Estimation Methods for Nonlinear ODE Models in AIDS Research Abstract In this project we propose identifiability methods and statistical estimation methods for ordinary differential equation (ODE) models to support HIV/AIDS research. Although many mathematical models and statistical methods have been developed for epidemiological and clinical studies in AIDS research, very few identifiability and estimation methods are developed for nonlinear ODE models which are widely used in AIDS research. It is challenging to estimate the parameters in the ODE models when no closed-form solution is available for nonlinear ODEs. Very few formal statistical estimation methods are available for ODE models. To fill this gap, in this project we propose novel statistical estimation methods for nonlinear ODE models derived from HIV/AIDS research. In particular, we propose four specific aims: 1) Integrate parameter identifiability techniques from different research disciplines to address the identifiability issues for ordinary differential equation (ODE) models;2) Develop novel statistical estimation methods for ODE models and study the asymptotic and finite-sample properties of the estimators;3) Evaluate the new methods by comparing them to the existing methods based on theoretical perspective, finite sample properties and computational efficiency, and test and validate the proposed methods using the examples and data from studies of immune response to viral infections;4) Develop efficient computational algorithms and user-friendly software packages to implement the proposed methods. We propose several novel estimation methods including sieve-based methods for estimating both constant and time-varying parameters, penalized kernel estimation methods and numerical algorithm-based regression approaches for ODE models. The model identifiability analysis for ODE models is also relatively innovative from statistical perspective. To achieve our aims, we have formed a strong interdisciplinary research team consisting of statisticians, computational scientists and software developers with necessary expertise for this project. The differential equation models are often developed based on mechanisms of biomedical systems. The model parameters usually have meaningful biological interpretations and are important in their own rights. It is very important to reliably estimate these model parameters from experimental data. The estimation results may help HIV/AIDS investigators better understand the biological mechanisms and pathogenesis of HIV infection, which may lead to novel scientific findings and provide guidance to develop treatment strategies.
The developed statistical methods for ODE models of HIV dynamics and AIDS epidemics allow to reliably estimate the unknown kinetic or epidemic parameters of HIV dynamics and AIDS epidemics. These parameters and the ODE models can be used to help HIV/AIDS investigators better understand the biological mechanisms and pathogenesis of HIV infection, which may lead to novel scientific findings and provide guidance to develop treatment strategies.
|Chen, Iris; Kelkar, Yogeshwar D; Gu, Yu et al. (2017) High-dimensional linear state space models for dynamic microbial interaction networks. PLoS One 12:e0187822|
|Sun, Xiaodian; Hu, Fang; Wu, Shuang et al. (2016) Controllability and stability analysis of large transcriptomic dynamic systems for host response to influenza infection in human. Infect Dis Model 1:52-70|
|Carey, Michelle; Wu, Shuang; Gan, Guojun et al. (2016) Correlation-based iterative clustering methods for time course data: The identification of temporal gene response modules for influenza infection in humans. Infect Dis Model 1:28-39|
|Qiu, Xing; Wu, Shuang; Hilchey, Shannon P et al. (2015) Diversity in Compartmental Dynamics of Gene Regulatory Networks: The Immune Response in Primary Influenza A Infection in Mice. PLoS One 10:e0138110|
|Wu, Hulin; Miao, Hongyu; Xue, Hongqi et al. (2015) Quantifying Immune Response to Influenza Virus Infection via Multivariate Nonlinear ODE Models with Partially Observed State Variables and Time-Varying Parameters. Stat Biosci 7:147-166|
|Zand, Martin S; Wang, Jiong; Hilchey, Shannon (2015) Graphical Representation of Proximity Measures for Multidimensional Data: Classical and Metric Multidimensional Scaling. Math J 17:|
|Ding, A Adam; Wu, Hulin (2014) Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression. Stat Sin 24:1613-1631|
|Qiu, Xing; Hu, Rui; Wu, Zhixin (2014) Evaluation of bias-variance trade-off for commonly used post-summarizing normalization procedures in large-scale gene expression studies. PLoS One 9:e99380|
|Linel, Patrice; Wu, Shuang; Deng, Nan et al. (2014) Dynamic transcriptional signatures and network responses for clinical symptoms in influenza-infected human subjects using systems biology approaches. J Pharmacokinet Pharmacodyn 41:509-21|
|Miao, Hongyu; Wu, Hulin; Xue, Hongqi (2014) Generalized Ordinary Differential Equation Models. J Am Stat Assoc 109:1672-1682|
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