Statistical Inferences for Deterministic Dynamic Models Containing both Constant and Time-varying Parameters with Applications to Infectious Diseases

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。确定性动力学模型在模拟人类免疫缺陷病毒(HIV)动力学、药代动力学/药效学分析、肿瘤细胞动力学和遗传网络方面已经变得非常流行。现有的从噪声数据中估计确定性动态模型中未知动态参数的统计方法需要大量的计算。这项研究为同时包含常量和时变参数的确定性动态模型发展了新的有效的统计估计、推断方法和计算算法。研究了三种估计方法，包括核平滑、离散化和样条化方法，以解决确定性动态模型中具有挑战性的统计问题。研究人员主要关注以下三个目标：(I)半参数和非参数方法在时变系数部分线性动态模型和时变系数动态模型中的方法和理论的发展；(Ii)通过这些估计技术建立HIV/细胞动力学模型；(Iii)部分线性动态系统和时变系数动态系统中有效的半参数和非参数估计和算法。渐近理论和仿真研究正在进行中，以研究所提出的方法、假设检验过程和自适应带宽选择的性质。新程序正在应用于艾滋病临床数据。除了开发一些创新的半参数和非参数技术和有用的确定性动态模型外，这项研究还为非参数推理提供了新的见解。正在开发的新技术除了直接应用于传染病外，在统计学上也很有趣，并将对统计思维、方法发展和理论研究产生重大影响。对传染病的动态系统进行建模对于理解感染的发病机制和为制定治疗策略提供指导是至关重要的。这不仅是研究人员的关切，也是制定公共卫生计划的决策者的关切。研究人员的研究为生物医学研究人员和从业者提供了有价值的建模诊断工具，以通过动态模型提高分析和解释临床数据的准确性。正在开发的新的统计动态模型和估计技术也将适用于工程问题和计量经济学。这项研究的教育部分扩大了学生学习现代统计建模技术及其在传染病中的应用的机会。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Deterministic dynamic models have become very popular in modeling human immunodeficiency virus (HIV) dynamics, pharmacokinetic/pharmacodynamic analysis, tumor cell kinetics, and genetic networks. Current statistical methods for estimating unknown dynamic parameters in deterministic dynamic models from noisy data require intensive computation. This research develops new and efficient statistical estimation, inference methods and computational algorithms for deterministic dynamic models containing both constant and time-varying parameters. Three estimation procedures including kernel smoothing, discretization and spline methods are being investigated to solve challenging statistical problems in deterministic dynamic models. The investigator is focusing on the following three aims: (i) methodological and theoretical development of the semiparametric and nonparametric approach to the time-varying coefficient partially linear dynamic model and the time-varying coefficient dynamic model; (ii) modeling of HIV/Cell dynamics via these estimation techniques; (iii) efficient semiparametric and nonparametric estimation and algorithms in the partially linear dynamic system and the time-varying coefficient dynamic system. Asymptotic theory and simulation studies are being implemented to investigate the properties of the proposed methods, hypothesis testing procedures and adaptive bandwidth selection. The new procedures are being applied to AIDS clinical data. In addition to developing a number of innovative semiparametric and nonparametric techniques and useful deterministic dynamic models, this research also provides new insights into nonparametric inference. The new techniques being developed are statistically interesting beyond their direct applications to infectious diseases and will have significant impact on statistical thinking, methodological development, and theoretical studies. Modeling dynamic systems for infectious diseases is critical for understanding pathogenesis of infection and providing guidance in the development of treatment strategies. It is of concern not only to researchers but also to decision makers developing plans for public health. The investigator's research provides valuable modeling diagnostic tools for biomedical researchers and practitioners to analyze and interpret clinical data with improved accuracy via dynamic models. The new statistical dynamic models and estimation techniques being developed will also be applicable to problems in engineering and for econometrics. The educational component of this research expands opportunities for students to learn about modern statistical modeling techniques and their applications in infectious diseases.