The ROC plot is a useful tool in the evaluation of the performance of medical tests for separating two populations. For a two-state decision rule based on such a test, the ROC plot is the graph of all observed (1-specificity, sensitivity) pairs. Each point on this empirical plot can be represented by a 2 × 2 contingency table. The non-parametric statistics of Mann-Whitney and Kolmogorov-Smirnov can be immediately identified on this plot. Local non-parametric confidence interval procedures related to the theoretical ROC curve are briefly reviewed. For continuous data, two new simultaneous confidence regions associated with the ROC curve are presented, one based on Kolmogorov-Smirnov confidence bands for distribution functions and the other based on bootstrapping.
Two different tests on the same patients can be compared on the ROC scale. For continuous data, one important problem concerns the comparison of two ROC plots (as would arise from two correlated diagnostic tests on each patient) using a sup norm (this metric can detect differences that the ROC area cannot). The distribution of a statistic based on this norm is studied, using the bootstrap. A biomedical example illustrates the methodologies.