Abstract

Multiple biomarkers are often combined for more accurate disease diagnosis. For

this purpose, one popular performance metric is the area under the receiving operating characteristic (ROC) curve (AUC). Optimizing the empirical AUC over

linear combinations of biomarkers, however, faces two primary challenges. First,

AUC is scale-invariant to the linear combinations, creating difficulties in both

the computation and asymptotic study. Most available approaches actually consider a restricted problem by setting one coefficient to a constant. Second, the

empirical AUC is piecewise-constant and standard gradient-based computational

algorithms are not applicable. Existing methods maximize kernel-smoothed AUC

instead, but they can be sensitive to bandwidth choice. In this article, we tackle

these challenges by developing a new empirical AUC maximization method. Computationally efficient algorithms are provided for both the point and variance

estimation of the estimated combination coefficients. Simulation studies show

good computational and statistical performance of the proposed methods. An

illustration is provided with a clinical application.

Information

Preprint No.SS-2024-0195
Manuscript IDSS-2024-0195
Complete AuthorsYuxuan Chen, Yijian Huang
Corresponding AuthorsYuxuan Chen
Emailsyuxuan.chen@emory.edu

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Acknowledgments

We sincerely thank the reviewers for their thoughtful comments and constructive suggestions, which have helped to enhance the quality of this

manuscript. The authors were supported in part by NIH grants R01 CA230268

and P30 AI050409.

Supplementary Materials

The online Supplementary Material contains additional simulation results.

Supplementary materials are available for download.