Model Building--Marginal Regression with Dependent Data

依赖性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Liang和Zeger（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）方法在分析此类数据方面变得越来越重要。然而，尽管有大量关于独立数据模型构建的文献，但对于GEE来说，包括模型检查和模型选择在内的模型构建相对被忽视。由于从统计分析中得出的任何科学结论都至关重要地取决于所使用的统计模型，并且由于有限的先验知识，正确的模型总是存在一些不确定性，因此模型构建的重要性和必要性是显而易见的。本研究的主题是依赖数据的边际回归模型构建技术。具体来说，首先要研究正式的拟合优度检验。其次，提出了利用边际模型图和广义加性模型图进行图形模型检验的方法。第三，我研究了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。以上模型构建技术将通过仿真和使用实际数据进行评估。所有技术将以常用的统计语言S-Plus实施，并免费提供给从业人员。

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.