Estimation Methods for Nonlinear ODE Models in AIDS Research

描述（由申请人提供）：艾滋病研究中非线性 ODE 模型的估计方法 摘要 在这个项目中，我们提出了常微分方程 (ODE) 模型的可识别性方法和统计估计方法，以支持 HIV/AIDS 研究。尽管针对艾滋病研究中的流行病学和临床研究已经开发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ODE模型，开发出的可辨识和估计方法却很少。当非线性 ODE 没有可用的封闭式解时，估计 ODE 模型中的参数是一项挑战。可用于 ODE 模型的正式统计估计方法很少。为了填补这一空白，在本项目中，我们提出了源自 HIV/AIDS 研究的非线性 ODE 模型的新颖统计估计方法。特别是，我们提出了四个具体目标：1）集成来自不同研究学科的参数可辨识性技术，以解决常微分方程（ODE）模型的可辨识性问题； 2）为ODE模型开发新颖的统计估计方法，并研究估计量的渐近和有限样本特性； 3）基于理论视角、有限样本特性和计算效率，通过将新方法与现有方法进行比较来评估新方法，并使用病毒感染免疫反应研究的例子和数据来测试和验证所提出的方法； 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。我们提出了几种新颖的估计方法，包括用于估计常数和时变参数的基于筛子的方法、惩罚核估计方法和用于 ODE 模型的基于数值算法的回归方法。 ODE模型的模型可辨识性分析从统计角度来看也比较有创新性。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，他们拥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制开发的。模型参数通常具有有意义的生物学解释，并且本身就很重要。根据实验数据可靠地估计这些模型参数非常重要。估计结果可能有助于艾滋病毒/艾滋病研究人员更好地了解艾滋病毒感染的生物学机制和发病机制，这可能会带来新的科学发现，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.