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An approximate method for generalized linear and nonlinear mixed effects models with a mechanistic nonlinear covariate measurement error model

Author

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  • Hongbin Zhang

    (City University of New York)

  • Lang Wu

    (University of British Columbia)

Abstract

The literature on measurement error for time-dependent covariates has mostly focused on empirical models, such as linear mixed effects models. Motivated by an AIDS study, we propose a joint modeling method in which a mechanistic nonlinear model is used to address the time-varying covariate measurement error for a longitudinal outcome that can be either discrete such as binary and count or continuous. We implement an inference procedure that uses first-order Taylor approximation to linearize both the covariate model and the response model. We study the asymptotic properties of the joint model based estimator and provide proof of consistency and normality. We then evaluate the performance of estimation in finite sample size scenario through simulation. Finally, we apply the new method to real data in an HIV/AIDS study.

Suggested Citation

  • Hongbin Zhang & Lang Wu, 2019. "An approximate method for generalized linear and nonlinear mixed effects models with a mechanistic nonlinear covariate measurement error model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 471-499, May.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:4:d:10.1007_s00184-018-0690-z
    DOI: 10.1007/s00184-018-0690-z
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    References listed on IDEAS

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    1. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    2. Vonesh E. F. & Wang H. & Nie L. & Majumdar D., 2002. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 271-283, March.
    3. Liyong Fu & Yuancai Lei & Ram P. Sharma & Shouzheng Tang, 2013. "Parameter estimation of nonlinear mixed-effects models using first-order conditional linearization and the EM algorithm," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 252-265, February.
    4. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    5. Hulin Wu & A. Adam Ding, 1999. "Population HIV-1 Dynamics In Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials," Biometrics, The International Biometric Society, vol. 55(2), pages 410-418, June.
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    Cited by:

    1. Hongbin Zhang, 2023. "Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies," Mathematics, MDPI, vol. 11(10), pages 1-14, May.

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