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Bayesian multi‐level mixed‐effects model for influenza dynamics

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  • Hanwen Huang

Abstract

Influenza A viruses (IAV) are the only influenza viruses known to cause flu pandemics. Understanding the evolution of different sub‐types of IAV on their natural hosts is important for preventing and controlling the virus. We propose a mechanism‐based Bayesian multi‐level mixed‐effects model for characterising influenza viral dynamics, described by a set of ordinary differential equations (ODE). Both strain‐specific and subject‐specific random effects are included for the ODE parameters. Our models can characterise the common features in the population while taking into account the variations among individuals. The random effects selection is conducted at strain level through re‐parameterising the covariance parameters of the corresponding random effect distribution. Our method does not need to solve ODE directly. We demonstrate that the posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and a real data from a study relating virus load estimates from influenza infections in ducks.

Suggested Citation

  • Hanwen Huang, 2022. "Bayesian multi‐level mixed‐effects model for influenza dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1978-1995, November.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:5:p:1978-1995
    DOI: 10.1111/rssc.12603
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    References listed on IDEAS

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    1. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
    2. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2015. "On the selection of ordinary differential equation models with application to predator-prey dynamical models," Biometrics, The International Biometric Society, vol. 71(1), pages 131-138, March.
    3. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    4. Yangxin Huang & Dacheng Liu & Hulin Wu, 2006. "Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System," Biometrics, The International Biometric Society, vol. 62(2), pages 413-423, June.
    5. Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    6. Yangxin Huang & Hulin Wu, 2006. "A Bayesian approach for estimating antiviral efficacy in HIV dynamic models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(2), pages 155-174.
    7. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
    8. Hongyu Miao & Carrie Dykes & Lisa M. Demeter & Hulin Wu, 2009. "Differential Equation Modeling of HIV Viral Fitness Experiments: Model Identification, Model Selection, and Multimodel Inference," Biometrics, The International Biometric Society, vol. 65(1), pages 292-300, March.
    9. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.
    10. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    11. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
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