Figure 2 shows the predicted ROC curves for diseases with a prevalence of K =1/200 and K =1/20, and a sibling relative risk of λS =9 and λS =3 for the three models. These values represent conservative parameter estimates for uncommon diseases, such as Crohn's disease or type 1 diabetes, and more common diseases such as cardiovascular disease. For the rarer disease, all the models give divergent answers, with the probit model giving an AUC of 0.98, a logit model an AUC of 0.96 and the log model an AUC of 0.89. For the common disease, the logit and probit models agree on an AUC of 0.93, although with a different sensitivity–specificity trade-off, and the log model gives a much lower AUC of 0.84. Part of this discrepancy is explained by an assumption in the log model that Kλs<<1, to avoid troublesome risk probabilities >1 (33). In practice, we have found that the log model is inaccurate if Kλs>0.01 (Supplementary Material, Fig. S1) and therefore agree with Wray and Goddard (33) that this model should not be used for common
