Fig. 10

PPV versus ROC AUC plots and NPV versus ROC AUC plots. We developed an R script where we randomly generated a binary ground truth vector of 10 elements, and then we executed a loop where we produced a list of synthesized predictions of real values between 0 and 1, for 10,000 times. For each prediction, we computed the ROC AUC and its corresponding precision (PPV) and negative predictive value (NPV) with cut-off threshold \(\tau = 0.5\). Negatively imbalanced ground truth (i,l): the ground truth labels are (0, 0, 0, 0, 0, 0, 0, 1, 1, 1), corresponding to 70% negative elements and 30% positive elements. Balanced ground truth (j,m): the ground truth labels are (0, 0, 0, 0, 0, 1, 1, 1, 1, 1), corresponding to 50% negative elements and 50% positive elements. Positively imbalanced ground truth (k,n): the ground truth labels are (0, 0, 0, 1, 1, 1, 1, 1, 1, 1), corresponding to 30% negative elements and 70% positive elements. In each plot, the ground truth is fixed and never changes, while our script generated 10 random real values in the [0; 1] interval 10,000 times: each time, our script calculates the resulting ROC AUC and normMCC, which corresponds to a single point in the plot. The ground truth values and the predictions are the same of Fig. 9. PPV: precision, positive predictive value (Eq. 3). NPV: negative predictive value (Eq. 4). ROC AUC: area under the receiver operating characteristics curve. ROC AUC, precision, and NPV range from 0 (minimum and worst value) to 1 (maximum and best value). Blue line: regression line made with smoothed conditional means