Abstract:
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Receiver operating characteristic (ROC) curve and its summary statistics (e.g. the area under curve AU C), are commonly used to evaluate the diagnostic accuracy for disease processes with binary classi- fication. The ROC curve has been extended to ROC surface for scenarios with three ordinal classes or to hyper-surface for scenarios with more than three classes. For classifier under tree or umbrella order- ing in which the marker measurement for one class is lower or higher than those for the other classes, the commonly adopted diagnostic measures are the naive AU C (N AU C) based on a pooled class of all the unordered classes and the umbrella volume (U V ) based on the concept of volume under surface. However, both N AU C and U V have some limitations. For example, N AU C depends on the sampling weights for all the classes in population, and U V has only been introduced for three-class settings. In this article, we initiate the idea of a new ROC framework for tree or umbrella ordering (denoted as T ROC), and propose the area under T ROC curve (denoted as T AU C) as an appropriate diagnostic measure. The proposed T ROC and T AU C share many nice features with the traditional ROC an
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