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Receiver operating characteristic (ROC) curves are used ubiquitously toevaluate covariates, markers, or features as potential predictors in binaryproblems. We distinguish raw ROC diagnostics and ROC curves, elucidate thespecial role of concavity in interpreting and modelling ROC curves, andestablish an equivalence between ROC curves and cumulative distributionfunctions (CDFs). These results support a subtle shift of paradigms in thestatistical modelling of ROC curves, which we view as curve fitting. Weintroduce the flexible two-parameter beta family for fitting CDFs to empiricalROC curves, derive the large sample distribution of the minimum distanceestimator and provide software in R for estimation and testing, including bothasymptotic and Monte Carlo based inference. In a range of empirical examplesthe beta family and its three- and four-parameter ramifications that allow forstraight edges fit better than the classical binormal model, particularly underthe vital constraint of the fitted curve being concave.

Receiver Operating Characteristic (ROC) Curves