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Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure After Surgery

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  • José R. Zubizarreta

Abstract

This article presents a new method for optimal matching in observational studies based on mixed integer programming. Unlike widely used matching methods based on network algorithms, which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls, this new method achieves covariate balance directly, either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance, or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances. The inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match. For example, the method minimizes or constrains differences in univariate moments, such as means, variances, and skewness; differences in multivariate moments, such as correlations between covariates; differences in quantiles; and differences in statistics, such as the Kolmogorov--Smirnov statistic, to minimize the differences in both location and shape of the empirical distributions of the treated units and matched controls. While balancing several of these measures, it is also possible to impose constraints for exact and near-exact matching, and fine and near-fine balance for more than one nominal covariate, whereas network algorithms can finely or near-finely balance only a single nominal covariate. From a practical standpoint, this method eliminates the guesswork involved in current optimal matching methods, and offers a controlled and systematic way of improving covariate balance by focusing the matching efforts on certain measures of covariate imbalance and their corresponding weights or tolerances. A matched case--control study of acute kidney injury after surgery among Medicare patients illustrates these features in detail. A new R package called mipmatch implements the method.

Suggested Citation

  • José R. Zubizarreta, 2012. "Using Mixed Integer Programming for Matching in an Observational Study of Kidney Failure After Surgery," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1360-1371, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1360-1371
    DOI: 10.1080/01621459.2012.703874
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    References listed on IDEAS

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    1. Lu, Bo & Greevy, Robert & Xu, Xinyi & Beck, Cole, 2011. "Optimal Nonbipartite Matching and Its Statistical Applications," The American Statistician, American Statistical Association, vol. 65(1), pages 21-30.
    2. Li Y.P. & Propert K. J. & Rosenbaum P. R., 2001. "Balanced Risk Set Matching," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 870-882, September.
    3. Ben B. Hansen, 2004. "Full Matching in an Observational Study of Coaching for the SAT," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 609-618, January.
    4. Ben B. Hansen, 2008. "The prognostic analogue of the propensity score," Biometrika, Biometrika Trust, vol. 95(2), pages 481-488.
    5. Rosenbaum, Paul R. & Ross, Richard N. & Silber, Jeffrey H., 2007. "Minimum Distance Matched Sampling With Fine Balance in an Observational Study of Treatment for Ovarian Cancer," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 75-83, March.
    6. Robert Bixby & Edward Rothberg, 2007. "Progress in computational mixed integer programming—A look back from the other side of the tipping point," Annals of Operations Research, Springer, vol. 149(1), pages 37-41, February.
    7. Iacus, Stefano M. & King, Gary & Porro, Giuseppe, 2012. "Causal Inference without Balance Checking: Coarsened Exact Matching," Political Analysis, Cambridge University Press, vol. 20(1), pages 1-24, January.
    8. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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