Estimation Methods for Nonlinear ODE Models in AIDS Research

摘要在本项目中，我们提出了常微分方程（ODE）模型的可辨识性方法和统计估计方法，以支持艾滋病研究。在艾滋病的流行病学和临床研究中，虽然已经建立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，却很少有可识别和估计的方法。对于非线性ODE，在没有封闭解的情况下，如何估计ODE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，在本项目中，我们提出了基于HIV/AIDS研究的非线性ODE模型的新的统计估计方法。具体而言，我们提出了四个具体目标：1)整合不同研究学科的参数可辨识性技术来解决常微分方程（ODE）模型的可辨识性问题；2)开发新的ODE模型统计估计方法，研究估计量的渐近和有限样本性质；3)从理论角度、有限样本性质和计算效率等方面对新方法进行评价，与现有方法进行比较，并利用病毒感染免疫应答研究的实例和数据对新方法进行验证；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，包括基于筛网的估计常数和时变参数的方法，惩罚核估计方法和基于数值算法的回归方法。从统计学角度来看，ODE模型的模型可识别性分析也是比较创新的。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，他们具备该项目的必要专业知识。微分方程模型通常是基于生物医学系统的机制而建立的。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。从实验数据中可靠地估计这些模型参数是非常重要的。这些估计结果可能有助于HIV/AIDS研究者更好地了解HIV感染的生物学机制和发病机制，从而可能导致新的科学发现，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.