Estimation Methods for Nonlinear ODE Models in AIDS Research

描述（由申请人提供）：艾滋病研究中的非线性常微分方程模型的估计方法摘要在这个项目中，我们提出了可识别的方法和统计估计方法的常微分方程（ODE）模型，以支持艾滋病毒/艾滋病的研究。尽管在艾滋病的流行病学和临床研究中已经发展了许多数学模型和统计方法，但对于艾滋病研究中广泛使用的非线性常微分方程模型，却很少有可辨识性和估计方法。当非线性常微分方程没有封闭解时，估计常微分方程模型中的参数是一个挑战。很少有正式的统计估计方法可用于ODE模型。为了填补这一空白，在这个项目中，我们提出了新的统计估计方法的非线性常微分方程模型来自艾滋病毒/艾滋病的研究。具体而言，我们提出了四个具体目标：1）整合不同研究领域的参数可辨识性技术，解决常微分方程（ODE）模型的可辨识性问题：2）发展新的常微分方程模型的统计估计方法，研究估计量的渐近性质和有限样本性质; 3）通过基于理论观点、有限样本性质和计算效率将新方法与现有方法进行比较来评估新方法，并利用病毒感染免疫反应研究的实例和数据对所提出的方法进行了验证; 4）开发高效的计算算法和用户友好的软件包来实现所提出的方法。我们提出了几种新的估计方法，包括基于筛子的方法估计常数和时变参数，惩罚核估计方法和基于数值算法的回归方法的常微分方程模型。从统计学的角度来看，常微分方程模型的可辨识性分析也是相对创新的。为了实现我们的目标，我们组建了一支强大的跨学科研究团队，由统计学家，计算科学家和软件开发人员组成，他们具有该项目所需的专业知识。微分方程模型通常是根据生物医学系统的机理建立的。模型参数通常具有有意义的生物学解释，并且其本身是重要的。从实验数据中可靠地估计这些模型参数是非常重要的。估计结果可能有助于HIV/AIDS研究人员更好地了解HIV感染的生物学机制和发病机制，这可能会导致新的科学发现，并为制定治疗策略提供指导。

DESCRIPTION (provided by applicant): 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.