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An empirical likelihood confidence interval for the volume under ROC surface

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  • Wan, Shuwen

Abstract

ROC surface analysis was recently developed as an extension of ROC curve analysis to accommodate tests with three outcomes. The volume under ROC surface (VUS) is the most commonly used summary measure of the diagnostic accuracy of a test. In this paper, we develop an empirical likelihood approach for the inference on VUS. First we define an empirical likelihood ratio for VUS and show that its limiting distribution is a scaled chi-square distribution. We then obtain an empirical likelihood confidence interval for VUS. A small simulation study as well as analysis of a real example is also presented in this paper.

Suggested Citation

  • Wan, Shuwen, 2012. "An empirical likelihood confidence interval for the volume under ROC surface," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1463-1467.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1463-1467
    DOI: 10.1016/j.spl.2012.04.007
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    References listed on IDEAS

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    1. Margaret Sullivan Pepe & Tianxi Cai, 2004. "The Analysis of Placement Values for Evaluating Discriminatory Measures," Biometrics, The International Biometric Society, vol. 60(2), pages 528-535, June.
    2. Gengsheng Qin & Xiao-Hua Zhou, 2006. "Empirical Likelihood Inference for the Area under the ROC Curve," Biometrics, The International Biometric Society, vol. 62(2), pages 613-622, June.
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    Cited by:

    1. Yueheng An & Yichuan Zhao, 2018. "Jackknife empirical likelihood for the difference of two volumes under ROC surfaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 789-806, August.
    2. Wan, Shuwen & Zhang, Biao, 2015. "Using proportional odds models for semiparametric ROC surface estimation," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 74-79.

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