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

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