Diagnostic Accuracy Measures and Optimal Cut-Off Points for Nested Disease Subtypes Within the Disease Ordinal States

In medical diagnostic testing, classifications are commonly divided into two primary types: binary tests, which distinguish between diseased and nondiseased cases, and ordinal states, which categorize cases into nondiseased states and disease stages ranging from 1 to k. Additionally, there exists a multiclass classification scheme, referred to as tree or umbrella ordering, in which a classifier determines whether a biomarker measurement for one class is higher or lower than that of the other classes. We introduce a novel concept called Nested Disease Subtypes Within the Disease Ordinal States, which extends the summary measures of receiver operating characteristic (ROC) curves to accommodate this unique classification approach. Our method aims to refine current diagnostic categorization by accounting for the complexity of certain diseases that do not conform to traditional classifications. To validate the effectiveness of our approach, we conducted simulation studies and applied it to real data on tuberculosis. These findings highlight the potential of our methods to enhance both the precision and comprehension of medical diagnostic testing, particularly, for complex diseases.