Confidence Intervals for the MADET Index and Its Corresponding Classification Thresholds Using Generalized Pivotal Quantities.

In medical contexts, especially in the diagnosis process of patients into different ordered stages of a disease (e.g., not diseased, early disease, and advanced disease) based on a continuous biomarker, the concept of the receiver operating characteristic (ROC) curve has been extended to that of the ROC surface and, consequently, the corresponding diagnostic performance measures as well. Specifically, the maximum absolute determinant (MADET) has been recently proposed, extending the classic concept of the Youden index. However, no method has been proposed for constructing confidence intervals (CIs) for the MADET index and its respective optimal cutoff points. In this work, we introduce an approach to construct CIs for these parameters based on the generalized pivotal quantity (GPQ) methodology assuming a trinormal model. A simulation study was conducted to evaluate the performance of the new CIs for the MADET index and its corresponding cut-off points. The results indicate a good performance in terms of coverage probability and average width for small sample sizes, unbalanced designs and different values across the range of the MADET index. This methodology was also applied to a real dataset on Alzheimer disease, which provides several biomarkers within the normality assumption, requiring or not a Box-Cox power transformation.