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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 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. 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 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.

The evaluation of the ability of a diagnostic test to separate diseased subjects from nondiseased subjects is a crucial issue in modern medicine. The accuracy of a continuous-scale test at a chosen cut-off level can be measured by its sensitivity and specificity, i.e. by the probabilities that the test correctly identifies the diseased and non-diseased subjects, respectively.In practice, sensitivity and specificity of the test are unknown. Moreover, which cut-off level to use is also generally unknown in that no preliminary indications driving its choice could be available.In this paper, we address the problem of making joint inference on pairs of quantities defining accuracy of a diagnostic test, in particular, when one of the two quantities is the cut-off level. We propose a technique based on an empirical likelihood statistic that allows, within a unified framework, to build bivariate confidence regions for the pair (sensitivity, cut-off level) at a fixed value of specificity as well as for the pair (specificity, cut-off level) at a fixed value of sensitivity or the pair (sensitivity, specificity) at a fixed cut-off value.A simulation study is carried out to assess the finite-sample accuracy of the method. Moreover, we apply the method to two real examples.

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