TWO STAGE DESIGNS FOR LINKAGE DISEQUILIBRIUM

连锁不平衡是指连锁基因座上等位基因的非随机关联，它可以作为一种基因定位技术来精确定位疾病易感基因座。 在最近的统计文献中，设计连锁不平衡研究很少受到关注，特别是当研究成本和可用样本量有限时。在这里，我们提出了两个两阶段的设计来解决这些问题。最优设计是指最大化确定真实疾病易感性位点的功效或机会的设计。 对于给定数量的标记，当研究的总成本是唯一的约束时，将评价第一种设计。 目标是在两阶段过程中确定样本量的最佳分配。 当总成本和可用样本量受到限制时，我们将考虑第二种设计。 该设计的目的是确定两阶段过程中待基因分型的标记的数量，以及将提供最佳设计的标记间间距。 最后，我们将在这两种设计下得到检验统计量的临界值。我们将首先获得近似的幂函数和临界值下的两个建议的设计。 我们将使用Monte Carlo模拟来研究这些值如何受到标记总数、标记间距离和总样本量的影响。 随着对全基因组研究的日益关注，这里提出的设计将允许研究人员以最大限度地提高识别疾病易感性位点（如果有的话）的能力的方式分配他们有限的资源。

Linkage disequilibrium is the nonrandom association of alleles at linked loci, which can be used as a gene mapping technique to refine the location of a disease susceptibility locus. Designing linkage disequilibrium studies have received very little attention in recent statistics literature, particularly when the cost of the study and the available sample size are limited. Here we address these issues by proposing two two-stage designs. An optimal design is one which maximizes the power or the chance of identifying the true disease susceptibility locus. The first design will be evaluated when the total cost of the study is the only constraint, for a given number of markers. The goal will be to determine the optimal allocation of sample size in a two-stage process. We will consider a second design when the constraints are on the total cost and the available sample size. The goal of this design will be to determine the number of markers to be genotyped in a two-stage process, and the intermarker spacing which will provide an optimal design. Finally, we will derive the critical value of a test statistics under these two designs. We will first obtain an approximation to the power function and the critical value under the two proposed designs. We will use Monte Carlo simulations to investigate how these values are affected by the choice of total number of markers, intermarker distance, and the total sample size. With increased attention on whole genome studies, the designs proposed here will permit researchers to allocate their limited resources in a manner whereby the power to identify the disease susceptibility locus, if any, is maximized.