A genotype-based approach to assessing the association between single nucleotide polymorphisms

Measuring the extent of linkage disequilibrium (LD) between single nucleotide polymorphisms (SNPs) is of considerable importance, and many different between SNP association measures including Lewontin's D' and Pearson's correlation coefficient rho have been proposed. The vast majority of these association measures are based on haplotypes instead of genotypes. If no family data are available, the required additional haplotype estimation step is based on the assumption of Hardy-Weinberg equilibrium (HWE). In this paper we propose to estimate the extent of LD by using a genotype- rather than haplotype-based measure. Furthermore, we require of an appropriate measure of LD that it should remain invariant under the transition from haplotypes to diploid genotypes if HWE holds. We show that Pearson's rhofulfills this invariance property in contrast to a variety of different LD measures including D'. We derive the asymptotic distribution of the empirical product-moment correlation R for counting variables and construct asymptotically valid confidence intervals using Fisher's z-transformation. We demonstrate the validity of our approach by a numerical study of the coverage properties. We show that the loss in precision encountered by using genotype rather than haplotype data for estimating the association between SNPs is negligible for practical purposes. We finally illustrate our approach with data from an association study of IL-4 associated phenotypes and polymorphisms from the human IL-4 receptor alpha chain gene (IL4R).