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）资助的。确定性动力学模型在人类免疫缺陷病毒（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等领域的建模中已变得非常流行。目前的统计方法估计未知的动态参数确定性的动态模型从噪声数据需要密集的计算。本研究开发了新的和有效的统计估计，推理方法和计算算法的确定性动态模型包含常数和时变参数。三个估计程序，包括核平滑，离散化和样条方法正在研究解决具有挑战性的统计问题，在确定性的动态模型。本研究的主要目的是：（i）时变系数部分线性动态模型和时变系数动态模型的半参数和非参数方法的方法和理论发展;（ii）通过这些估计技术建立HIV/细胞动态模型;（iii）部分线性动态系统和时变系数动态系统的有效半参数和非参数估计及算法。渐近理论和仿真研究正在实施调查所提出的方法，假设检验程序和自适应带宽选择的属性。新的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，这项研究还提供了新的见解非参数推断。正在开发的新技术在统计学上是有趣的，超出了它们对传染病的直接应用，并将对统计思想，方法发展和理论研究产生重大影响。 传染病动力学系统的建模对于理解感染的发病机理和为治疗策略的发展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人员提供了有价值的建模诊断工具，通过动态模型分析和解释临床数据，提高准确性。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和计量经济学中的问题。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.