Hypervolume under ROC manifold for discrete biomarkers with ties

Abstract

Medical multi-category diagnostic problems may involve discrete biomarkers. Many traditional accuracy measures are based on the assumption that all biomarkers follow continuous distributions and consequently may underestimate the true discrimination ability of the discrete markers. In particular, we focus on Hypervolume Under ROC Manifold (HUM) in this paper and propose an extension of the familiar continuous version of HUM to incorporate discrete biomarkers with ties. Statistical estimation and inference procedures are proposed along with asymptotic properties. We carry out simulation studies to examine the performance of our proposed estimators for the new HUM measure. A real medical example is analysed to illustrate our methodology.

Keywords:

• Diagnostic medicine
• discrete distribution
• biomarkers
• multi-category classification
• hypervolume under ROC manifold

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Feng's work is supported by NSFC (grant number 11771418). Li's work was partly supported by Academic Research Funds R-155-000-205-114, R-155-000-195-114 and Tier 2 MOE funds in Singapore MOE2017-T2-2-082: R-155-000-197-112 (Direct cost) and R-155-000-197-113 (IRC).