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Various Practical Issues in Matching

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Design of Observational Studies

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Abstract

Having constructed a matched control group, one must check that it is satisfactory, in the sense of balancing the observed covariates. If some covariates are not balanced, then adjustments are made to bring them into balance. Three adjustments are near-exact matching, exact matching, and the use of small penalties. Exact matching has a special role in extremely large problems, where it can be used to accelerate computation. Matching when some covariates have missing values is discussed.

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Notes

  1. 1.

    This statement is not exactly correct, owing to the discreteness of a randomization distribution, but it is close enough.

  2. 2.

    Near-exact matching is sometimes called almost-exact matching. These are two phrases with the same meaning.

  3. 3.

    Technically, the fitted probabilities in logit regression are invariant under affine transformations of the predictors.

References

  1. Avriel, M. : Nonlinear Programming. Prentice Hall, Englewood Cliffs, NJ (1976)

    Google Scholar 

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

    Google Scholar 

  3. Bertsekas, D.P.: Network Optimization. Athena Scientific, Belmont, MA (1998)

    Google Scholar 

  4. Bickel, P.J.: A distribution free version of the Smirnov two sample test in the p-variate case. Ann. Math. Stat. 40, 1–23 (1969)

    Google Scholar 

  5. Bruce, M.L., Ten Have, T.R., Reynolds, C.F. III, Katz, I.I., Schulberg, H.C., Mulsant, B.H., Brown, G.K., McAvay, G.J., Pearson, J.L., Alexopoulos, G.S.: Reducing suicidal ideation and depressive symptoms in depressed older primary pare patients: a randomized trial. J. Am. Med. Assoc. 291, 1081–1091 (2004)

    Google Scholar 

  6. Cleveland, W.S. : The Elements of Graphing Data. Hobart Press, Summit, NJ (1994)

    Google Scholar 

  7. Cochran, W.G.: The planning of observational studies of human populations (with Discussion). J. R. Stat. Soc. A 128, 234–265 (1965)

    Google Scholar 

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

    Google Scholar 

  9. Donner, A., Klar, N.: Pitfalls of and controversies in cluster randomization trials. Am. J. Public Health 94, 416–422 (2004)

    Google Scholar 

  10. Fisher, M.L.: The Lagrangian relaxation method for solving integer programming problems. Manag. Sci. 27, 1–18 (1981)

    Google Scholar 

  11. Garfinkel, R.S.: An improved algorithm for the bottleneck assignment problem. Oper. Res. 9, 1747–1751 (1971)

    Google Scholar 

  12. Glover, F.: Maximum matching in a convex bipartite graph. Nav. Res. Logist. Q 14, 313–316 (1967)

    Google Scholar 

  13. Hansen, B.B. , Bowers, J. : Covariate balance in simple, stratified and clustered comparative studies. Stat. Sci. 23, 219–236 (2008)

    Google Scholar 

  14. Hansen, B.B.: The essential role of balance tests in propensity-matched observational studies. Stat. Med. 12, 2050–2054 (2008)

    Google Scholar 

  15. Hansen, B.B., Rosenbaum, P.R., Small, D.S.: Clustered treatment assignments and sensitivity to unmeasured biases in observational studies. J. Am. Stat. Assoc. 109, 133–144 (2014)

    Google Scholar 

  16. Imai, K., King, G., Stuart, E.A.: Misunderstandings between experimentalists and observationalists about causal inference. J. R. Stat. Soc. A 171 , 481–502 (2008)

    Google Scholar 

  17. Imai, K., King, G., Nall, C.: The essential role of pair matching in cluster-randomized experiments, with application to the Mexican universal health insurance evaluation. Stat. Sci. 24, 29–53 (2009)

    Google Scholar 

  18. Karmanov, V.G.: Mathematical Programming. Mir, Moscow (1989)

    Google Scholar 

  19. Korte, B., Vygen, J.: Combinatorial Optimization, 5th edn. Springer, New York (2012)

    Google Scholar 

  20. Lipski, W., Preparata, F.P.: Efficient algorithms for finding maximum matchings in convex bipartite graphs and related problems. Acta Informa 15, 329–346 (1981)

    Article  Google Scholar 

  21. Marcus, S.M., Siddique, J., Ten Have, T.R., Gibbons, R.D., Stuart, E., Normand, S-L.T.: Balancing treatment comparisons in longitudinal studies. Psychiatr. Ann. 38, 12 (2008)

    Google Scholar 

  22. Pimentel, S.D., Kelz, R.R., Silber, J.H., Rosenbaum, P.R.: Large, sparse optimal matching with refined covariate balance in an observational study of the health outcomes produced by new surgeons. J. Am. Stat. Assoc. 110, 515–527 (2015)

    Google Scholar 

  23. Pimentel, S.D., Page, L.C., Lenard, M., Keele, L.: Optimal multilevel matching using network flows: an application to a summer reading intervention. Ann. Appl. Stat. 12, 1479–1505 (2018)

    Google Scholar 

  24. 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  MathSciNet  Google Scholar 

  25. Rosenbaum, P.R., Rubin, D.B.: Reducing bias in observational studies using subclassification on the propensity score. J. Am. Stat. Assoc. 79, 516–524 (1984)

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  28. Rosenbaum, P.R., Ross R.N. , Silber, J.H. : Minimum distance matched sampling with fine balance in an observational study of treatment for ovarian cancer. J. Am. Stat. Assoc. 102, 75–83. (2007)

    Google Scholar 

  29. Rosenbaum, P.R.: Imposing minimax and quantile constraints on optimal matching in observational studies. J. Comput. Graph Stat. 26, 66–78 (2017)

    Article  MathSciNet  Google Scholar 

  30. 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)

    Google Scholar 

  31. Small, D.S., Ten Have, T.R., Rosenbaum, P.R.: Randomization inference in a group randomized trial of treatments for depression: covariate adjustment, noncompliance, and quantile effects. J. Am. Stat. Assoc. 103, 271–279 (2008)

    Google Scholar 

  32. Wolsey, L.A.: Integer Programming. Wiley, New York (1998)

    Google Scholar 

  33. Yu, R., Silber, J.H., Rosenbaum, P.R.: Matching methods for observational studies derived from large administrative databases. Stat. Sci. (2020, to appear)

    Google Scholar 

  34. Yu, R., Rosenbaum, P.R.: Directional penalties for optimal matching in observational studies. Biometrics 75, 1380–1390 (2019)

    Article  MathSciNet  Google Scholar 

  35. Zubizarreta, J.R., Keele, L.: Optimal multilevel matching in clustered observational studies: A case study of the effectiveness of private schools under a large-scale voucher system. J. Am. Stat. Assoc. 109, 547–560 (2017)

    Google Scholar 

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Authors and Affiliations

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

    Paul R. Rosenbaum

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  1. Paul R. Rosenbaum
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R. Rosenbaum, P. (2020). Various Practical Issues in Matching. In: Design of Observational Studies. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-46405-9_10

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