Where does area under the curve collide?

In economics, a central quantity is an area under a curve: consumer surplus is the area beneath the demand curve and above the market price, the aggregate gain buyers enjoy from paying less than the most they would have been willing to pay. Marshall's Principles of economics (1890) made this geometric welfare measure standard, reading the gain to buyers off the region under demand. The referent is a monetary welfare magnitude obtained by integrating willingness to pay, and despite the identical 'area under the curve' phrasing it has nothing to do with drug exposure or a classifier's accuracy.[1]

Unit

Monetary welfare: the integrated gap between willingness to pay and price

Recovery means

Not applicable

Measured by

Computed as the definite integral between the demand curve and the price line over the quantity traded

In diagnostic testing and machine learning, the area under the receiver operating characteristic curve (AUC, or AUC-ROC) summarises how well a classifier separates two classes across all decision thresholds. Hanley and McNeil's 1982 The meaning and use of the area under a receiver operating characteristic (ROC) curve showed this area equals the probability that a randomly chosen positive case is ranked above a randomly chosen negative one. The referent is a threshold-free discrimination index between 0.5 (chance) and 1 (perfect), an entirely different construct from drug exposure or economic surplus despite sharing the 'area under the curve' name.[2]

Unit

A discrimination probability from 0.5 (chance) to 1 (perfect separation)

Recovery means

Not applicable

Measured by

Computed as the integral of the ROC curve (sensitivity vs. one minus specificity), equivalently the Mann-Whitney rank statistic

In pharmacokinetics, AUC is the area under the plasma drug concentration-versus-time curve, the standard measure of total systemic exposure to a dose. Gibaldi and Perrier's Pharmacokinetics sets out how AUC is computed and how it anchors bioavailability, clearance, and dose comparisons. The referent is an exposure quantity in concentration-time units that scales with how much drug reaches the circulation and how slowly the body clears it, unrelated to economic surplus or classifier accuracy beyond the shared integral.[3]

Unit

Drug exposure in concentration × time (e.g., mg·h/L)

Recovery means

Not applicable

Measured by

Estimated from timed plasma concentrations by the trapezoidal rule and extrapolated to infinity, or as dose divided by clearance