Semiparametric Regression Modeling for Longitudinal Data

纵向数据的半参数回归建模

• 批准号: 0304922
• 负责人: Yanqing Sun
• 金额: $ 14.53万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0304922&HistoricalAwards=false
• 关键词: Semiparametric; Regression; Modeling; Longitudinal; Data

In this proposal, the investigator proposes a semiparametric method for joint modeling of longitudinal responses and measurement times. The semiparametric varying-coefficient regression model postulates that the influences of some covariates vary nonparametrically with time while the effects of the remaining covariates follow certain parametric functions of time. The measurement times of responses are modeled by Cox's proportional model for conditional mean rate. The modeling by Aalen's additive model will also be studied. The investigator employs the approach of Lin and Ying (2001) to estimate the nonparametric regression coefficients. The parametric components are estimated by a weighted least squares method. More efficient smoothing techniques are used for response processes. The investigator proposes a data-driven bandwidth selection criterion based on the sum of squares of residuals. This selection method will be further studied and tested empirically through simulations. Constructions of confidence bands for the parametric components, nonparametric regression coefficient functions and their cumulatives are proposed. Goodness-of-fit test procedures are proposed to check whether some regression coefficient functions follow certain parametric forms by comparing the nonparametric estimators and the corresponding estimators of the cumulative regression coefficient functions under the null hypothesis. A preliminary simulation study demonstrates that the proposed estimation and hypothesis testing methods are promising. The investigator will study the asymptotic properties, such as consistency, weak convergence and consistency of the estimators of the asymptotic variances, for all the proposed estimators. Finite sample properties of the proposed estimation methods and goodness-of-fit tests will be evaluated through extensive numerical simulation studies. The investigator also proposes to study related problems in optimal choice of the weight function, optimal design of measurement times and informative censoring.The investigator proposes to seek statistical models with a physical or biological basis and biologically interpretable parameters and to develop statistically efficient methods to better understand linear or nonlinear behavior of response process. The proposed semiparametric varying-coefficient regression model allows for additional flexibility to explore how covariate effects change over time and provides a base to test whether simpler models with scientific relevance hold. The proposed research when carried out would help to enrich a collection of statistical tools which have important impact on the analysis of longitudinal data. Giudelines for practical applications will be developed. The methods will be used to analyze longitudinal data in AIDS related medical research to develop more effective treatments and to other real examples in medical studies. The research of the problems proposed here will also generate many research topics at different levels suitable for graduate and undergraduate studies, therefore promotes involvement of students in current scientific research.

在这个建议中，研究者提出了一种半参数方法，用于纵向响应和测量时间的联合建模。半参数变系数回归模型假设部分协变量的影响随时间非参数变化，其余协变量的影响随时间的参数函数变化。响应的测量次数采用条件平均速率的Cox比例模型建模。本文还将研究Aalen加性模型的建模方法。研究者采用Lin和Ying（2001）的方法估计非参数回归系数。采用加权最小二乘法对参数分量进行估计。更有效的平滑技术用于响应过程。研究者提出了一种基于残差平方和的数据驱动带宽选择准则。该选择方法将通过仿真进一步研究和实证检验。提出了参数分量、非参数回归系数函数及其累积量的置信带构造。提出了拟合优度检验程序，通过比较零假设下累积回归系数函数的非参数估计量和相应的估计量来检验某些回归系数函数是否遵循一定的参数形式。初步的仿真研究表明，所提出的估计和假设检验方法是有希望的。研究者将研究渐近性质，如渐近方差估计的相合性，弱收敛性和相合性，对于所有提出的估计。所提出的估计方法的有限样本性质和拟合优度检验将通过广泛的数值模拟研究进行评估。研究了权重函数的优化选择、测量次数的优化设计和信息筛选等相关问题。研究者建议寻求具有物理或生物基础和生物可解释参数的统计模型，并开发统计有效的方法来更好地理解响应过程的线性或非线性行为。提出的半参数变系数回归模型允许额外的灵活性来探索协变量效应如何随时间变化，并提供一个基础来测试是否具有科学相关性的更简单的模型。拟议的研究一旦进行，将有助于丰富对纵向数据分析有重要影响的统计工具集合。将制定实际应用的准则。这些方法将用于分析艾滋病相关医学研究中的纵向数据，以开发更有效的治疗方法，并用于医学研究中的其他实际例子。本文提出的问题的研究也将产生许多适合研究生和本科生学习的不同层次的研究课题，从而促进学生参与当前的科学研究。