aucs

Area under the curve (AUC) is a measure used across disciplines to quantify the size of a curve over a specified interval. It is defined as the integral of a function with respect to its variable, and its numerical value depends on the units of the axes. Because it aggregates information across the range of interest, AUCs are often used to summarize processes that accumulate over time or across categories.

In statistics and machine learning, the term AUC most commonly refers to the area under the receiver operating characteristic (ROC) curve, AUC-ROC. It summarizes a classifier’s ability to discriminate between classes across thresholds. An AUC of 0.5 indicates random performance, 1.0 represents perfect discrimination, and intermediate values reflect varying levels of separability. The ROC AUC is invariant to monotone transformations of the scoring function but can be influenced by class imbalance and does not directly reflect calibration of predicted probabilities.

In pharmacokinetics and related fields, AUC refers to the area under the plasma concentration–time curve after drug administration, reflecting total systemic exposure. It is typically expressed in concentration × time units (for example mg·h/L). It is commonly estimated by the trapezoidal rule using measured concentrations over time. Key variants include AUC0-t (from time zero to the last measurable concentration) and AUC0-∞ (including the extrapolated tail). For intravenous dosing, AUC = Dose/Clearance (Cl); for oral dosing, AUC = F×Dose/Cl, where F is bioavailability.

Estimation and interpretation considerations include the influence of sampling schedule, assay sensitivity, and modeling approach. Over longer periods, AUCs can increase with extended monitoring, and extrapolation introduces uncertainty.