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Statistical Inference for a Two-Stage Outcome-Dependent Sampling Design with a Continuous Outcome

Authors

  • Haibo Zhou,

    Corresponding author
    1. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
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  • Rui Song,

    Corresponding author
    1. Department of Statistics, Colorado State University, Fort Collins, Colorado 80523, U.S.A.
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  • Yuanshan Wu,

    Corresponding author
    1. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-7420, U.S.A.
    2. School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China
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  • Jing Qin

    Corresponding author
    1. Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, NIH, 6700B Rockledge Drive, MSC 7609, Bethesda, Maryland 20892, U.S.A.
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email:zhou@bios.unc.edu

email:song@stat.colostate.edu

email:yswu@bios.unc.edu

email:jingqin@niaid.nih.gov

Abstract

Summary The two-stage case–control design has been widely used in epidemiology studies for its cost-effectiveness and improvement of the study efficiency (White, 1982, American Journal of Epidemiology115, 119–128; Breslow and Cain, 1988, Biometrika75, 11–20). The evolution of modern biomedical studies has called for cost-effective designs with a continuous outcome and exposure variables. In this article, we propose a new two-stage outcome-dependent sampling (ODS) scheme with a continuous outcome variable, where both the first-stage data and the second-stage data are from ODS schemes. We develop a semiparametric empirical likelihood estimation for inference about the regression parameters in the proposed design. Simulation studies were conducted to investigate the small-sample behavior of the proposed estimator. We demonstrate that, for a given statistical power, the proposed design will require a substantially smaller sample size than the alternative designs. The proposed method is illustrated with an environmental health study conducted at National Institutes of Health.

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