Generalized Semiparametric Regression with Longitudinal Data

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This proposal explores the generalized semiparametric regression model (GSRM) for longitudinal data. The GSRM model allows the effects of some covariates to be constant and others to be time-varying. The model is an extension of the generalized linear model for cross-sectional data. Different link functions can be selected to provide a rich family of models for longitudinal data. Both categorical and continuous longitudinal responses can be modeled with appropriately chosen link functions. Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). The proposed research includes two parts with important applications. In the first part, the investigator proposes to examine the GSRM model when the time origin is observed for all subjects. In the second part, the exact time origin may be unknown. The GSRM model provides a big platform for model building and variable selection. The investigator proposes a sampling adjusted profile local linear estimation approach. The nonparametric components of the model will be estimated using the local linear estimating equations and the parametric components are to be estimated through weighted profile estimating functions. In the situation where the exact time origin may be unknown, an EM procedure based on the missing data principle will be investigated. The proposed method will automatically adjust for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically modeling such dependence. Many important issues will be investigated, including variance estimation, hypothesis testing of covariate effects, weight function and bandwidth selections, and goodness of fit. The estimation and hypothesis testing of the link function will also be investigated. The proposed research will be applied to real examples from AIDS clinical trials and vaccine efficacy trials.Longitudinal data are common in medical and public health research. Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event. The proposed research investigates a unified approach to the generalized semiparametric regression model for longitudinal data for both the situations where the time of the initial event is known and where the exact time of the initial event may be censored. The proposed research is motivated by real problems in AIDS clinical trials and HIV vaccine efficacy trials. By pursuing the directions outlined in the proposal, significant progress could be made in building biologically interpretable models and in developing statistically efficient methods to deal with the complexity of longitudinal data. The proposed research will contribute to efforts to overcome the medical and public health challenges facing the world today.