A test for crossing receiver operating characteristic (roc) curves

The receiver operating characteristic (ROC) curve gives a graphical representation of sensitivity and specificity of a prediction model when varying the decision treshold on a diagnostic criterion. A classical test for comparing the overall accuracies for two models -1 and 2- is based on the difference between ROC curves areas - related to its standard error. This test is designed for the situation where ROC curve 1 caps ROC curve 2. Often both curves cross :in this paper, a new test, based on the integrated difference between the curves, is proposed to deal with this situation. In a simulation experiment, the new test was less powerful than the old test for detecting an overall superiority, but much more powerfull against the crossing alternative.