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Generalized case‐control sampling under generalized linear models

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  • Jacob M. Maronge
  • Ran Tao
  • Jonathan S. Schildcrout
  • Paul J. Rathouz

Abstract

A generalized case‐control (GCC) study, like the standard case‐control study, leverages outcome‐dependent sampling (ODS) to extend to nonbinary responses. We develop a novel, unifying approach for analyzing GCC study data using the recently developed semiparametric extension of the generalized linear model (GLM), which is substantially more robust to model misspecification than existing approaches based on parametric GLMs. For valid estimation and inference, we use a conditional likelihood to account for the biased sampling design. We describe analysis procedures for estimation and inference for the semiparametric GLM under a conditional likelihood, and we discuss problems with estimation and inference under a conditional likelihood when the response distribution is misspecified. We demonstrate the flexibility of our approach over existing ones through extensive simulation studies, and we apply the methodology to an analysis of the Asset and Health Dynamics Among the Oldest Old study, which motives our research. The proposed approach yields a simple yet versatile solution for handling ODS in a wide variety of possible response distributions and sampling schemes encountered in practice.

Suggested Citation

  • Jacob M. Maronge & Ran Tao & Jonathan S. Schildcrout & Paul J. Rathouz, 2023. "Generalized case‐control sampling under generalized linear models," Biometrics, The International Biometric Society, vol. 79(1), pages 332-343, March.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:1:p:332-343
    DOI: 10.1111/biom.13571
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    References listed on IDEAS

    as
    1. Ran Tao & Donglin Zeng & Dan-Yu Lin, 2017. "Efficient Semiparametric Inference Under Two-Phase Sampling, With Applications to Genetic Association Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1468-1476, October.
    2. N. E. Breslow & N. Chatterjee, 1999. "Design and analysis of two‐phase studies with binary outcome applied to Wilms tumour prognosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 457-468.
    3. Weaver, Mark A. & Zhou, Haibo, 2005. "An Estimated Likelihood Method for Continuous Outcome Regression Models With Outcome-Dependent Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 459-469, June.
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