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Constructing Matched Sets and Strata

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Observational Studies

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

Abstract

This chapter discusses the construction of matched sets or strata when there are several, perhaps many, observed covariates x. There are three topics: the propensity score, the form of an optimal stratification, and the construction of optimal matched sets. This introduction summarizes the main issues and findings.

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References

  • Ahuja, R. K., Magnanti, T. L., and Orlin, J. B. (1993) Network Flows: Theory, Algorithms, and Applications. New York: Prentice-Hall.

    MATH  Google Scholar 

  • Bergstralh, E. J., Kosanke, J. L., and Jacobsen, S. L. (1996) Software for optimal matching in observational studies. Epidemiology, 7, 331–332. http://www.mayo.edu/hsr/sasmac.html.

    Google Scholar 

  • Bertsekas, D. (1991) Linear Network Optimization: Algorithms and Codes. Cambridge, MA: MIT Press. http://www.mit.edu:8001//people/dimitrib/home.html.

    Google Scholar 

  • Bertsekas, D. (2001) Auction algorithms. Encyclopedia of Optimization, C. A. Foudas and P. M. Pardalos, eds., Kluwer.

    Google Scholar 

  • Carpenter, R. (1977) Matching when covariables are normally distributed. Biometrika, 64, 299–307.

    Article  MATH  Google Scholar 

  • Cochran, W. G. (1968) The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics, 24, 205–213.

    Article  MathSciNet  Google Scholar 

  • Cochran, W. G. and Rubin, D. B. (1973) Controlling bias in observational studies: A review. Sankya, Series A, 35, 417–446.

    MATH  Google Scholar 

  • Cox, D. R. (1970) The Analysis of Binary Data. London: Methuen.

    MATH  Google Scholar 

  • Cox, D. R. and Snell, E. J. (1981) Applied Statistics: Principles and Examples. London: Chapman & Hall.

    MATH  Google Scholar 

  • Dehejia, R. H. and Wahba, S. (1999) Causal effects in nonexperimental studies. Reevaluating the evaluating of training programs. Journal of the American Statistical Association, 94, 1053–1062.

    Article  Google Scholar 

  • Ford, L. and Fulkerson, D. (1962) Flows in Networks. Princeton, NJ: Princeton University Press.

    MATH  Google Scholar 

  • Ghavamian, R., Bergstralh, E. J., Blute, M. L., Slezak, J., and Zincke, H. (1999) Radical retropubic prostatectomy plus orchectomy versus orchietomy for pTxN+ prostate cancer: A matched comparison. Journal of Urology, 161, 1223 – 1227.

    Article  Google Scholar 

  • Gu, X. S. and Rosenbaum, P. R. (1993) Comparison of multivariate matching methods: Structures, distances and algorithms. Journal of Computational and Graphical Statistics, 2, 405–420.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Joffe, M. M. and Rosenbaum, P. R. (1999) Propensity scores. American Journal of Epidemiology, 150, 327 – 333.

    Article  Google Scholar 

  • Kuhn, H. W. (1955) The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2, 83–97.

    Article  MathSciNet  Google Scholar 

  • Lechner, M. (2000) An evaluation of public-sector-sponsored continuous vocational training programs in East Germany. Journal of Human Resources, 35, 347 – 375.

    Article  Google Scholar 

  • Li, Y., Propert, K. J. and Rosenbaum, P. R. (2001) Balanced risk set matching. Journal of the American Statistical Association, 96, September, to appear.

    Google Scholar 

  • Lu, B., Zanutto, E., Hornik, R., and Rosenbaum, P. R. (2002) Matching with doses in an observational study of a media campaign against drug abuse. Journal of the American Statistical Association, to appear.

    Google Scholar 

  • McCullagh, P. (1980) Regression models for ordinal data. Journal of the Royal Statistical Society, B, 42, 109 – 142.

    MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Ming, K. and Rosenbaum, P. R. (2001) A note on optimal matching with variable controls using the assignment algorithm. Journal of Computational and Graphical Statistics, to appear.

    Google Scholar 

  • Normand, S. T., Landrum, M. B., Guadagnoli, E., Ayanian, J. Z., Ryan, T. J., Cleary, P. D., and McNeil, B. J. (2001) Validating recommendations for coronary angiography following acute myocardial infarction in the elderly: A matched analysis using propensity scores. Journal of Clinical Epidemiology, 54, 387 – 398.

    Article  Google Scholar 

  • Nuako, K. W., Ahlquist, D. A., Sandborn, W. J., Mahoney, D. W., Siems, D. M., and Zinsmeister, A. R. (1998) Primary sclerosing cholangitis and colorectal carcinoma in patients with chronic ulcerative colitis: A case-control study. Cancer, 82, 822 – 826.

    Article  Google Scholar 

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

    MATH  Google Scholar 

  • Petersen, L. A., Normand, S., Daley, J., and McNeil, B. (2000) Outcome of myocardial infarction in Veterans Health Administration patients as compared with medicare patients. New England Journal of Medicine, 343, December 28, 2000, 1934 – 1941.

    Article  Google Scholar 

  • Phillips C. D., Spry K. M., Sloane P. D., and Hawes, C. (2000) Use of physical restraints and psychotropic medications in Alzheimer special care units in nursing homes. American Journal of Public Health, 90, 92 – 96.

    Article  Google Scholar 

  • Powers, D. E. and Rock, D. A. (1999) Effects of coaching on SAT I: Reasoning test scores. Journal of Educational Measurement, 36, 93 – 118.

    Article  Google Scholar 

  • Rephann, T. and Isserman, A. (1994) New highways as economic development tools-An evaluation using quasi-experimental matching methods. Regional Science and Urban Economics, 24, 723 – 751.

    Article  Google Scholar 

  • Rockafellar, R. T. (1984) Network Flows and Monotropic Optimization. New York: Wiley.

    MATH  Google Scholar 

  • Rosenbaum, P. R. (1984) Conditional permutation tests and the propensity score in observational studies. Journal of the American Statistical Association, 79, 565–574.

    Article  MathSciNet  Google Scholar 

  • Rosenbaum, P. R. (1987) Model-based direct adjustment. Journal of the American Statistical Association, 82, 387–394.

    Article  MATH  Google Scholar 

  • Rosenbaum, P. R. (1989) Optimal matching for observational studies. Journal of the American Statistical Association, 84, 1024–1032.

    Article  Google Scholar 

  • Rosenbaum, P. R. (1991) A characterization of optimal designs for observational studies. Journal of the Royal Statistical Society, Series 13, 53, 597–610.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Rosenbaum, P. R. and Rubin, D. B. (1984) Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association, 79, 516–524.

    Article  Google Scholar 

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

    Google Scholar 

  • Rosenbaum, P. R. and Silber, J. H. (2001) Matching and thick description in an observational study of mortality after surgery. Biostatistics, 2, 217 – 232.

    Article  MATH  Google Scholar 

  • Rubin, D. B. (1973) The use of matched sampling and regression adjustment to remove bias in observational studies. Biometrics, 29, 185–203.

    Article  Google Scholar 

  • Rubin, D. B. (1979) Using multivariate matched sampling and regression adjustment to control bias in observational studies. Journal of the American Statistical Association, 74, 318–328.

    MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Silber, J. H., Kennedy, S. K., Even-Shoshan, O., Chen, W., Koziol, L. F., Showan, A. M., Longnecker, D. E. (2000) Anesthesiologist direction and patient outcomes. Anesthesiology, 93, 152 – 163.

    Article  Google Scholar 

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

    Google Scholar 

  • Smith, A., Kark, J., Cassel, J., and Spears, G. (1977) Analysis of prospective epidemiologic studies by minimum distance case- control matching. American Journal of Epidemiology, 105, 567–574.

    Google Scholar 

  • Smith, H. (1997) Matching with multiple controls to estimate treatment effects in observational studies. Sociological Methodology, 27, 325 – 353.

    Article  Google Scholar 

  • Snyder, T. L. and Steele, J. M. (1990) Worst case greedy matching in the unit d-cube. Networks, 20, 779 – 800.

    Article  MathSciNet  MATH  Google Scholar 

  • Tarjan, R. (1983) Data Structures and Network Algorithms. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  • Walkup, D. (1979) On the expected value of a random assignment problem. SIAM Journal on Computing, 8, 440–442.

    Article  MathSciNet  MATH  Google Scholar 

  • Warner, D. O., Warner, M. A., Offord, K. P., Schroeder, D. R., Maxson, P., and Scanlon, P. D. (1999) Airway obstruction and perioperative complications in smokers undergoing abdominal surgery. Anesthesiology, 90, 372 – 379.

    Article  Google Scholar 

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© 2002 Springer Science+Business Media New York

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Rosenbaum, P.R. (2002). Constructing Matched Sets and Strata. In: Observational Studies. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3692-2_10

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  • DOI: https://doi.org/10.1007/978-1-4757-3692-2_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-3191-7

  • Online ISBN: 978-1-4757-3692-2

  • eBook Packages: Springer Book Archive

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