Fig. 4

Conditions under which \(tpAUC = 0\). Panel a shows that because the ROC curve is monotonic it follows that the curve will not cross the region of interest (red rectangle) if the specificity at the \(b_{se}\) sensitivity, denoted by \(c_{sp}\) and highlighted by the blue arrow, is smaller than \(b_{sp}\). Panel b shows the equivalent condition in terms of sensitivity values, where we see that the ROC curve does not cross the region of interest if the sensitivity at the \(b_{sp}\) specificity, \(c_{se}\), is smaller than \(b_{se}\). When these conditions hold, we have that the tpAUC is 0. In our implementation, we check the condition in panel a