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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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“6 SD will remove approximate 90% of the bias in observed confounders.[13] Patient who did not have an acceptable range of match would be excluded.”
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Yoo, S., Bonilha, H. S., & Hong, I. (2024) · Dysphagia · doi:10.1007/s00455-024-10770-7 · Cited by 9
International remittances and political participation in Ghana
Anaman, G., Allor, P. W., & Kuffuor, O. (2023) · Scientific African · doi:10.1016/j.sciaf.2023.e01941 · Cited by 8
Hausam, J., Franke, M., Lehmann, R. J. B., & Dahle, K. (2022) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2022.909781 · Cited by 8
Joynt, C. (2022) · Meditari Accountancy Research · doi:10.1108/medar-01-2022-1571 · Cited by 8
Propensity Scoring in Plastic Surgery Research: An Analysis and Best Practice Guide
Chu, J. J., Shamsunder, M. G., Yin, S., Rubenstein, R., Slutsky, H. L., Fischer, J., & Nelson, J. A. (2022) · Plastic and Reconstructive Surgery, Global Open · doi:10.1097/gox.0000000000004003 · Cited by 8
Adamus, C., Mötteli, S., Jäger, M., & Richter, D. (2020) · BMC Psychiatry · doi:10.1186/s12888-020-02712-y · Cited by 8
“As matching method, many-to-one matching (m:1) with nearest neighbour approach (without replacement) will be applied [80].”
MethodEstimating heterogeneous treatment effects in nonstationary time series with state-space models
Li, S., & Bühlmann, P. (2018) · doi:10.48550/arxiv.1812.04063 · Cited by 8
“, [12]), blocking (e.”
Schroeder, K., Jia, H.-M., & Smaldone, A. (2016) · Nursing Research · doi:10.1097/nnr.0000000000000187 · Cited by 8
“Optimal matching has been found to benobetter than greedymatching in reducing estimator bias (Gu & Rosenbaum, 1993).”
BackgroundHospital Revisits Within 30 Days After Conventional and Robotically Assisted Hysterectomy
Friedman, B., Barbash, G., Glied, S., & Steiner, C. (2016) · Medical Care · doi:10.1097/mlr.0000000000000482 · Cited by 8
“The main method of the study uses matching by propensity scores to construct pairs of comparable RA and nonRA patients, and then tests for differences in revisits between groups.(21,22) Propensity scores come from a logistic regression for the use of a robot (yes or no) on the following variables: age group of the pat…”
MethodMatching and Imputation Methods for Risk Adjustment in the Health Insurance Marketplaces
Rose, S., Shi, J., Mcguire, T., & Normand, S. (2015) · Statistics in Biosciences · doi:10.1007/s12561-015-9135-7 · Cited by 8
“For a comparison of propensity score methods for matching, we refer to other literature [2,6,14,22,31].”
Marcus, S., & Gibbons, R. (2012) · Pharmacoepidemiology and Drug Safety · doi:10.1002/pds.3202 · Cited by 8
Exact, Nonparametric Inference When Doses Are Measured With Random Errors
Rosenbaum, P. (2005) · doi:10.1198/016214504000001628 · Cited by 8
“With normal data, the relative efficiency of the Wilcoxon signed rank test compared with the t-test is quite high even in quite small samples (Hettmansperger 1984, table 2.4, p. 75; Lehmann 1998, table 4.4, p. 174). The normal model (7) may also be used in sample size calculations when planning a study. In particular,…”
BackgroundMethodInfluentialSelf-citationReducing bias in Observational Studies: An Empirical Comparison of Propensity Score Matching Methods
Amusa, L. (2018) · Turkiye Klinikleri Journal of Biostatistics · doi:10.5336/biostatic.2017-58633 · Cited by 8
Gnas, J., Urban, J., Feuchter, M. D., & Preckel, F. (2024) · Social Psychology of Education · doi:10.1007/s11218-024-09915-1 · Cited by 8
“The propensity score (PS), a person’s conditional probability of belonging to one of the index groups given their individual set of matching variable scores, has proven to be a reliable composite measure for matching procedures (Gu & Rosenbaum, 1993 ; Li, 2013).”
Health Expenditures After Bariatric Surgery: A Retrospective Cohort Study
Smith, V. A., Zepel, L., Kawatkar, A., Arterburn, D. E., Baecker, A., Theis, M., Sloan, C., Clark, A. G., Saurabh, S., Coleman, K. J., et al. (2024) · Annals of Surgery · doi:10.1097/sla.0000000000006333 · Cited by 7
Lee, J., Lee, H., & Kang, H. (2021) · BMC Psychiatry · doi:10.1186/s12888-021-03550-2 · Cited by 9
“We used the patients’ demographic characteristics, such as sex, age, and the type of NHS program enrolled, as the variables in greedy matching, which is a method that produces balanced matched samples [11].”
MethodDesai, R., Wyss, R., Jin, Y.-Z., Bohn, J., Toh, S., Cosgrove, A., Kennedy, A., Kim, J., Kim, C., Ouellet-Hellstrom, R., et al. (2018) · American Journal of Epidemiology · doi:10.1093/aje/kwy130 · Cited by 7
Maciejewski, M., Zepel, L., Smith, V. A., Arterburn, D. E., Theis, M., Baecker, A., Sloan, C., Clark, A. G., Kane, R. M., Daigle, C. R., et al. (2025) · Annals of Internal Medicine · doi:10.7326/annals-24-00480 · Cited by 6
Assessing the Impact of Covid-19 in Mozambique in 2020
Salvucci, V., & Tarp, F. (2023) · European Journal of Development Research · doi:10.1057/s41287-023-00613-w · Cited by 6
“We did not use the Mahalanobis distance, since it appears to be working better when only few covariates are in the analysis (Rubin 1979; Zhao 2004; Gu and Rosenbaum 1993; Stuart 2010).”
Causal Analysis on the Anchor Store Effect in a Location-based Social Network
Vallapuram, A. K., Kwon, Y. D., Lee, L.-H., Xu, F.-L., & Hui, P. (2022) · International Conference on Advances in Social Networks Analysis and Mining · doi:10.1109/asonam55673.2022.10068687 · Cited by 6
“lowing several works in this area [22], [33], [34].”
Background
Metadata
- 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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