Generalized Semiparametric Varying-Coefficient Models for Longitudinal Data

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This research focuses on the development of new theory, methods, and computational algorithms for analysis of longitudinal data, motivated by problems in AIDS clinical trials and HIV vaccine efficacy trials. The methods will enhance our understanding of the benefits of treatment switching in an AIDS clinical trial, and how HIV vaccination modifies the disease progression in HIV infected individuals over time. The broader impacts of the research include the development of statistical theory for longitudinal data, applications to medicine, public health and the social sciences, advancing statistical learning and training for undergraduate and graduate students, and promoting the participation of women in scientific research. The statistical models and methods will provide a broad platform for investigating complex covariate effects including linear and nonlinear effects, time-varying effects, and nonlinear interactions among the covariates.The project investigates a class of generalized semiparametric varying-coefficient models for longitudinal data. These models can be used to analyze both categorical and continuous longitudinal responses through a link function, and flexibly model three types of covariate effects: constant effects, time-varying effects, and covariate-varying effects. Part I studies the generalized semiparametric varying-coefficients model (GSVCM), where the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters, and Part II investigates the GSVCM model, where both the covariate-varying effects and the time-varying effects are unspecified functions. In Part III, the generalized semiparametric single-index varying-coefficients model (single-index GSVCM) is investigated. The model is more powerful for assessing interactions among multiple covariates. Estimation procedures for the model based on multivariate local linear smoothing and generalized weighted least squares are proposed. Large sample theory will be developed for the proposed estimation and hypothesis testing procedures. Other important problems that will be investigated include variance estimation, hypothesis testing of covariate effects, weight function and bandwidth selection, goodness-of-fit diagnostics, and estimation and hypothesis testing of link functions. Computational algorithms will be developed to facilitate the applications of the proposed methods to real data from AIDS clinical trials and vaccine efficacy trials. By pursuing the directions outlined in the project, significant progress may be made in building biologically interpretable models, and in developing statistically efficient methods to handle the complexity of longitudinal data.