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Basic Tools of Multivariate Matching

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Design of Observational Studies

Part of the book series: Springer Series in Statistics ((SSS))

Abstract

The basic tools of multivariate matching are introduced, including the propensity score, distance matrices, calipers imposed using a penalty function, optimal matching, matching with multiple controls and full matching. The tools are illustrated with a tiny example from genetic toxicology (n = 46), an example that is so small that one can keep track of individuals as they are matched using different techniques.

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References

  • Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Upper Saddle River, NJ: Prentice Hall (1993)

    Google Scholar 

  • Avriel, M.: Nonlinear Programming. Upper Saddle River, New Jersey: Prentice Hall. (1976)

    MATH  Google Scholar 

  • Bergstralh, E.J., Kosanke, J.L., Jacobsen, S.L.: Software for optimal matching in observational studies. Epidemiology 7, 331–332\ (1996)

    Google Scholar 

  • Bertsekas, D.P.: A new algorithm for the assignment problem. Math Program 21, 152–171 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas, D.P.: Linear Network Optimization. Cambridge, MA: MIT Press (1991)

    MATH  Google Scholar 

  • Braitman, L.E., Rosenbaum, P.R.: Rare outcomes, common treatments: Analytic strategies using propensity scores. Ann Intern Med 137, 693–695 (2002)

    Google Scholar 

  • Carpaneto, G., Toth, P.: Algorithm 548: Solution of the Assignment Problem [H]. ACM Trans Math Software 6, 104–111 (1980)

    Article  Google Scholar 

  • Cochran, W.G.: The planning of observational studies of human populations (with Discussion). J Roy Statist Soc A 128, 234–265.

    Google Scholar 

  • Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. New York: Wiley (1998)

    MATH  Google Scholar 

  • Costa, M., Zhitkovich, A., Toniolo, P.: DNA-protein cross-links in welders: Molecular implications. Cancer Res 53, 460–463 (1993)

    Google Scholar 

  • Dell’Amico, M. and Toth, P.: Algorithms and codes for dense assignment problems: the state of the art. Discrete App Math 100, 17–48 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Fleiss, J.L., Levin, B., Paik, M.C.: Statistical Methods for Rates and Proportions. New York: Wiley (2001)

    Google Scholar 

  • Gu, X.S., Rosenbaum, P.R.: Comparison of multivariate matching methods: Structures, distances, and algorithms. J Comput Graph Statist 2, 405–420 (1993)

    Article  Google Scholar 

  • Hansen, B.B.: Full matching in an observational study of coaching for the SAT. J Am Statist Assoc 99, 609–618 (2004)

    Article  MATH  Google Scholar 

  • Hansen, B.B., Klopfer, S.O.: Optimal full matching and related designs via network flows. J Comp Graph Statist 15, 609–627 (2006)

    Article  MathSciNet  Google Scholar 

  • Hansen, B.B.: Optmatch: Flexible, optimal matching for observational studies. R News 7, 18–24 (2007)

    Google Scholar 

  • Haviland, A.M., Nagin, D.S., Rosenbaum, P.R.: Combining propensity score matching and group-based trajectory analysis in an observational study. Psychol Methods 12, 247–267 (2007)

    Article  Google Scholar 

  • Haviland, A.M., Nagin, D.S., Rosenbaum, P.R., Tremblay, R.: Combining group-based trajectory modeling and propensity score matching for causal inferences in nonexperimental longitudinal data. Dev Psychol 44, 422–436 (2008)

    Article  Google Scholar 

  • Heller, R., Manduchi, E., Small, D.: Matching methods for observational microarray studies. Bioinformatics 25, 904–909 (2009)

    Article  Google Scholar 

  • Ho, D., Imai, K., King, G., Stuart, E.A.: Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Polit Anal 15, 199–236 (2007)

    Article  Google Scholar 

  • Karmanov, V.G.: Mathematical Programming. Moscow: Mir.

    Google Scholar 

  • Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Res Logist Quart 2, 83–97 (1955)

    Article  MathSciNet  Google Scholar 

  • Lehmann, E.L.: Nonparametrics. San Francisco: Holden Day (1975)

    MATH  Google Scholar 

  • Mahalanobis, P.C.: On the generalized distance in statistics. Proc Natl Inst Sci India 12, 49–55 (1936)

    Google Scholar 

  • Maindonald, J., Braun, J.: Data Analysis and Graphics Using R. New York: Cambridge University Press (2005)

    Google Scholar 

  • Ming, K., Rosenbaum, P. R . Substantial gains in bias reduction from matching with a variable number of controls. Biometrics 56, 118–124 (2000)

    Article  MATH  Google Scholar 

  • Ming, K., Rosenbaum, P.R.: A note on optimal matching with variable controls using the assignment algorithm. J Comp Graph Statist 10, 455–463 (2001)

    Article  MathSciNet  Google Scholar 

  • R Development Core Team.: R: A Language and Environment for Statistical Computing. Vienna: R Foundation, http://www.R-project.org (2007)

  • Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall (1982)

    MATH  Google Scholar 

  • Rosenbaum, P.R., Rubin, D.B. : The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Conditional permutation tests and the propensity score in observational studies. J Am Statist Assoc 79, 565–574 (1984)

    Article  MathSciNet  Google Scholar 

  • Rosenbaum, P.R., Rubin, D.B. : Constructing a control group by multivariate matched sampling methods that incorporate the propensity score. Am Statistician 39, 33–38 (1985)

    Article  Google Scholar 

  • Rosenbaum, P.R.: Model-based direct adjustment. J Am Statist Assoc 82, 387–394 (1987)

    Article  MATH  Google Scholar 

  • Rosenbaum, P.R.: Optimal matching in observational studies. J Am Statist Assoc 84, 1024–1032 (1989)

    Article  Google Scholar 

  • Rosenbaum, P.R.: A characterization of optimal designs for observational studies. J Roy Statist Soc B 53, 597–610 (1991)

    MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Covariance adjustment in randomized experiments and observational studies (with Discussion). Statist Sci 17, 286–327 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R.: Observational Studies. New York: Springer (2002)

    MATH  Google Scholar 

  • Rubin, D.B. : Matching to remove bias in observational studies. Biometrics 29, 159–183 (1973)

    Article  Google Scholar 

  • Rubin D.B.: Bias reduction using Mahalanobis metric matching. Biometrics 36, 293–298 (1980)

    Article  MATH  Google Scholar 

  • Sekhon, J.S.: Opiates for the matches: Matching methods for causal inference. Annu Rev Pol Sci 12, 487–508 (2009)

    Article  Google Scholar 

  • Silber, J.H., Rosenbaum, P.R., Trudeau, M.E., Even-Shoshan, O., Chen, W., Zhang, X., Mosher, R.E. : Multivariate matching and bias reduction in the surgical outcomes study. Medical Care 39, 1048–1064 (2001)

    Article  Google Scholar 

  • Silber, J.H., Rosenbaum, P.R., Trudeau, M.E., Chen, W., Zhang, X., Lorch, S.L., Rapaport-Kelz, R., Mosher, R.E, Even-Shoshan, O.: Preoperative antibiotics and mortality in the elderly, Ann Surg 242, 107–114 (2005)

    Article  Google Scholar 

  • Silber, J.H., Rosenbaum, P.R., Polsky, D., Ross, R.N., Even-Shoshan, O., Schwartz, S., Armstrong, K.A., Randall, T.C.: Does ovarian cancer treatment and survival differ by the specialty providing chemotherapy? J Clin Oncol 25, 1169–1175 (2007)

    Article  Google Scholar 

  • Silber, J.H., Lorch, S.L., Rosenbaum, P.R., Medoff-Cooper, B., Bakewell-Sachs, S., Millman, A., Mi, L., Even-Shoshan, O., Escobar, G.E. : Additional maturity at discharge and subsequent health care costs. Health Serv Res 44, 444–463 (2009)

    Article  Google Scholar 

  • Smith, H.L. : Matching with multiple controls to estimate treatment effects in observational studies. Sociol Method 27, 325–353 (1997)

    Article  Google Scholar 

  • Stuart, E.A., Green, K.M. : Using full matching to estimate causal effects in nonexperimental studies: Examining the relationship between adolescent marijuana use and adult outcomes. Dev Psychol 44, 395–406 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. Statistics Department Wharton School, University of Pennsylvania, 19104-6340, Philadelphia, PA, USA

    Paul R. Rosenbaum

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  1. Paul R. Rosenbaum
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Correspondence to Paul R. Rosenbaum .

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Rosenbaum, P.R. (2010). Basic Tools of Multivariate Matching. In: Design of Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1213-8_8

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