non-centrality parameter of the test for association of with is(4)on 1df, and the power of the two-tailed test of association at significance level is(5)Binary traits are assumed to arise from a liability threshold model [24] leading to calculation of the AUC also in terms of and , with the expressions given in the Methods. For binary traits the coefficient of determination in equation (2) may be transformed to the liability scale for more satisfactory interpretation [25], the details also given in the Methods.
