Pancreatic ductal adenocarcinoma (PDAC) is the most deadly cancer and currently there is strong clinical interest in novel biomarkers that contribute to its early detection. Assessing appropriately the accuracy of such biomarkers is a crucial issue and often one needs to take into account that many assays include biospecimens of individuals coming from three groups: healthy, chronic pancreatitis, and PDAC. The ROC surface is an appropriate tool for assessing the overall accuracy of a marker employed under such trichotomous settings. A decision/classification rule is often based on the so-called Youden index and its three-dimensional generalization. However, both the clinical and the statistical literature have not paid the necessary attention to the underlying false classification (FC) rates that are of equal or even greater importance. In this article we provide a framework to make inferences around all classification rates as well as comparisons. We explore the trinormal model, flexible models based on power transformations, and robust non-parametric alternatives. We provide a full framework for the construction of confidence intervals, regions, and spaces for joint inferences or for clinically meaningful points of interest. We further discuss the implications of costs related to different FCs. We evaluate our approaches through extensive simulations and illustrate them using data from a recent PDAC study conducted at the MD Anderson Cancer Center.
Keywords: 3-class classification; Box-Cox; ROC surface; Youden; costs; false class rates; kernel density estimators; monotone likelihood ratio; prevalence.
© 2022 John Wiley & Sons Ltd.