Receiver Operating Characteristic (ROC) Curves

Understand

Receiver operating characteristic (ROC) curves are used ubiquitously to evaluate covariates, markers, or features as potential predictors in binary problems.

• We distinguish raw ROC diagnostics and ROC curves, elucidate the special role of concavity in interpreting and modelling ROC curves, and establish an equivalence between ROC curves and cumulative distribution functions (CDFs).
• These results support a subtle shift of paradigms in the statistical modelling of ROC curves, which we view as curve fitting.
• We introduce the flexible two-parameter beta family for fitting CDFs to empirical ROC curves, derive the large sample distribution of the minimum distance estimator and provide software in R for estimation and testing, including both asymptotic and Monte Carlo based inference.