Extension of the Haseman-Elston method to multiple alleles and multiple loci: theory and practice for candidate genes

The Haseman & Elston (1972) sibling-pair regression method has been used to detect and estimate the variance contribution to observed values of a quantitative trait by allelic variation in specific candidate genes. The procedure was developed under a model with a single biallelic trait locus. This assumption does not hold for several known systems. In this paper we prove that for candidate gene analysis the Haseman-Elston procedure extends to the case of multiple trait loci, each possibly having more than two alleles. Simulation experiments comparing single-locus to two-locus models show that fitting the extended regression equations maintains nominal significance levels, but the power to detect linkage to trait variation is not improved by including additional loci. These results indicate that the original proposal is statistically robust to violations of the underlying genetic model. Practical issues associated with quantifying the relative variance contribution by individual loci are also discussed. Applications of the extended regression equations to lipoprotein(a) and high density lipoprotein cholesterol are given for illustration.