Mathematical Sciences: Exact Confidence Regions for Multi- dimensional Contingency Tables

摘要Hardy-Weinberg不平衡和连锁不平衡是群体遗传学中的重要概念。在实践中，估计单倍型数据中的连锁不平衡相当于估计一个大的、稀疏的、多维的列联表中的相互作用。在多基因座基因型数据上同时估计Hardy-Weinberg和连锁不平衡引入了额外的信息缺失和边缘概率对称约束的复杂性。为了避免可能对这些数据不可靠的大样本近似值，一种方法是使用“精确”统计方法，将观察到的边际总数作为推断条件。不幸的是，计算精确的置信区间和区域目前是不可行的，因为大量的表与观测表的边际总数一致。主要研究者设计和研究了多维列联表的精确推理方法。这些方法采用马尔可夫链蒙特卡罗算法来模拟为表的相互作用参数构造精确置信区域所需的条件分布。本研究涉及的主题包括：开发有用的遗传不平衡统计模型；算法的设计、优化和收敛性；以及结果估计的统计性质。遗传不平衡可以指向特定等位基因与疾病风险增加的关联，揭示群体亚结构，或作为定位克隆的指导。这项研究为遗传学家提供了一种工具来估计由一组数据证明的遗传不平衡的程度和形式，并评估这些估计的精度。这些方法对于估计在其他环境中出现的大型、稀疏、多维列联表中的相互作用也很有用。

9510516 Lazzeroni Abstract Hardy-Weinberg disequilibrium and linkage disequilibrium are important concepts in population genetics. In practice, estimation of linkage disequilibrium in haplotype data is equivalent to estimation of the interactions in a large, sparse, multidimensional contingency table. Simultaneous estimation of Hardy-Weinberg and linkage disequilibrium on multilocus genotype data introduces the additional complications of missing information and symmetry constraints on marginal probabilities. To avoid large-sample approximations that can be unreliable for these data, one approach is to use "exact" statistical methods that condition inference on observed marginal totals. Unfortunately, computing exact confidence intervals and regions is presently infeasible because of the large number of tables consistent with the marginal totals of an observed table. The principal investigator designs and studies methods for exact inference for multidimensional contingency tables. These methods employ Markov chain Monte Carlo algorithms to simulate the conditional distributions required to construct exact confidence regions for the interaction parameters of a table. Topics addressed by this research include: development of useful statistical models of genetic disequilibrium; design, optimization, and convergence properties of the algorithms; and statistical properties of the resulting estimates. Genetic disequilibrium can point to the association of particular alleles with an increased risk of disease, reveal population substructure, or serve as a guide in positional cloning. This research provides geneticists with tools for estimating the degree and form of genetic disequilibrium evidenced by a set of data, and to evaluate the precision of those estimates. The methods will also be useful for estimating interactions in large, sparse, multidimensional contingency tables that arise in other settings.