Entropy as a Measure for Linkage Disequilibrium over Multilocus Haplotype Blocks

Objective: The presence of linkage disequilibrium (LD) forms the basis for a range of uses, including the fine-mapping of diseases and studies on human genealogy. Recent findings indicate that single nucleotide polymorphisms (SNP) can occur in blocks of limited haplotypic diversity with high degrees of LD. Commonly used measures for LD, such as r2and D′, consider only two loci and might miss information to appropriately describe LD in larger haplotypic structures. Methods: We introduce the Normalized Entropy Difference, ε, as a new multilocus measure for LD. A related quantity, ΔS, provides an approximate χ2 test for the significance of LD. The ability of the measure to detect haplotype blocks is investigated using simulated data sets as well as a real data set previously analyzed by Daly et al. (2001). Results: ε allows for arbitrary numbers of loci, describes LD with regard to the loci sequence, and can be interpreted as a multilocus extension of r2. The application of ε to the data sets demonstrated the measure's ability to appropriately describe simultaneous multilocus LD and to detect haplotype blocks. Conclusions: ε is a reasonable multilocus LD measure and might be of potential use in the construction of the human haplotype map