# How to interpret AUC?

### How to interpret AUC?

How to interpret his AUC ? The area under the ROC curve (or Area Under the Curve, AUC) maybe interpreted as the probability that, among two chosen subjects to chance, a sick and a non-sick, the value of the marker is higher for the sick than for the non-sick.

### How to calculate a ROC curve?

Fictitious data of 15 individuals for the calculations coordinates of a ROC curve. A ROC curve must necessarily start with the point of coordinates (0,0) and end with the point of coordinates (1,1). The points are then connected by a segment (segment which can be vertical, oblique, or horizontal).

### How to calculate false negatives?

Predictive Value negative : proportion of cases actually negatives from negatives detected by the test. We have VPN = VN/(VN+FN), or VPP= Specificity(1- Prevalence) / [Spécificité(1- Prévalence) + (1- Sensibilité)Prévalence]. This index also depends on the prevalence, a data independent of the quality of the test.

### How to calculate sensitivity and specificity?

the calculation of the index of sensitivity Is simple. This involves making the arithmetic ratio of the “true” cases correctly identified by the instrument (VP) with all the real cases, ie VP + FN.

### How to calculate false positive?

The mathematical definition is: Specificity = VN/(VN + FP). Fraction of false positives (FFP): proportion of negatives detected as positive by the test (1-Specificity).

### What is the AUC Roc value?

The AUC ROC is therefore equal to 100% for a perfect model: Figure 4. Area under the ROC Curve of a perfect model.

### What is the difference between measured and theoretical ROC curve?

The variations of the measured ROC curve (in red) with the theoretical curve (in blue) are explained by the fact that we are using a data set of limited size. The law of large numbers therefore does not apply and the hazard generates “oscillations” of the curve.

### What is the ROC Curve?

The ROC curve of a non-informative model follows a diagonal. The variations of the measured ROC curve (in red) with the theoretical curve (in blue) are explained by the fact that we are using a data set of limited size. The law of large numbers therefore does not apply and the hazard generates “oscillations” of the curve.

### How to calculate AUC with least number of operations?

Thus, the U-test calculates the AUC with the fewest operations and should be the fastest method. To verify this result in a concrete way, I implemented all these methods in python3 and I obtained the figure below.