Joint Statistical Inference for the Area under the ROC Curve and Youden Index under a Density Ratio Model

Siyan Liu, Qinglong Tian, Yukun Liu () and Pengfei Li
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Siyan Liu: KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai 200062, China
Qinglong Tian: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Yukun Liu: KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai 200062, China
Pengfei Li: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Mathematics, 2024, vol. 12, issue 13, 1-21

Abstract: The receiver operating characteristic (ROC) curve is a valuable statistical tool in medical research. It assesses a biomarker’s ability to distinguish between diseased and healthy individuals. The area under the ROC curve ( A U C ) and the Youden index ( J ) are common summary indices used to evaluate a biomarker’s diagnostic accuracy. Simultaneously examining A U C and J offers a more comprehensive understanding of the ROC curve’s characteristics. In this paper, we utilize a semiparametric density ratio model to link the distributions of a biomarker for healthy and diseased individuals. Under this model, we establish the joint asymptotic normality of the maximum empirical likelihood estimator of ( A U C , J ) and construct an asymptotically valid confidence region for ( A U C , J ) . Furthermore, we propose a new test to determine whether a biomarker simultaneously exceeds prespecified target values of A U C 0 and J 0 with the null hypothesis H 0 : A U C ≤ A U C 0 or J ≤ J 0 against the alternative hypothesis H a : A U C > A U C 0 and J > J 0 . Simulation studies and a real data example on Duchenne Muscular Dystrophy are used to demonstrate the effectiveness of our proposed method and highlight its advantages over existing methods.

Keywords: AUC; bootstrap method; confidence region; density ratio model; empirical likelihood; Youden index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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