model assumes that odds ratios are log-normally distributed, and as a result has similar properties to, and is easy to integrate with, the logistic regression techniques used in GWAS. The probit (or liability threshold) model is a generalization of the variance component models used in quantitative trait modelling, and assumes a continuous distribution of a disease phenotype (called the liability) in the population, with heritable and non-heritable components. An individual who develops the disease is assumed to have a liability value above a certain threshold. Clayton (11) derived expressions for the AUC and the ROC curves given the log model, which showed surprisingly small AUCs for most scenarios. However, Wray and Goddard (33)'s calculations based on the probit model showed very high AUCs for a similar range of heritabilities. Similar expressions cannot be easily derived for the logistic model, although they can be calculated numerically.
