Diagnostic tests with multinomial outcomes are often used in medical decision making. Examples include cancer type classification, disease staging, and severity assessment, just to name a few. Since errors may occur in any diagnostic process based on data, the accuracy of a polytomous diagnostic test is as important as that of a dichotomous one. However, current statistical methods are not well developed for the evaluation of diagnostic tests that result in more than a positive/negative result.
We extend the principle of dichotomous diagnostics to polytomous cases by defining accuracy measurements for a K-category diagnostic test as probability of test = i | true category = i, where i = 1,2, … K and discuss the interpretability of these measurements, including the impact from omitted information, i.e., where test ^= i | true category = i. We explore methods of determining the K – 1 cutoff points by standard classification methods and an ROC-like approach. We conclude that a benefit-risk based approach can be readily extended to the evaluation of polytomous diagnostic tests, allows the use of partially correct outcomes, and can be useful in optimizing cutoff points.