Exact Inference Software for Correlated Categorical Data

描述（由申请人提供）：这是Cytel旗舰软件StatXact的主要扩展的II期SBIR提案，用于对相关分类数据执行小样本精确推断。这些数据在生物医学研究中很常见，特别是在遗传学、眼科学和发育毒理学等领域。在这个第二阶段的工作中，我们将为目前StatXact软件中提供的独立数据的大多数现有小样本程序开发相关的数据类似物。具体而言，所得到的模块将实现以下相关数据扩展：1)无序和有序R × C列联表独立性的精确检验。2)两个有序多项式总体分布差异的检验。3)精确的mantel - haenszel型检验用于评估分层2x2表的相对优势同质性；4)精确的相关数据方法用于在集群内不同观测值的独立因素不同的情况。这一扩展将扩大这种方法的适用性，以更广泛的纵向和多重结果设置。由于实现上述过程可能在计算上很复杂，因此建议的最终目标是开发新的算法，使这些工具适用于一般用途。这些包括新的高效的基于网络的算法和用于模型拟合的蒙特卡罗仿真策略。这项工作的最终成果将是一个精确程序的工具箱，它将使用户在分析小样本相关分类数据时避免依赖可能较差的大样本近似。这一优势最终将导致对此类数据进行更可靠的分析。除了在本提案的第一阶段开发的有限原型之外，目前还没有用于此类方法的软件。

DESCRIPTION (provided by applicant): This is a Phase II SBIR proposal for a major extension to Cytel's flagship software, StatXact, to perform small sample exact inference for correlated categorical data. Such data are common in biomedical research, especially in areas such as genetics, ophthalmology, and developmental toxicology. In this Phase II effort, we will develop correlated data analogues for most of the existing small sample procedures for independent data currently provided in the StatXact software. Specifically the resulting module will implement correlated data extensions of: 1) Exact tests of independence in unordered and ordered R x C contingency table. 2) Tests for differences in the distributions of 2 ordered multinomial populations. 3) Exact Mantel-Haenszel-type tests for assessing homogeneity of relative odds for stratified 2x2 tables, 4) Exact correlated data methods for situations in which independent factors vary across observations within a cluster. This extension will expand the applicability of such methods to a wider range of longitudinal and multiple outcome settings. Because implementing the above procedures can be computationally complex, a final goal of the proposal is the development of new algorithms to make these tools practical for general use. These include new efficient network-based algorithms and Monte Carlo simulation strategies for model fitting. The final product of this effort will be a toolbox of exact procedures will enable users to avoid relying on potentially poor large sample approximations when analyzing small sample correlated categorical data. This advantage will ultimately lead to more reliable analyses of such data. There is currently no software for such methods other than a limited prototype developed in Phase I of this proposal.