Simple nonparametric condence regions for the evaluation of continuous-scale diagnostic tests.

The evaluation of the ability of a diagnostic test to separate diseaded from non-diseaded 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 diseaded and non-diseaded subjects, respectively. In practice, sensitivity and specificity of the test are unknown. Moreover, the cut-o level to use is also generally unknown, in that no preliminary indications driving its choice could be available. In this paper, we try to 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 make inference about the pair (sensitivity, cut-off level), at a fixed value of specificity, as well as about the pair (specificity, cut-off level), at a fixed value of sensitivity, or about 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.