysis (Rosenbaum and Rubin, 985); while Mahalanobis distance does not perform well when the ovariates are not normally di…”
Background
Liraglutide use and evaluation of pancreatic outcomes in a US commercially insured population
Funch, D., Mortimer, K. M., Ziyadeh, N., Seeger, J., Li, L., Norman, H., Major-Pedersen, A., Bosch-Traberg, H., Gydesen, H., & Dore, D. (2019) · Diabetes, obesity and metabolism · doi:10.1111/dom.13739 · Cited by 16
“To account for changes in prescribing patterns and availability of ADs on the market, PS estimation and matching were performed within calendar periods for each comparator.(25) For the first three years, cohorts were created by calendar quarter and annually thereafter for the remaining recruitment time.”
Method
Evaluation of a hepatitis C clinical care coordination programme’s effect on treatment initiation and cure: A surveillance‐based propensity score matching approach
Deming, R., Ford, M. M., Moore, M. S., Lim, S., Perumalswami, P., Weiss, J. J., Wyatt, B., Shukla, S., Litwin, A. H., Reynoso, S., et al. (2018) · Journal of Viral Hepatitis · doi:10.1111/jvh.12929 · Cited by 16
Propensity Score Matching Helps to Understand Sources of DIF and Mathematics Performance Differences of Indonesian, Turkish, Australian, and Dutch Students in PISA
Arıkan, S., van de Vijver, F., & Yağmur, K. (2018) · doi:10.21890/ijres.382936 · Cited by 16
“Therefore, nearest neighbor matching could be used when the aim is to create well-matched pairs, whereas optimal matching could give better results when the aim is to create well-matched groups (Gu & Rosenbaum, 1993).”
Method
The Effect of Propensity Score Matching Method on the Quantity and Quality of Matches
Jacovidis, J., Foelber, K. J., & Horst, S. J. (2016) · The Journal of Experimental Education · doi:10.1080/00220973.2016.1250209 · Cited by 16
“When choosing a matching method, consider the following: (1) the algo-rithm that is employed, (2) the structure of the matched sets (i.e., the ratio of matched comparison group members to treatment group members; Gu & Rosenbaum, 1993), and (3) whether to match with or without replacement.”
Method
Comparison of Endovascular Stent Grafts for Abdominal Aortic Aneurysm Repair in Medicare Beneficiaries
Buck, D., Soden, P., Deery, S., Zettervall, S., Ultee, K., Landon, B. E., O'Malley, A., & Schermerhorn, M. (2017) · Annals of Vascular Surgery · doi:10.1016/j.avsg.2017.08.021 · Cited by 16
Sagittal Alignment Two Years After Selective and Nonselective Thoracic Fusion for Lenke 1C Adolescent Idiopathic Scoliosis
Celestre, P. C., Carreon, L., Lenke, L., Sucato, D., & Glassman, S. (2013) · Spine Deformity · doi:10.1016/j.jspd.2015.05.002 · Cited by 16
“Matched pairs were then created using optimal [14,15] matching without replacement using nearest-neighbor matching [16].”
Method
Costs and health outcomes associated with primary vs secondary care after an asthma-related hospitalization: a population-based study.
Sadatsafavi, M., Fitzgerald, M., Marra, C., & Lynd, L. (2013) · Chest · doi:10.1378/chest.12-2773 · Cited by 16
Different or Equal Treatment? Donor Priority Strategy and Fundraising Performance Assessed by a Propensity Score Matching Study
Scherhag, C., & Boenigk, S. (2013) · Nonprofit Management and Leadership · doi:10.1002/nml.21074 · Cited by 16
TAX LIMIT REPEAL AND SCHOOL SPENDING
Nguyen-Hoang, P. (2013) · National tax journal · doi:10.17310/ntj.2013.1.05 · Cited by 16
“This study employs the full (optimal) matching algorithm introduced in Rosenbaum (1991), because full matching has been proven to perform better than other matching algorithms in minimizing variance and bias (Gu and Rosenbaum, 1993; Hansen, 2004).”
Method
Statistical Matching Using Propensity Scores: Theory and Application to the Levy Institute Measure of Economic Well-BeingPreprint
Kum, H., & Masterson, T. (2008) · SSRN Electronic Journal · doi:10.2139/ssrn.1136363 · Cited by 16
A quantitative causal analysis and optimization framework for inclusions of steel products
Wu, Y., Zhang, H.-D., Jian, L.-S., & Lv, Z.-M. (2024) · Advanced Engineering Informatics · doi:10.1016/j.aei.2024.102629 · Cited by 16
Prevalence of obesity in people with and without type 1 diabetes across Belgium, Kuwait, and Mexico: an IMI2 SOPHIA study
al-Ozairi, E., Steenackers, N., Pazmino, S., Alattar, A. T., Kandari, J. A., Almeda-Valdés, P., Antonio-Villa, N., Delfin, C., Faradji, R., Aili García-Tuomola, A., et al. (2024) · EClinicalMedicine · doi:10.1016/j.eclinm.2024.102869 · Cited by 15
“22,23 To further reduce the distance between pairs, exact matching was chosen for sex.”

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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