Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient <b><i>D</i></b> = <b><i>p</i></b><sub><i>AB</i></sub> – <b><i>p</i></b><sub><i>A</i></sub><b><i>p</i></b><sub><i>B</i></sub>

Source abstract

<b><i>Background:</i></b> Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient <i>D</i>. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use. <b><i>Methods:</i></b> 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. <b><i>Results:</i></b> We produce detailed characterizations of these properties for the statistics <i>d</i> and <i>ρ</i>, analogous to computations previously performed for <i>r</i><sup>2</sup>. We examine the relationships among the statistics, uncovering conditions under which some of them have close connections. <b><i>Conclusion:</i></b> 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.