Bivariate Marker Measurements and ROC Analysis

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Shanshan Li*+ and Mei-Cheng Wang
• Companies: The Johns Hopkins University and The Johns Hopkins University
• Keywords: Concordance probability ; Correlated ROC curves ; Prediction accuracy ; U-statistics

Abstract

This paper considers receiver operating characteristic (ROC) analysis for bivariate marker measurements. The research interest is to extend rules and tools from univariate marker to bivariate marker setting for evaluating predictive accuracy of markers. Using an and-or classifier, an ROC function together with a weighted ROC function (WROC) and their conjugate counterparts are proposed for examining the performance of bivariate markers. The proposed functions evaluate the performance of and-or classifier among all possible combinations of marker values, and are ideal measures for understanding the predictability of biomarkers in target population. Specific features of ROC and WROC functions and other related statistics are discussed in comparison with those familiar properties for univariate marker. Nonparametric methods are developed for estimating ROC-related functions, (partial) area under curve and concordance probability. The inferential results developed in this paper also extend to multivariate marker measurements with a sequence of combined and-or classifier.