# How to interpret AUC?

**Sommaire de notre article**

- How to interpret AUC?
- How to calculate a ROC curve?
- How to calculate false negatives?
- How to calculate sensitivity and specificity?
- How to calculate false positive?
- What is the AUC Roc value?
- What is the difference between measured and theoretical ROC curve?
- What is the ROC Curve?
- How to calculate AUC with least number of operations?

### 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.