Confidence intervals and bands for the binormal ROC curve revisited

Abstract

Two types of confidence intervals (CIs) and confidence bands (CBs) for the receiver operating characteristic (ROC) curve are studied: pointwise CIs and simultaneous CBs. An optimized version of the pointwise CI with the shortest width is developed. A new ellipse-envelope simultaneous CB for the ROC curve is suggested as an adaptation of the Working–Hotelling-type CB implemented in a paper by Ma and Hall (1993). Statistical simulations show that our ellipse-envelope CB covers the true ROC curve with a probability close to nominal while the coverage probability of the Ma and Hall CB is significantly smaller. Simulations also show that our CI for the area under the ROC curve is close to nominal while the coverage probability of the CI suggested by Hanley and McNail (1982) uniformly overestimates the nominal value. Two examples illustrate our simultaneous ROC bands: radiation dose estimation from time to vomiting and discrimination of breast cancer from benign abnormalities using electrical impedance measurements.