Assuming Hardy-Weinberg equilibrium in the general population from which the cases and controls were selected, we used our model assumptions (allele frequencies, disease prevalence and GRR) to calculate the penetrance functions and we used Bayes’ theorem to ascertain the conditional probability of each genotype given affection status, Pji, where j indexes affection status and i = 0 (dd), 1 (Dd), 2 (DD) indexes genotype. Namely, for the cases these probabilities were PA0 = Pr(dd | case), PA1 = Pr(Dd | case), and PA2 = Pr(DD | case) and for the unaffected (screened) controls the probabilities were PU0 = Pr(dd | unaffected control), PU1 = Pr(Dd | unaffected control), PU2 = Pr(DD | unaffected control). We assumed no disease misclassification among study cases or screened study controls. Derivations of the conditional genotype probabilities are provided for the multiplicative model in the Supplementary materials. For public controls, the genotype probabilities were set to the genotype probabilities in the general population, namely PPU0 = fd2, PPU1 = 2fd fD, PPU2 = fD2, since affection status was not assumed to be known.
