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Smooth estimation of ROC curve in the presence of auxiliary information

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Abstract

Receiver operating characteristic (ROC) curve is often used to study and compare two-sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error (MSE). Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators.

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Author information

Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yong Zhou & Yunbei Ma

  2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Yong Zhou

  3. Department of Biostatistics, University of North Carolina Chapel Hill, Chapel Hill, NC, 27599-7420, USA

    Haibo Zhou

Authors
  1. Yong Zhou
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  2. Haibo Zhou
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  3. Yunbei Ma
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Corresponding author

Correspondence to Yong Zhou.

Additional information

This research was partially supported by National Natural Science Funds for Distinguished Young Scholar under Grant No. 70825004 and National Natural Science Foundation of China (NSFC) under Grant No. 10731010, the National Basic Research Program under Grant No. 2007CB814902, Creative Research Groups of China under Grant No.10721101 and Shanghai University of Finance and Economics through Project 211 Phase III and Shanghai Leading Academic Discipline Project under Grant No. B803.

This paper was recommended for publication by Editor Guohua ZOU.

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Zhou, Y., Zhou, H. & Ma, Y. Smooth estimation of ROC curve in the presence of auxiliary information. J Syst Sci Complex 24, 919–944 (2011). https://doi.org/10.1007/s11424-011-7095-7

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  • DOI: https://doi.org/10.1007/s11424-011-7095-7

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