We used simulation under the liability threshold model [11],[14] to check our derivations. We simulated 100,000 nuclear families sampling risk on the liability scale, P = A + E, A ∼ N(0, ) for parents, and A = ½Adad+½Amum+Amend for children, where the Mendelian segregation terms were random numbers sampled as Amend ∼ N(0, ½); E ∼ N(0,1 - ). Individuals were considered affected, P 01 = 1, if P >Φ−1(1-K) = T, otherwise individuals were not affected and P 01 = 0. Genetic values on the observed scale, G01, were calculated as the normal probability, . From this we could calculate , , (using the G01 and P01 of the first child from each family) and sibling recurrence risk. AUCmax was calculated from the mean rank of diseased individuals using equation 2 when ranked on A.
