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: 8207860
• 负责人: Hulin Wu
• 金额: $ 34.41万
• 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/8207860
• 关键词: AIDS/HIV problem; Accounting; Acquired Immunodeficiency Syndrome; Address; Adherence; Adverse effects; Algorithms; Behavior; Biological; Clinical; Clinical Research; Communities; Computational algorithm; Computer software; Data; Detection; Development; Discipline; Disease; Drug Kinetics; Drug resistance; Engineering; Epidemic; Epidemiologic Studies; 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(申请人提供)：艾滋病研究中非线性常微分方程模型的估计方法在本项目中，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HIV/AIDS研究。虽然已有许多数学模型和统计方法被用于艾滋病研究中的流行病学和临床研究，但对于在艾滋病研究中广泛应用的非线性常微分方程组模型的可辨识性和估计方法却很少。当非线性常微分方程组没有闭合形式的解时，常微分方程组的参数估计是具有挑战性的。很少有正式的统计估计方法可用于常微分方程模型。为了填补这一空白，在这个项目中，我们提出了来自HIV/AIDS研究的非线性常微分方程模型的新的统计估计方法。具体地说，我们提出了四个具体目标：1)集成不同研究领域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)发展新的常微分方程模型统计估计方法，并研究估值器的渐近性质和有限样本性质；3)从理论角度、有限样本性质和计算效率方面与现有方法进行比较，并使用病毒感染免疫反应研究的实例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。我们提出了几种新的估计方法，包括基于筛子的常量和时变参数估计方法、惩罚核估计方法和基于数值算法的回归方法。从统计学的角度来看，对常微分方程模型的模型可识别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，由具有该项目所需专业知识的统计学家、计算科学家和软件开发人员组成。微分方程模型通常是基于生物医学系统的机理而建立的。模型参数通常具有有意义的生物学解释，它们本身就很重要。从实验数据中可靠地估计这些模型参数是非常重要的。评估结果可能有助于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：为艾滋病毒动态和艾滋病流行的ODE模型开发的统计方法允许可靠地估计艾滋病毒动态和艾滋病流行的未知动力学或流行病参数。这些参数和ODE模型可以帮助HIV/AIDS研究者更好地了解HIV感染的生物学机制和发病机制，这可能导致新的科学发现，并为制定治疗策略提供指导。