An alternative to the liability threshold model is the log-risk model for binary traits, which is equivalent to the logistic model in the limit of low prevalence. Here the polygenic score estimates the log risk of disease, which is assumed to be normally distributed in the population with mean and variance , where is the sibling relative recurrence risk [17], [20]. Under this model the log risk has the same variance in cases and controls, but the mean log risk among cases is increased by that same variance, becoming . This model allows a simpler calculation of AUC for rare disease, which is given here but not pursued further.
