Estimation Methods for Nonlinear ODE Models in AIDS Research

艾滋病研究中非线性 ODE 模型的估计方法

• 批准号: 7839355
• 负责人: Hulin Wu
• 金额: $ 34.23万
• 依托单位: UNIVERSITY OF ROCHESTER
• 依托单位国家: 美国
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-01-15 至 2013-12-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/7839355
• 关键词: AIDS/HIV problem; Accounting; Acquired Immunodeficiency Syndrome; Address; Adherence; Adverse effects; Algorithms; Arts; Behavior; Biological; Clinical; Clinical Data; Clinical Research; Communities; Computational algorithm; Computer software; Data; Detection; Development; Discipline; Disease; Drug Kinetics; Drug resistance; Engineering; Epidemic; Epidemiology; Equation; Goals; Guidelines; HIV; HIV Infections; Highly Active Antiretroviral Therapy; Immune response; Interdisciplinary Study; Intervention; Kinetics; Lead; Least-Squares Analysis; Life; Measurement; Methods; Modeling; Outcome; Pathogenesis; Patients; Performance; Pharmaceutical Preparations; Plasma; Preventive Intervention; Property; Public Health; RNA; Regimen; Research; Research Personnel; Rights; Sampling; Scientist; Solutions; Statistical Methods; Study models; Surrogate Markers; System; Techniques; Testing; Time; Vaccine Therapy; Viral Load result; Virus Diseases; abstracting; base; cost; data modeling; improved; innovation; mathematical model; novel; novel strategies; pandemic disease; public health relevance; research study; simulation; theories; transmission process; treatment strategy; user friendly software; user-friendly; web site

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. PUBLIC HEALTH RELEVANCE: 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.

描述（由申请人提供）：在本项目的AIDS研究摘要中的非线性ODE模型的估计方法我们提出了普通微分方程（ODE）模型的可识别性方法和统计估计方法，以支持HIV/AIDS研究。尽管已经开发了许多数学模型和统计方法用于AIDS研究中的流行病学和临床研究，但是对于非线性ODE模型而言，很少开发出很少的可识别性和估计方法，这些模型被广泛用于AIDS研究。当没有封闭形式的解决方案可用于非线性ODE时，估算ODE模型中的参数是一项挑战。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，在此项目中，我们提出了针对来自艾滋病毒/艾滋病研究的非线性ODE模型的新型统计估计方法。特别是，我们提出了四个具体目标：1）整合来自不同研究学科的参数可识别性技术，以解决普通微分方程（ODE）模型的可识别性问题； 2）为ODE模型开发新的统计估计方法，并研究估计器的渐近样本和有限样本的特性； 3）通过根据理论观点，有限的样本属性和计算效率将新方法与现有方法进行比较，并使用免疫反应对病毒感染的示例和数据进行测试和验证； 4）开发有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，包括基于筛子的方法，用于估计恒定和时变参数，惩罚的内核估计方法以及基于数值算法的ODE模型的回归方法。从统计的角度来看，ODE模型的模型可识别性分析也相对创新。为了实现我们的目标，我们组成了一个强大的跨学科研究团队，该研究团队由统计学家，计算科学家和软件开发人员组成，并为该项目提供必要的专业知识。微分方程模型通常是根据生物医学系统机制开发的。模型参数通常具有有意义的生物学解释，并且在其自身权利中很重要。从实验数据可靠地估算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理，这可能导致新的科学发现，并为制定治疗策略提供指导。 公共卫生相关性：HIV动力学和AIDS流行病的ODE模型的开发统计方法允许可靠地估计HIV动力学和AIDS流行病的未知动力学或流行参数。这些参数和ODE模型可用于帮助艾滋病毒/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理，这可能导致新的科学发现，并为制定治疗策略提供指导。