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Matching (statistics)
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<h2 id="analysis">Analysis</h2> <p>When the outcome of interest is binary, the most general tool for the analysis of matched data is <a href="/facts/Conditional_logistic_regression/9ptpssu1">conditional logistic regression</a> as it handles strata of arbitrary size and continuous or binary treatments (predictors) and can control for covariates. In particular cases, simpler tests like <a href="/facts/Paired_difference_test/lCLuSGUL">paired difference test</a>, <a href="/facts/McNemar_test/AFry9wG5">McNemar test</a> and <a href="/facts/Cochran%25E2%2580%2593Mantel%25E2%2580%2593Haenszel_test/NKrrFbpD">Cochran–Mantel–Haenszel test</a> are available. </p><p>When the outcome of interest is continuous, estimation of the <a href="/facts/Average_treatment_effect/rju6xf4B">average treatment effect</a> is performed. </p><p>Matching can also be used to "pre-process" a sample before analysis via another technique, such as <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a>.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> </p> <h2 id="overmatching">Overmatching</h2> <p><i>Overmatching,</i> or <i>post-treatment bias,</i> is matching for an apparent mediator that actually is a result of the exposure.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> If the mediator itself is stratified, an obscured relation of the exposure to the disease would highly be likely to be induced.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> Overmatching thus causes <a href="/facts/Statistical_bias/Pql981K3">statistical bias</a>.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> </p><p>For example, matching the control group by gestation length and/or the number of <a href="/facts/Multiple_birth/bVVVhRvs">multiple births</a> when estimating <a href="/facts/Perinatal_mortality/ua1GwEAL">perinatal mortality</a> and birthweight after <a href="/facts/In_vitro_fertilization/kQNMtaBu">in vitro fertilization</a> (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> </p><p>It may be regarded as a <a href="/facts/Sampling_bias/nrr4qR2T">sampling bias</a> in decreasing the <a href="/facts/External_validity/M5Q3z42b">external validity</a> of a study, because the controls become more similar to the cases in regard to exposure than the general population. </p> <h2 id="see-also">See also</h2> <ul> <li>Mathematics portal</li><li>Medicine portal</li></ul> <ul><li><a href="/facts/Propensity_score_matching/ajVY6GqP">Propensity score matching</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Angrist, Joshua D.; Pischke, Jörn-Steffen (2009). "Regression Meets Matching". <i>Mostly Harmless Econometrics: An Empiricist's Companion</i>. Princeton University Press. pp. 69–80. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-691-12034-8.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Rubin, Donald B. (1973). "Matching to Remove Bias in Observational Studies". Biometrics. 29 (1): 159–183. doi:10.2307/2529684. JSTOR 2529684. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Anderson, Dallas W.; Kish, Leslie; Cornell, Richard G. (1980). "On Stratification, Grouping and Matching". Scandinavian Journal of Statistics. 7 (2): 61–66. JSTOR 4615774. <a href="/wiki/JSTOR_(identifier)" target="_blank">/wiki/JSTOR_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>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. CiteSeerX 10.1.1.154.1197. doi:10.2307/2530417. JSTOR 2530417. PMID 7272415. <a href="/wiki/CiteSeerX_(identifier)" target="_blank">/wiki/CiteSeerX_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>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. <a href="https://doi.org/10.1093%2Fbiomet%2F70.1.41" target="_blank">https://doi.org/10.1093%2Fbiomet%2F70.1.41</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>King, Gary; Nielsen, Richard (October 2019). "Why Propensity Scores Should Not Be Used for Matching". Political Analysis. 27 (4): 435–454. doi:10.1017/pan.2019.11. hdl:1721.1/128459. ISSN 1047-1987. <a href="https://doi.org/10.1017%2Fpan.2019.11" target="_blank">https://doi.org/10.1017%2Fpan.2019.11</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Iacus, Stefano M.; King, Gary; Porro, Giuseppe (2011). "Multivariate Matching Methods That Are Monotonic Imbalance Bounding". Journal of the American Statistical Association. 106 (493): 345–361. doi:10.1198/jasa.2011.tm09599. hdl:2434/151476. ISSN 0162-1459. S2CID 14790456. <a href="http://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm09599" target="_blank">http://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm09599</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>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. <a href="https://doi.org/10.1093%2Fbiomet%2F70.1.41" target="_blank">https://doi.org/10.1093%2Fbiomet%2F70.1.41</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>LaLonde, Robert J. (1986). "Evaluating the Econometric Evaluations of Training Programs with Experimental Data". American Economic Review. 76 (4): 604–620. JSTOR 1806062. <a href="/wiki/American_Economic_Review" target="_blank">/wiki/American_Economic_Review</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Dehejia, R. H.; Wahba, S. (1999). "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs" (PDF). Journal of the American Statistical Association. 94 (448): 1053–1062. doi:10.1080/01621459.1999.10473858. <a href="http://www.nber.org/papers/w6586.pdf" target="_blank">http://www.nber.org/papers/w6586.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>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. S2CID 37012563. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>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. <a href="/wiki/Elizabeth_A._Stuart" target="_blank">/wiki/Elizabeth_A._Stuart</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>King, Gary; Zeng, Langche (2007). "Detecting Model Dependence in Statistical Inference: A Response". International Studies Quarterly. 51 (1): 231–241. doi:10.1111/j.1468-2478.2007.00449.x. ISSN 0020-8833. JSTOR 4621711. S2CID 12669035. <a href="https://www.jstor.org/stable/4621711" target="_blank">https://www.jstor.org/stable/4621711</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>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. <a href="/wiki/Jane_Hutton" target="_blank">/wiki/Jane_Hutton</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>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. <a href="/wiki/Jane_Hutton" target="_blank">/wiki/Jane_Hutton</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>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. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> </ol>