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Matching Without Groups

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Design of Observational Studies

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Abstract

Optimal matching without groups, or optimal nonbipartite matching, offers many additional options for matched designs in both observational studies and experiments. One starts with a square, symmetric distance matrix with one row and one column for each subject recording the distance between any two subjects. Then the subjects are divided into pairs to minimize the total distance within pairs. The method may be used to match with doses of treatment, or with multiple control groups, or as an aid to risk-set matching. An extended discussion of Card and Krueger’s study of the minimum wage is used to illustrate.

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References

  • Cahuc, P., Zylberberg, A.: Labor Economics. Cambridge, MA: MIT Press (2004)

    Google Scholar 

  • Card, D., Krueger, A.B.: Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania. Am Econ Rev 84, 772–793 (1994)

    Google Scholar 

  • Card, D., Krueger, A.B.: Myth and Measurement: The New Economics of the Minimum Wage. Princeton, NJ: Princeton University Press (1995) Data: http://www.irs.princeton.edu/

  • Cochran, W.G., Cox, G.M.: Experimental Designs. New York: Wiley (1957)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Cook, W., Rohe, A. : Computing minimum-weight perfect matchings. INFORMS J Comput 11, 138–148 (1999) Software: http://www2.isye.gatech.edu/~wcook/

  • Cox, D.R., Reid, N.: The Theory of the Design of Experiments. New York: Chapman and Hall/CRC (2000)

    MATH  Google Scholar 

  • Daniel, S., Armstrong, K., Silber, J.H., Rosenbaum, P.R.: An algorithm for optimal tapered matching, with application to disparities in survival. J Comput Graph Statist 17, 914–924 (2008)

    Article  Google Scholar 

  • Derigs, U. : Solving nonbipartite matching problems by shortest path techniques. Ann Operat Res 13, 225–261 (1988)

    Article  MathSciNet  Google Scholar 

  • Edmonds, J. : Matching and a polyhedron with 0–1 vertices. J Res Nat Bur Stand 65B, 125–130 (1965)

    MathSciNet  Google Scholar 

  • Greevy, R., Lu, B., Silber, J.H., Rosenbaum, P.R.: Optimal matching before randomization. Biostatistics 5, 263–275 (2004)

    Article  MATH  Google Scholar 

  • Hornik, R., Jacobsohn, L., Orwin, R., Piesse, A., Kalton, G.: Effects of the national youth anti-drug media campaign on youths. Am J Public Health 98, 2229–2236 (2008)

    Article  Google Scholar 

  • Imai, K., van Dyk, D.A. : Causal inference with general treatment regimes: generalizing the propensity score. J Am Statist Assoc 99, 854–866 (2004)

    Article  MATH  Google Scholar 

  • Imbens, G.W. : The role of the propensity score in estimating dose-response functions. Biometrika 87, 706–710 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Joffe, M.M., Rosenbaum, P.R.: Propensity scores. Am J Epidemiol 150, 327–333 (1999)

    Google Scholar 

  • Li, Y.F.P., Propert, K.J., Rosenbaum, P.R.: Balanced risk set matching. J Am Statist Assoc 96, 870–882 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Lu, B., Zanutto, E., Hornik, R., Rosenbaum, P.R.: Matching with doses in an observational study of a media campaign against drug abuse. J Am Statist Assoc 96, 1245–1253 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Lu, B., Rosenbaum, P.R.: Optimal matching with two control groups. J Comput Graph Statist 13, 422–434 (2004)

    Article  MathSciNet  Google Scholar 

  • Lu, B.: Propensity score matching with time-dependent covariates. Biometrics 61, 721–728 (2005) http://cph.osu.edu/divisions/biostatistics/

    Google Scholar 

  • Lu, B., Greevy, R., Xu, X., Beck, C.: Optimal nonbipartite matching and its statistical applications. Manuscript. (2009)

    Google Scholar 

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

    MATH  Google Scholar 

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

  • Rosenbaum, P.R.: An exact, distribution free test comparing two multivariate distributions based on adjacency. J Royal Statist Soc B 67, 515–530 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Rosenbaum, P.R., Silber, J.H.: Sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units. J Am Statist Assoc 104, 501–511 (2009)

    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 

  • Stigler, G.J. : The economics of minimum wage legislation. Am Econ Rev 36, 358–365 (1946)

    Google Scholar 

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Correspondence to Paul R. Rosenbaum .

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Rosenbaum, P.R. (2010). Matching Without Groups. In: Design of Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1213-8_11

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