Fig. 1

ROC curves. Panels a and b show, respectively, the ROC curve defined in terms of FPR/TPR and specificity/sensitivity. In this illustrative example, the ROC curve was parameterized according to the binormal ROC model [18], where \(X \sim N(1.5, 1)\), \(Y \sim N(0, 1)\), \(S_F(c) = \Phi ((\mu _x - c)/\sigma _x) = \Phi (1.5 - c)\), \(S_G(c) = \Phi ((\mu _y - c)/\sigma _y) = \Phi (-c)\), and \(\Phi (.)\) represents the cumulative distribution function of a standard normal random variable. (Further details about the binormal ROC model are presented in the Bias comparison section.) In this example, we adopt \(c = 1.1\), so that the FPR value in panel a (red arrow) is \(u = S_G(1.1) = 0.136\) and the respective ROC value (blue arrow) is \(ROC(0.136) = \Phi \left(1.5 - S_G^{-1}(0.136)\right) = 0.655\)