Exact Regression Software for Correlated Categorical Data

 描述（由申请人提供）：拟议研究的总体目标是为相关分类数据的小样本或稀疏样本开发实用的建模工具，包括精确的回归程序。这样的结果在生物医学研究中很常见，特别是在遗传学、眼科学和畸形学等领域。人们可能会遇到相关的分类数据，无论是在一个人身上测量多个结果，还是在几个有共同遗传或环境暴露的不同个体身上。已经开发了大量的方法来分析相关的分类结果，这些方法通常依赖于大样本分布假设（例如，近似正态性）来证明他们的推论。当面对分类数据的小样本或稀疏样本时，研究者几乎没有可行的分析选择，并且没有一个允许关于估计的精确推断。我们提出的工作将填补这一空白，建立在适当的模型和计算技术的关键最近的发展。在本项目的第一阶段，我们将通过以下方式实现这一目标：（1）为相关分类数据开发条件逻辑回归的模拟;（2）构建一个有效的网络图形算法，用于Aim 1中精确分布的快速计算;以及（3）研究把这些程序纳入一个标准化会计系统的可行性。我们计划在第二阶段把我们的新工具纳入这项工作作为LogXact软件包中的一个模块;扩展精确的回归过程，以适应相关数据的泊松和多色回归;并通过有效的Monte Carlo采样和并行处理显着提高这些新工具的计算效率。我们还将为SAS PROC创建一个模块，使这些方法尽可能广泛地提供给研究人员和分析师。

 DESCRIPTION (provided by applicant): The overarching goal of the proposed research is to develop practical modeling tools - including exact regression procedures - for small or sparse samples of correlated categorical data. Such outcomes are common in biomedical research, especially in areas such as genetics, ophthalmology, and teratology. One can encounter correlated categorical data wherever multiple outcomes are measured on an individual over time, or on several different individuals who share common genetic or environmental exposures. A large body of methods has been developed for analyzing correlated categorical outcomes, which conventionally rely on large-sample distributional assumptions (e.g., approximate normality) to justify their inferences. When faced with a small or sparse sample of categorical data investigators have few viable analytic options, and none that allow for exact inferences with regard to estimation. Our proposed work will fill this gap, building on critical recent developments of both appropriate models and computational technology. During Phase I of this project, we will accomplish this by (1) developing an analogue to conditional logistic regression for correlated categorical data; (2) constructing an efficient network graphical algorithm for rapi computation of the exact distribution in Aim 1; and (3) Investigating the feasibility of incorporating these procedures into a SAS PROC. We plan to expand this work in Phase II by incorporating our new tools as a module in the LogXact software package; extending the exact regression procedure to accommodate Poisson and polychromous regression for correlated data; and significantly improving the computational efficiency of these new tools through efficient Monte Carlo sampling and parallel processing. We will also create a module for a SAS PROC, making these methods as widely available as possible to researchers and analysts.