On diagnostic accuracy measures and optimal cut-point selection measures for multi-stage diseases via generalized total Kullback–Leibler divergence

The accuracy of a diagnostic test has always been crucial for detecting disease staging. Numerous diagnostic precision tests have been extensively used in binary diagnosis. Some existing measures apply to multi-stage diagnosis. However, implementation has limitations, and performance strongly depends on the distribution of diagnostic results. Considering the rule-in/out information provided by the Kullback-Leibler divergence, we propose a new measure that generalizes the total Kullback-Leibler (GTKL) divergence as an accuracy measure in the multi-stage diagnosis. We further examine the fact that the generalized measure can serve as an optimal cut-point selection criterion when the number of stages increases. Moreover, we conduct a series of simulation studies to compare existing measures’ power and optimal cut-point selection and performance, including the generalized Youden index, maximum absolute determinant, closest-to-perfection, and maximum volume. Furthermore, we illustrate the application of our measures and the comparison with other measures using an example of Alzheimer’s disease data. The results show GTKL’s outstanding performance in some situations. A detailed performance analysis of existing metrics is also presented throughout the document.