Matching (statistics)

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Matching is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated units in an observational study or quasi-experiment (i.e. when the treatment is not randomly assigned). The goal of matching is, for every treated unit, to find one (or more) non-treated unit(s) with similar observable characteristics against whom the effect of the treatment can be assessed. By matching treated units to similar non-treated units, matching enables a comparison of outcomes among treated and non-treated units to estimate the effect of the treatment reducing bias due to confounding.[1][2][3] Propensity score matching, an early matching technique, was developed as part of the Rubin causal model.[4]

Matching has been promoted by Donald Rubin.[4] It was prominently criticized in economics by LaLonde (1986),[5] who compared estimates of treatment effects from an experiment to comparable estimates produced with matching methods and showed that matching methods are biased. Dehejia and Wahba (1999) reevaluted LaLonde's critique and show that matching is a good solution.[6] Similar critiques have been raised in political science[7] and sociology[8] journals.


Matched samples of treated and non-treated units can often be analyzed with a paired difference test to estimate the average treatment effect. Matching can also be used to "pre-process" a sample before analysis via another technique, such as regression analysis.[9]


Overmatching is matching for an apparent confounder that actually is a result of the exposure. True confounders are associated with both the exposure and the disease, but if the exposure itself leads to the confounder, or has equal status with it, then stratifying by that confounder will also partly stratify by the exposure, resulting in an obscured relation of the exposure to the disease.[10] Overmatching thus causes statistical bias.[10]

For example, matching the control group by gestation length and/or the number of multiple births when estimating perinatal mortality and birthweight after in vitro fertilization (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.[11]

It may be regarded as a sampling bias in decreasing the external validity of a study, because the controls become more similar to the cases in regard to exposure than the general population.

See also[edit]


  1. ^ Rubin, Donald B. (1973). "Matching to Remove Bias in Observational Studies". Biometrics 29 (1): 159–183. doi:10.2307/2529684. JSTOR 2529684. 
  2. ^ Anderson, Dallas W.; Kish, Leslie; Cornell, Richard G. (1980). "On Stratification, Grouping and Matching". Scandinavian Journal of Statistics 7 (2): 61–66. JSTOR 4615774. 
  3. ^ Kupper, Lawrence L.; Karon, John M.; Kleinbaum, David G.; Morgenstern, Hal; Lewis, Donald K. (1981). "Matching in Epidemiologic Studies: Validity and Efficiency Considerations". Biometrics 37 (2): 271–291. doi:10.2307/2530417. JSTOR 2530417. PMID 7272415. 
  4. ^ a b Rosenbaum, Paul R.; Rubin, Donald B. (1983). "The Central Role of the Propensity Score in Observational Studies for Causal Effects". Biometrika 70 (1): 41–55. doi:10.1093/biomet/70.1.41. 
  5. ^ LaLonde, Robert J. (1986). "Evaluating the Econometric Evaluations of Training Programs with Experimental Data". American Economic Review 76 (4): 604–620. JSTOR 1806062. 
  6. ^ Dehejia, R. H.; Wahba, S. (1999). "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs". Journal of the American Statistical Association 94 (448): 1053–1062. doi:10.1080/01621459.1999.10473858. 
  7. ^ Arceneaux, Kevin; Gerber, Alan S.; Green, Donald P. (2006). "Comparing Experimental and Matching Methods Using a Large-Scale Field Experiment on Voter Mobilization". Political Analysis 14 (1): 37–62. doi:10.1093/pan/mpj001. 
  8. ^ Arceneaux, Kevin; Gerber, Alan S.; Green, Donald P. (2010). "A Cautionary Note on the Use of Matching to Estimate Causal Effects: An Empirical Example Comparing Matching Estimates to an Experimental Benchmark". Sociological Methods & Research 39 (2): 256–282. doi:10.1177/0049124110378098. 
  9. ^ Ho, Daniel E.; Imai, Kosuke; King, Gary; Stuart, Elizabeth A. (2007). "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference". Political Analysis 15 (3): 199–236. doi:10.1093/pan/mpl013. 
  10. ^ a b Marsh, J. L.; Hutton, J. L.; Binks, K. (2002). "Removal of radiation dose response effects: an example of over-matching". British Medical Journal 325 (7359): 327–330. doi:10.1136/bmj.325.7359.327. PMC 1123834. PMID 12169512. 
  11. ^ Gissler, M.; Hemminki, E. (1996). "The danger of overmatching in studies of the perinatal mortality and birthweight of infants born after assisted conception". Eur J Obstet Gynecol Reprod Biol 69 (2): 73–75. doi:10.1016/0301-2115(95)02517-0. PMID 8902436. 

Further reading[edit]

  • Angrist, Joshua D.; Pischke, Jörn-Steffen (2009). "Regression Meets Matching". Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press. pp. 69–80. ISBN 978-0-691-12034-8.