Receiver Operating Characteristic Surfaces: Inference and Applications

• Activity Number: 383
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Christopher A. Beck*+ and Michael P. McDermott
• Companies: University of Rochester Medical Center and University of Rochester
• Keywords: diagnostic test ; diagnostic accuracy ; discrimination ; compositional data

Abstract

Receiver operating characteristic (ROC) curves are commonly used to describe the performance of a diagnostic test in terms of discriminating between healthy and diseased populations. A popular index of the discriminating ability or accuracy of the diagnostic test is the area under the ROC curve. When there are three or more populations, the concept of an ROC curve can be generalized to that of an ROC surface, with the volume under the ROC surface (VUS) serving as an index of diagnostic accuracy. This paper discusses parametric and nonparametric methods for estimating ROC surfaces and VUS's given three-part compositional data that are of the form (p, q, 1-p-q), with each coordinate representing a guessed probability that the experimental unit arose from the corresponding population. This type of compositional data can be plotted in a ternary diagram, an equilateral triangle with each vertex representing one of the three unit vectors. A classification rule partitions this triangle into three regions, with data points classified according to which region they fall into. Several families of classification rules are discussed. Examples are provided to illustrate the proposed methods.