With a predefined correlation coefficient (R) of linkage disequilibrium (LD) between D and S, we can derive the haplotype frequencies as follows:(20)where q1 and q2 are the population frequencies of the SNP alleles S1 and S2. To simplify our model, we will assume pi = qi, where i = 1 or 2. The rationale behind this is that if the SNP marker and disease allele have very different frequencies, then R 2 is small and there is little power. Keeping both frequencies equal allow R to vary the full range from −1 to +1.
