Model Building--Marginal Regression with Dependent Data

相依反应数据在生物医学研究中很常见。一个典型的例子是纵向数据。在梁和泽格(1986)的开创性工作之后，边际回归及其相关的广义估计方程(GEE)方法在分析这些数据方面变得越来越重要。然而，尽管已有大量文献针对独立数据建立模型，但对包括模型检验和模型选择在内的模型建立问题的研究相对较少。由于统计分析得出的任何科学结论都取决于所使用的统计模型，而且由于先验知识有限，对于正确的模型总是存在一些不确定性，因此建立模型的重要性和必要性是显而易见的。本研究的主题是相依数据的边际回归建模技术。具体地说，首先，要调查正式的拟合优度测试。其次，提出了基于边际模型图和广义加性模型图的图模型检验方法。第三，研究如何调整小样本的统计推断，因为通常使用的大样本结果可能不适用。上述建模技术将通过仿真和使用真实数据进行评估。所有技术都将以常用的统计语言S+实施，并向从业人员免费提供。

Dependent response data are common in biomedical studies. One typical example is longitudinal data. Subsequent to the seminal work by Liang and Zeger (1986), marginal regression and its associated generalized estimating equations (GEE) method have become increasingly important in analyzing such data. However, model building, including model checking and model selection, have been relatively neglected for GEE, although there is a large literature in model building for independent data. Since any scientific conclusions drawn from statistical analysis crucially depend on the statistical model being used, and there is always some uncertainty with regard to the correct model due to limited prior knowledge, the importance and necessity of model building are apparent. The subject of this proposed research is model building techniques in marginal regression for dependent data. Specifically, first, formal goodness-of-fit tests are to be investigated. Second, I propose graphical model checking using marginal model plots and the generalized additive model plots. Third, I investigate how to adjust statistical inference with small samples since the commonly used large sample results may not be applicable. The above model building techniques will be evaluated by simulation and using real data. All the techniques will be implemented in the commonly used statistical language S-Plus and made freely available to practitioners.