Jackknife empirical likelihood based confidence intervals for partial areas under ROC curves

Abstract

The partial area under the ROC curve (partial AUC) summarizes the accuracy of a diagnostic or screening\ntest over a relevant region of the ROC curve and represents a useful tool for the evaluation and the\ncomparison of tests. In this paper, we propose a jackknife empirical likelihood method for making inference\non partial AUCs. Following the idea in Jing, Yuan, and Zhou (2009), we combine the empirical\nlikelihood function with suitable jackknife pseudo-values obtained from a nonparametric estimator of\nthe normalized partial AUC. This leads to a jackknife empirical likelihood function for normalized partial\nAUCs, for which a Wilks-type result is obtained. Then, such a pseudo-likelihood can be used, in a\nstandard way, to construct confidence intervals or perform tests of hypotheses. We also give some simulation\nresults that indicate that the jackknife empirical likelihood based confidence intervals compare\nfavorably with other alternatives in terms of coverage probability. The proposed method is extended to\ninference on the difference between two partial AUCs. Finally, an application to the Wisconsin Breast\nCancer Data is discussed.