Fig. 2

Receiver operating characteristic (ROC) and global information ratio (GIR) analyses of data reported in Table 1. The blue points in the figures denotes the 6 possible cutoffs, i.e., all the category below the ith one, where \(i\in\;\left[0,5\right]\) are considered negative diagnoses. a The ROC analysis plots the cutoff points in the (1—SP) × SE space, and it connects them by using the ROC curve. The area under this curve is a cutoff-independent measure of the effectiveness of the diagnostic approach: the higher the area, the better the approach. The ROC area under the curve (AUC) ranges in the [0, 1] interval. The figure represents the ROC curve and its AUC as a black line and a dark gray region, respectively. In the depicted scenario, the AUC is about 0.793. b The GIR analysis of the same data depicts the cutoff points in the (1—SP) × IR space. The point themselves are connected by the information ratio curve (IRC) which is represented as a black line. As the ROC AUC, the IRC AUC (the dark gray region in the figure) is a measure of the effectiveness of the diagnostic approach, but, since it is computed by using IR, it is prevalence-independent. Unfortunately, it does not range in the interval [0, 1], and to normalize it, it must be divided by the IRC AUC of the best theoretical diagnostic approach, i.e., those whose sensitivity is always 1: the limit information curve (LIC). The LIC AUC (the light and dark gray regions in the figure) always equals \(2-{\pi }^{2}/6\) [4]; thus, the ratio between IRC and LIC AUCs, i.e., the global information ratio (GIR), equals IRC AUC divided by \(2-{\pi }^{2}/6\). In the scenario depicted by panel b, IRC AUC and GIR are about 0.116 and 0.326, respectively