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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Siyan Liu & Qinglong Tian & Yukun Liu & Pengfei Li, 2024. "Joint Statistical Inference for the Area under the ROC Curve and Youden Index under a Density Ratio Model," Mathematics, MDPI, vol. 12(13), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2118-:d:1429798
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    References listed on IDEAS

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    1. Lori E. Dodd & Margaret S. Pepe, 2003. "Partial AUC Estimation and Regression," Biometrics, The International Biometric Society, vol. 59(3), pages 614-623, September.
    2. Zhang, Biao, 2006. "A semiparametric hypothesis testing procedure for the ROC curve area under a density ratio model," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1855-1876, April.
    3. Leonidas E. Bantis & Christos T. Nakas & Benjamin Reiser, 2014. "Construction of confidence regions in the ROC space after the estimation of the optimal Youden index-based cut-off point," Biometrics, The International Biometric Society, vol. 70(1), pages 212-223, March.
    4. Jing Qin, 2003. "Using logistic regression procedures for estimating receiver operating characteristic curves," Biometrika, Biometrika Trust, vol. 90(3), pages 585-596, September.
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