Fig. 1

The red line is the MI-curve for SE 0.9 and SP 0.8 as the prevalence of the disease ranges in the interval [0, 1]. The point p represents the value of MI (value on the MI axis) when the prevalence is 0.2 (value on the prevalence axis). The dark gray region is the area under the MI-curve for SE 0.9 and SP 0.8. It summarizes all the values of MI as the prevalence changes for a diagnostic method whose sensitivity and specificity are 0.9 and 0.8, respectively. This AUC does not range in an interval [0, 1], and it never reach 1. In order to normalize it in the [0, 1] range and get the information ratio, we must divide it by the maximum of the AUC among those obtainable by changing the sensitivity and the specificity. This is the AUC of the diagnostic method that has the best sensitivity and specificity, i.e., 1 and 1. The blue line depicts the MI-curve for SE 1.0 and SP 1.0, i.e., the gold standard, and the gray region (i.e., the light gray plus the dark gray regions) represents its AUC. In [4] it is proved that the latter equals \(1/\mathrm{ln}4\); hence, the information ratio of the method whose SE and SP are 0.9 and 0.8, respectively, is the AUC of the red curve multiplied by \(\mathrm{ln}4\). AUC Area under the curve, MI Mutual information, SE Sensitivity, SP Specificity, PREV Prevalence