that the dc is non-negative is satisfied for the ‘haplotype-driven’ models because of the constraints on the population frequencies and the model susceptibilities. Consider the recessive model: g1 > g2; g2 = g3 … = g10. Under this model, the difference that defines the sign, is always non-negative, therefore, the signs of dh and dc are in the same direction. This difference is similarly non-negative for other haplotype-driven models. Thus, the composite difference can be used as a basis for testing haplotypic associations. More generally, the composite difference provides a direct test of association between sets of alleles across genetic loci and the phenotype, without assuming HWE. Multilocus, multiallelic composite extension is obtained very simply. There are as many composite frequencies as there are haplotypes, and the notation for the composite classes is the same as that for the haplotypes, e.g. ‘A2B1C1D1' may refer to either a haplotypic or a composite set of alleles (A2, B1, C1, D1) at four loci. Denote a particular set of alleles such as this by Sk. The composite sample frequency of this four loci allele set is where H(Gi) is the number of single-locus heterozygotes in the multilocus genotype Gi of the ith individual,
