In our derivations we have assumed the liability threshold model [11],[14]. Slatkin [26] demonstrated that the threshold model was one of several genetic models that provided the necessary steep increase in probability of disease with increasing load of genetic risk alleles [26]. The main assumption of the liability threshold model is that the distribution of liability scores is unimodal which should be achieved as long as there is no single unidentified genetic or environmental of very large effect [11]. The model accommodates any distribution of risk allele effect sizes and risk allele frequencies as long as there are sufficient (“more than one or a few” [11]) risk alleles in the population to create an approximately normal distribution of genetic liability scores. Since our simulation results of AUCmax vs (Figure 3) based on the liability threshold model agree with those of Janssens et al [3] who used a logit model to combine genetic risks from individual genetic variants, it is clear that the dependence of AUCmax on heritability and disease prevalence is not a function of the threshold model.
