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Generalized Linear Models with Covariate Measurement Error and Zero-Inflated Surrogates

Author

Listed:
  • Ching-Yun Wang

    (Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA)

  • Jean de Dieu Tapsoba

    (Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA)

  • Catherine Duggan

    (Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA)

  • Anne McTiernan

    (Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA)

Abstract

Epidemiological studies often encounter a challenge due to exposure measurement error when estimating an exposure–disease association. A surrogate variable may be available for the true unobserved exposure variable. However, zero-inflated data are encountered frequently in the surrogate variables. For example, many nutrient or physical activity measures may have a zero value (or a low detectable value) among a group of individuals. In this paper, we investigate regression analysis when the observed surrogates may have zero values among some individuals of the whole study cohort. A naive regression calibration without taking into account a probability mass of the surrogate variable at 0 (or a low detectable value) will be biased. We developed a regression calibration estimator which typically can have smaller biases than the naive regression calibration estimator. We propose an expected estimating equation estimator which is consistent under the zero-inflated surrogate regression model. Extensive simulations show that the proposed estimator performs well in terms of bias correction. These methods are applied to a physical activity intervention study.

Suggested Citation

  • Ching-Yun Wang & Jean de Dieu Tapsoba & Catherine Duggan & Anne McTiernan, 2024. "Generalized Linear Models with Covariate Measurement Error and Zero-Inflated Surrogates," Mathematics, MDPI, vol. 12(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:309-:d:1321211
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    References listed on IDEAS

    as
    1. C. Y. Wang & Naisyin Wang & Suojin Wang, 2000. "Regression Analysis When Covariates Are Regression Parameters of a Random Effects Model for Observed Longitudinal Measurements," Biometrics, The International Biometric Society, vol. 56(2), pages 487-495, June.
    2. Ching‐Yun Wang & Xiao Song, 2021. "Semiparametric regression calibration for general hazard models in survival analysis with covariate measurement error; surprising performance under linear hazard," Biometrics, The International Biometric Society, vol. 77(2), pages 561-572, June.
    3. Victor Kipnis & Douglas Midthune & Dennis W. Buckman & Kevin W. Dodd & Patricia M. Guenther & Susan M. Krebs-Smith & Amy F. Subar & Janet A. Tooze & Raymond J. Carroll & Laurence S. Freedman, 2009. "Modeling Data with Excess Zeros and Measurement Error: Application to Evaluating Relationships between Episodically Consumed Foods and Health Outcomes," Biometrics, The International Biometric Society, vol. 65(4), pages 1003-1010, December.
    4. C. Y. Wang & Yijian Huang & Edward C. Chao & Marjorie K. Jeffcoat, 2008. "Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 64(1), pages 85-95, March.
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