Regression Analysis for the Partial Area under the Roc Curve

Performance evaluation of any classification method is fundamental to its acceptance in practice. Evaluation should consider the dependence of a classifier’s accuracy on relevant covariates in addition to its overall accuracy. When developing a classifier with a continuous output that allocates units into one of two groups, receiver operating characteristic (ROC) curve analysis is appropriate. The partial area under the ROC curve (pAUC) is a summary measure of the ROC curve used to make statistical inference when only a region of the ROC space is of interest. We propose a new pAUC regression method to evaluate covariate effects on the diagnostic accuracy. We provide asymptotic distribution theory and inference procedures that allow for correlated observations. Graphical methods and goodness-of-fit statistics for model checking are also developed. Simulation studies demonstrate that the large-sample theory provides reasonable inference in small samples and the new estimator is considerably more efficient than the estimator proposed by Dodd and Pepe (2003a). Application to an analysis of prostate-specific antigen (PSA), a biomarker for early detection of prostate cancer, demonstrates the utility of the method in practice.