For a continuous phenotype, the overall and the individual test statistics for association are F-statistics in a linear regression with the design matrix where columns indicate all haplotype classes of interest, rows correspond to the individuals and entries are 1/H(Gi), the reciprocals of the individual’s heterozygosity, or 0 if the genotype is incompatible with the allele set corresponding to the column. For one locus, the test reduces to the allelic trend test (53). As an association test for joint frequencies of alleles across multiple loci, the CHM is a valid test to detect allelic interactions between loci that are involved in an association with the studied trait. The CHM does not rely on LD between the loci and in fact can be used to detect interactions among multiple loci with weak or no LD. Moreover, Morris and Kaplan (74) showed that usage of haplotype association methods might be advantageous under weak LD, because single-locus-based approaches tend to provide high power when the LD is strong. Further details of the CHM will be described elsewhere.
