Kang Jonathan T L, Rosenberg Noah A
Department of Biology, Stanford University, Stanford, California, USA,
Department of Biology, Stanford University, Stanford, California, USA.
Hum Hered. 2019;84(3):127-143. doi: 10.1159/000504171. Epub 2020 Feb 11.
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.
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.
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.
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.
许多用于测量连锁不平衡（LD）的统计量采用LD系数D的归一化形式。不同的归一化产生具有不同范围、解释以及支持其使用的论据的统计量。
在此，为了比较这些归一化的数学性质，我们考虑其中5个归一化统计量，描述它们的上界、在可能的等位基因频率对集合上其最大值的均值，以及给定统计量特定值时可及的等位基因频率区域的大小。
我们给出了统计量d和ρ这些性质的详细特征描述，类似于之前对r2所进行的计算。我们研究了这些统计量之间的关系，揭示了其中一些统计量具有紧密联系的条件。
这些结果有助于深入了解LD测量，特别是在对相同数据进行计算时，对不同LD测量特征差异的理解。
