The Average Area under Correlated Receiver Operating Characteristic Curves: A Nonparametric Approach Based on Generalized Two-Sample Wilcoxon Statistics

SUMMARY It is well known that, when sample observations are independent, the area under the receiver operating characteristic (ROC) curve corresponds to the Wilcoxon statistics if the area is calculated by the trapezoidal rule. Correlated ROC curves arise often in medical research and have been studied by various parametric methods. On the basis of the Mann–Whitney U-statistics for clustered data proposed by Rosner and Grove, we construct an average ROC curve and derive nonparametric methods to estimate the area under the average curve for correlated ROC curves obtained from multiple readers. For the more complicated case where, in addition to multiple readers examining results on the same set of individuals, two or more diagnostic tests are involved, we derive analytic methods to compare the areas under correlated average ROC curves for these diagnostic tests. We demonstrate our methods in an example and compare our results with those obtained by other methods. The nonparametric average ROC curve and the analytic methods that we propose are easy to explain and simple to implement.