Let N be the number of case-mother duos and M the number of SNPs to be analyzed. (Genotype counts for case-father duos are adjusted in the same manner, but we only consider case-mother duos here for simplicity.) Let X = {x1,…,xM} be the sequence of observed SNP case-mother duo data such that each xi is a vector of cell counts {xij} for SNP i for case-mother duo cells j = 1, 2, 3, 4a, 4b, 5, 6, and 7. Let pi be the minor allele frequency of SNP i, then, assuming Hardy-Weinberg equilibrium and random mating, xi is given by a multinomial distribution with ∑jxij=N and eight probabilities θij, with probabilities for cells 4a and 4b given by θi(4a)=pi2(1−pi) and θi(4b)=pi(1−pi)2, respectively. Let Σi be the covariance matrix where the variances for cells 4a and 4b are given by Σi(4a,4a)=Nθi(4a)(1−θi(4a)) and Σi(4b,4b)=Nθi(4b)(1−θi(4b)), respectively, with covariance Σi(4a,4b)=−Nθi(4a)θi(4b).