General nonparametric ROC curve comparison

Although the equality among two or more ROC (receiver operating characteristic) curves is usually contrasted from the respective AUCs (area under the ROC curve), two different ROC curves can share the same AUC and, in order to compare the ROC curves equality, most general criteria must be considered. In this paper, the authors deal with the general ROC curve comparison problem on paired design. They extend the tests for the classical cumulative distribution functions (CDF) comparison to the ROC curves context. To approximate the statistic distribution, two different resampling plans are considered; the usual one based on permutations and a new bootstrap procedure which does not require the exchangeability   assumption. As usual, from Monte Carlo simulations, the performance of the proposed methodology is studied for two traditional tests; one based on the Kolmogorov–Smirnov criteria and the other one on the L2L2-measure. The observed results suggest that the proposed bootstrap provides a good statistic distribution approximation for medium sample size. Therefore the studied methodology allows us to compare the equality of ROC curves by defining a criteria according to the needs of the problem.