Inference on the symmetry point-based optimal cut-off point and associated sensitivity and specifcity with application to SARS-CoV-2 antibody data

In the presence of a continuous response test/biomarker, it is often necessary to identify a cut-off point value to aid binary classifcation between diseased and non-diseased subjects. The symmetry-point approach which maximizes simultaneously both types of correct classifcation is one way to determine an optimal cut-off point. In this article, we study methods for constructing confdence intervals independently for the symmetry point and its corresponding sensitivity, as well as respective joint nonparametric confdence regions. We illustrate using data on the generation of antibodies elicited two weeks post-injection after the second dose of the Pfzer/BioNTech vaccine in adult healthcare workers.