Sensitivity and specificity are often of interest in the prediction of binary traits. In particular, the accuracy of a predictor can be assessed by the AUC constructed as follows. Subjects are classified such that those with a polygenic score above a fixed threshold are predicted to have the trait, those below the threshold to not have it. Sensitivity is the proportion of subjects with the trait who are correctly predicted as such, and specificity the proportion of subjects without the trait correctly predicted as such. Each possible threshold leads to a value of sensitivity and specificity, defining the receiver operator characteristic curve by plotting sensitivity against 1-specificity. The AUC can be defined as the probability that a pair of subjects, one with the trait and one without, is correctly classified by the predictor. Because the central limit theorem implies that the polygenic score is normally distributed, the expected AUC can be calculated as [21] (12)In this expression, is formed from effects on estimated on the observed scale whereas the conditional means and variances are conveniently calculated on the liability scale
