Our model regresses the phenotype Y on both the sum and the difference of the allelic dosage (0,1,2,3 or 4) for the two alleles, A and B:Y=b0+b1(A+B)+b2(A−B)+eA 2-degree-of-freedom test of the null hypothesis H0: b1 = b2 = 0 provides a combined test of CNV and allelic variation; the null H0: b1 = 0 gives a test of copy number variation; the null H0: b2 = 0 gives a test of allelic SNP effects. If there is either no copy number variation or no SNP variation at a site, we fit a reduced model by removing the appropriate term (A + B or A - B, respectively), equivalent to a standard regression of phenotype on allele dosage (assuming constant copy number) or copy number alone (assume a constant allelic background). Moderate correlation between CNV and allelic variation can impact the interpretation of specific tests of either b1 or b2, although the joint 2-d.f. test will be valid.
