Generalized Semiparametric Regression with Longitudinal Data

本文探讨了纵向数据的广义半参数回归模型。GSRM模型允许一些协变量的影响是恒定的，而另一些协变量的影响是时变的。该模型是横断面数据广义线性模型的推广。可以选择不同的链接函数来为纵向数据提供丰富的模型系列。分类的和连续的纵向响应都可以用适当选择的链接函数来建模。纵向数据的统计分析通常涉及自初始事件(时间来源)以来对临床相关纵向生物标记物的治疗效果进行建模。提出的研究包括两个具有重要应用价值的部分。在第一部分中，研究人员建议在观察到所有受试者的时间来源时检验GSRM模型。在第二部分，确切的时间来源可能是未知的。GSRM模型为模型的建立和变量的选择提供了一个大的平台。研究人员提出了一种采样调整轮廓局部线性估计方法。模型的非参数分量用局部线性估计方程估计，参数分量用加权轮廓估计函数估计。在确切时间来源可能未知的情况下，将研究基于丢失数据原理的EM过程。该方法将自动调整采样时间的异质性，允许采样策略依赖于过去的采样历史以及可能的时间相关协变量，而无需专门建模这种相关性。许多重要的问题将被研究，包括方差估计，协变量效应的假设检验，权函数和带宽的选择，以及拟合优度。还将研究链路函数的估计和假设检验。拟议的研究将应用于艾滋病临床试验和疫苗效力试验的真实例子。纵向数据在医学和公共卫生研究中很常见。纵向数据的统计分析通常涉及自初始事件以来对临床相关纵向生物标记物的治疗效果进行建模。在初始事件时刻已知和初始事件时刻可能被删失的两种情况下，研究了纵向数据的广义半参数回归模型的统一方法。这项拟议的研究是由艾滋病临床试验和艾滋病毒疫苗效力试验中的实际问题推动的。通过追求提案中概述的方向，可以在建立生物学上可解释的模型和开发统计上有效的方法来处理纵向数据的复杂性方面取得重大进展。拟议的研究将有助于克服当今世界面临的医疗和公共卫生挑战。

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.