A useful property of AUC (as discussed above) is that for a given disease the estimated AUC is independent of the relative proportions of cases and controls in the sample being classified [7], i.e. the mean rank is approximately the same if the proportion of cases: controls is K: (1-K) or 1∶1. Or equally, the probability of a randomly selected case and control being correctly ranked is independent (except for sampling) of the number of cases and controls measured. We can use equation 3 to estimate the variance on the liability scale explained by a genomic profile, x, by making the subject of the equation, but renaming it as , recognising that it represents the proportion of variance explained by the profile. Then, from two measurable parameters, K and AUC, we can calculate ,(4)
