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.
