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Stat Med. 2016 Sep 20;35(21):3792-809. doi: 10.1002/sim.6956. Epub 2016 Apr 5.

Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.

Fong Y1,2, Yin S1, Huang Y1,2.

Author information

1
Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N., M2-B500, Seattle, 98109, WA, U.S.A.
2
Department of Biostatistics, University of Washington, Seattle, 98195, WA, U.S.A.

Abstract

In biomedical studies, it is often of interest to classify/predict a subject's disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on area under the receiver operating characteristic curve (AUC). Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in suboptimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data are generated from a semiparametric generalized linear model, just as the smoothed AUC method. Through simulation studies and real data examples, we demonstrate that RAUC outperforms smooth AUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial.

KEYWORDS:

AUC; ROC curve; biomarker combination; classification; kernel; ramp loss

PMID:
27058981
PMCID:
PMC4965290
DOI:
10.1002/sim.6956
[Indexed for MEDLINE]
Free PMC Article

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