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，无论是在一段时间内对一个人的多个结果进行测量，还是对几个共享共同遗传或环境暴露的不同个人进行测量。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，近似正态分布)来证明其推断的合理性。当面对少量或稀疏的分类数据样本时，调查人员几乎没有可行的分析选择，而且没有一个能够对估计做出准确的推断。我们拟议的工作将填补这一空白，建立在适当模型和计算技术的关键最近发展的基础上。在这个项目的第一阶段，我们将通过(1)为相关的分类数据开发一个类似于条件Logistic回归的方法来实现这一点；(2)构建一个有效的网络图形算法，用于在AIM 1中计算准确的分布；以及(3)研究将这些程序整合到SAS过程中的可行性。我们计划在第二阶段扩展这项工作，将我们的新工具作为模块纳入LogXact软件包；扩展精确回归程序，以适应相关数据的泊松和多色回归；并通过高效的蒙特卡罗采样和并行处理显著提高这些新工具的计算效率。我们还将为SAS过程创建一个模块，使这些方法尽可能广泛地供研究人员和分析师使用。

 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.