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Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB - pApB.
Human Heredity ( IF 1.8 ) Pub Date : 2020-02-11 , DOI: 10.1159/000504171
Jonathan T L Kang 1 , Noah A Rosenberg 2
Affiliation  

Background: Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient D. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use. Methods: Here, to compare the mathematical properties of these normalizations, we consider 5 of these normalized statistics, describing their upper bounds, the mean values of their maxima over the set of possible allele frequency pairs, and the size of the allele frequency regions accessible given specified values of the statistics. Results: We produce detailed characterizations of these properties for the statistics d and ρ, analogous to computations previously performed for r2. We examine the relationships among the statistics, uncovering conditions under which some of them have close connections. Conclusion: The results contribute insight into LD measurement, particularly the understanding of differences in the features of different LD measures when computed on the same data.
Hum Hered 2019;84:127–143


中文翻译:

通过系数D = pAB-pApB的归一化定义的连锁不平衡统计的数学性质。

背景:许多用于测量连锁不平衡(LD)的统计数据均采用LD系数D的归一化形式。不同的规范化会产生具有不同范围,解释和参数的统计信息,从而有利于使用它们。方法:在这里,为了比较这些归一化的数学性质,我们考虑其中的5个归一化统计量,描述它们的上限,在可能的等位基因频率对集合上的最大值的平均值以及可访问的等位基因频率区域的大小给定指定的统计值。结果:我们针对统计量dρ生成了这些属性的详细表征,类似于先前对r 2进行的计算。我们检查了统计数据之间的关系,并揭示了其中一些紧密联系的条件。结论:结果有助于深入了解LD测量,尤其是对基于相同数据计算的不同LD测量的特征差异的理解。
嗡嗡声到来的2019; 84:127–143
更新日期:2020-02-11
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