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Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies

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  • Hongbin Zhang

    (Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY 40536, USA)

Abstract

We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm’s convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2317-:d:1148239
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    References listed on IDEAS

    as
    1. 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.
    2. Fengkai Yang, 2018. "A Stochastic EM Algorithm for Quantile and Censored Quantile Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 555-582, August.
    3. Samson, Adeline & Lavielle, Marc & Mentre, France, 2006. "Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1562-1574, December.
    4. Charlotte Baey & Samis Trevezas & Paul-Henry Cournède, 2016. "A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(6), pages 1643-1669, March.
    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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