Resampling Methods for the Area Under the ROC Curve

Receiver Operating Characteristic (ROC) analysis is a common tool for assessing the performance of various classification tools including biological markers, diagnostic tests, technologies or practices and statistical models. ROC analysis gained popularity in many fields including diagnostic medicine, quality control, human perception studies and machine learning. The area under the ROC curve (AUC) is widely used for assessing the discriminative ability of a single classification method, for comparing performances of several procedures and as an objective quantity in the construction of classification systems. Resampling methods such as bootstrap, jackknife and permutations are often used for statistical inferences about AUC and related indices when the alternative approaches are questionable, difficult to implement or simply unavailable. Except for the simple versions of the jackknife, these methods are often implemented approximately, i.e. based on the random set of resamples, and, hence, result in an additional sampling error while often remaining computationally burdensome. As demonstrated in our recent publications, in the case of the nonparametric estimator of the AUC these difficulties can sometimes be circumvented by the availability of closed-form solutions for the ideal (exact) quantities. Using these exact solutions we discuss the relative merits of the jackknife, permutation test and bootstrap in application to a single AUC or difference between two correlated AUCs.