Nonparametric confidence regions for the symmetry point-based optimal cutpoint and associated sensitivity of a continuous-scale diagnostic test

In medical research, diagnostic tests with continuous values are widely employed to attempt to distinguish between diseased and non-diseased subjects. The diagnostic accuracy of a test (or a biomarker) can be assessed by using the receiver operating characteristic (ROC) curve of the test. To summarize the ROC curve and primarily to determine an "optimal" threshold for test results to use in practice, several approaches may be considered, such as those based on the Youden index, on the so-called close-to-(0,1) point, on the concordance probability and on the symmetry point. In this paper, we focus on the symmetry point-based approach, that simultaneously controls the probabilities of the two types of correct classifications (healthy as healthy and diseased as diseased), and show how to get joint nonparametric confidence regions for the corresponding optimal cutpoint and the associated sensitivity (= specificity) value. Extensive simulation experiments are conducted to evaluate the finite sample performances of the proposed method. Real datasets are also used to illustrate its application.