Diagnostic thresholds with three ordinal groups

In practice, there exist many disease processes with three ordinal disease classes; for example, in the detection of Alzheimer's disease (AD) a patient can be classified as healthy (disease-free stage), mild cognitive impairment (early disease stage), or AD (full disease stage). The treatment interventions and effectiveness of such disease processes will depend on the disease stage. Therefore, it is important to develop diagnostic tests with the ability to discriminate between the three disease stages. Measuring the overall ability of diagnostic tests to discriminate between the three classes has been discussed extensively in the literature. However, there has been little proposed on how to select clinically meaningful thresholds for such diagnostic tests, except for a method based on the generalized Youden index by Nakas et al. (2010). In this article, we propose two new criteria for selecting diagnostic thresholds in the three-class setting. The numerical study demonstrated that the proposed methods may provide thresholds with less variability and more balance among the correct classification rates for the three stages. The proposed methods are applied to two real examples: the clinical diagnosis of AD from the Washington University Alzheimer's Disease Research Center and the detection of liver cancer (LC) using protein segments.