Area of the ROC curve when one point is available.

In this paper, the method of extension is proposed for the calculation of the area under the ROC curve, if only one pair of specificity (Sp0=1-FP0) and sensitivity (Se0) is available. The method of extension is algebraic and is based on the assumption that the ROC curve is continuous, concave, truly ascending and has the form Se=κ0+κ1FP+κ2FP2 in parts. The area under ROC curve is calculated by the formula: AUC=(7Sp0+7Se0-2Sp0Se0)/12.