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Smoothed jackknife empirical likelihood inference for the difference of ROC curves

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  • Yang, Hanfang
  • Zhao, Yichuan

Abstract

For the comparison of two diagnostic markers at a flexible specificity, people apply the difference of two correlated receiver operating characteristic (ROC) curves to identify the diagnostic test with stronger discrimination ability. In this paper, we employ the jackknife empirical likelihood (JEL) method to construct confidence intervals for the difference of two correlated continuous-scale ROC curves. Using the jackknife pseudo-sample, we can avoid estimating several nuisance variables which have to be estimated in the existing methods. We prove that the smoothed jackknife empirical log likelihood ratio is asymptotically chi-squared distributed. Furthermore, the simulation studies in terms of the coverage probability and the average length of confidence intervals show good performance in small samples with a moderate computational cost. A real data set is used to illustrate our method.

Suggested Citation

  • Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:270-284
    DOI: 10.1016/j.jmva.2012.10.010
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    3. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    4. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    5. Yang, Hanfang & Zhao, Yichuan, 2012. "Smoothed empirical likelihood for ROC curves with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 254-263.
    6. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
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    Cited by:

    1. Zhong, Ping-Shou & Chen, Sixia, 2014. "Jackknife empirical likelihood inference with regression imputation and survey data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 193-205.
    2. 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.
    3. Hanfang Yang & Yichuan Zhao, 2017. "Smoothed jackknife empirical likelihood for the difference of two quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1059-1073, October.
    4. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
    6. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    7. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    8. Xiaohui Yuan & Huixian Li & Tianqing Liu, 2021. "Empirical likelihood inference for rank regression with doubly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 25-73, March.
    9. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    10. Chen, Sixia & Haziza, David, 2018. "Jackknife empirical likelihood method for multiply robust estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 258-268.
    11. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.

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