Advertisement
Original article| Volume 56, ISSUE 3, P230-237, March 2003

Optimal matching with a variable number of controls vs. a fixed number of controls for a cohort study

trade-offs
  • M.Soledad Cepeda
    Affiliations
    Center for Clinical Epidemiology and Biostatistics and Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, 824 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA

    Javeriana University School of Medicine, Department of Anesthesiology and Clinical Epidemiology Unit, Cra 7 #40-62, Bogota, Colombia
    Search for articles by this author
  • Ray Boston
    Affiliations
    Center for Clinical Epidemiology and Biostatistics and Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, 824 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA

    New Bolton Center, School of Veterinary Medicine, University of Pennsylvania, 382 West Street Road, Kennett Square, Philadelphia, PA 19348, USA
    Search for articles by this author
  • John T. Farrar
    Affiliations
    Center for Clinical Epidemiology and Biostatistics and Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, 824 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA
    Search for articles by this author
  • Brian L. Strom
    Correspondence
    Corresponding author. Tel.: 215-898-2368; fax: 215-573-5315.
    Affiliations
    Center for Clinical Epidemiology and Biostatistics and Department of Biostatistics and Epidemiology, University of Pennsylvania School of Medicine, 824 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA
    Search for articles by this author

      Abstract

      Matching is used to control for imbalances between groups, but the preferable strategy for matching is not always clear. We sought to compare two algorithms—optimal matching with a fixed number of controls (OMFC), and optimal matching with a variable number of controls (OMVC). We compared the degree of bias reduction and relative precision using Monte Carlo simulations. We systematically changed the magnitude of the matching variable difference, the variance ratios of the matching variable in the exposed and unexposed groups, the sample size, and the number of unexposed subjects available for matching. OMVC always produced larger removal of bias than the OMFC. The mean percentage reduction of bias was 38.3 with the OMFC and 52.6 with OMVC. OMVC increased the variance 6%. OMVC should be employed when researchers have access to a pool of unexposed subjects because it removes more bias with little loss in precision.

      Keywords

      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'

      Subscribe:

      Subscribe to Journal of Clinical Epidemiology
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect

      References

        • Rosenbaum P.R.
        Observational studies.
        in: Rosenbaum P.R. Observational studies. Springer-Verlag;, New York1995: 1-12
        • Rothman K.J.
        • Greenland S.
        Matching.
        in: Rothman K.J. Greenland S. Modern epidemiology. 2nd ed. Lippincott-Raven;, New York1998: 147-161
        • Cologne J.B.
        • Shibata Y.
        Optimal case–control matching in practice.
        Epidemiology. 1994; 6: 271-275
        • Rosenbaum P.R.
        Optimal matching for observational studies.
        JASA. 1989; 84: 1024-1032
        • Rosenbaum P.R.
        A characterization of optimal designs for observational studies.
        J R Stat Soc Series B. 1988; 53: 597-610
        • Greenland S.
        Applications of stratified analysis methods.
        in: Rothman K.J. Greenland S. Modern epidemiology. 2nd ed. Lippincott-Raven Publishers;, Philadelphia1998: 281-300
        • Gu X.S.
        • Rosenbaum P.R.
        Comparison of multivariate matching methods.
        J Comput Graph Stat. 1993; 2: 405-420
        • Ming K.
        • Rosenbaum P.R.
        Substantial gains in bias reduction from matching with a variable number of controls.
        Biometrics. 2000; 56: 118-124
        • Mooney C.Z.
        Introduction.
        in: Lewis-Beck M.S. Monte Carlo simulation. Sage Publications;, Thousands Oaks, CA1997: 3-4
        • Ury H.K.
        Efficiency of case control studies with multiple controls per case.
        Biometrics. 1975; 31: 643-649
        • Rubin D.B.
        • Thomas N.
        Matching using estimated propensity score.
        Biometrics. 1996; 52: 249-264
        • Rubin D.R.
        Using multivariate matched sampling and regression adjustment to control bias in observational studies.
        JASA. 1979; 74: 318-328
        • Rubin D.R.
        The use of matched sampling and regression adjustment to remove bias in observational studies.
        Biometrics. 1973; 29: 185-203
        • Bergstralh E.J.
        • Kosanke J.L.
        • Jacobsen S.J.
        Software for optimal matching in observational studies.
        Epidemiology. 1996; 7: 331-332
        • Kelsey J.L.
        • Whittemore A.S.
        • Evans A.S.
        • Thompson W.D.
        Methods of sampling and estimation of sample size.
        in: Kelsey J.L. Whittemore A.S. Evans A.S. Thompson W.D. Methods in observational epidemiology. 2nd ed. Oxford University Press;, New York1996: 311-340
      1. Bradley EL. Overlapping coefficient. In: Kotz S, Johnson NL, Read CB, editors. Encyclopedia of Statistical Sciences. New York: Wiley, 1985; Vol. 6, p. 546–47.

        • Assmant S.F.
        • Pocock S.J.
        • Enos L.E.
        • Kasten L.E.
        Subgroup analysis and other (mis)uses of baseline data in clinical trials.
        Lancet. 2000; 355: 1064-1069
        • Cochran W.G.
        The planning of observational studies of human populations.
        J R Stat Soc Series A. 1965; 128: 234-255
        • Rosenbaum P.R.
        • Rubin D.R.
        Constructing a control group using multivariate matched sampling methods that incorporate the propensity score.
        Am Stat. 1985; 39: 33-38
        • D'Agostino R.B.
        Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group.
        Stat Med. 1998; 17: 2265-2281
        • Cepeda M.S.
        The use of propensity score in pharmaco epidemiologic research.
        Pharmacoepidemiol Drug Saf. 2000; 9: 103-104