IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v109y2012icp254-263.html
   My bibliography  Save this article

Smoothed empirical likelihood for ROC curves with censored data

Author

Listed:
  • Yang, Hanfang
  • Zhao, Yichuan

Abstract

The receiver operating characteristic (ROC) curve is an attractive basis for the comparison of distribution functions between two populations. In this paper, we apply the censored empirical likelihood method with kernel smoothing to investigate the ROC curve. It is shown that the smoothed empirical likelihood ratio converges to a chi-square distribution, which is the well-known Wilks theorem. We also propose a bootstrap procedure for obtaining the censored empirical likelihood confidence band for the ROC curve. The performance of the proposed empirical likelihood method is illustrated through extensive simulation studies in terms of coverage probability and average length of confidence intervals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:254-263
    DOI: 10.1016/j.jmva.2012.03.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000711
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.03.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shen, Junshan & He, Shuyuan, 2006. "Empirical likelihood for the difference of two survival functions under right censorship," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 169-181, January.
    2. Zhao, Yichuan & Zhao, Meng, 2011. "Empirical likelihood for the contrast of two hazard functions with right censoring," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 392-401, March.
    3. Einmahl, J.H.J. & McKeague, I.W., 1999. "Confidence tubes for multiple quantile plots via empirical likelihood," Other publications TiSEM b64493f8-1c01-40fd-b16d-7, Tilburg University, School of Economics and Management.
    4. 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.
    5. Horváth, Lajos, 1983. "The rate of strong uniform consistency for the multivariate product-limit estimator," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 202-209, March.
    6. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
    7. Anna N. Angelos Tosteson & Colin B. Begg, 1988. "A General Regression Methodology for ROC Curve Estimation," Medical Decision Making, , vol. 8(3), pages 204-215, August.
    8. Li, Gang, 1995. "On nonparametric likelihood ratio estimation of survival probabilities for censored data," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 95-104, November.
    9. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    10. McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
    11. Junshan Shen & Shuyuan He, 2007. "Empirical likelihood for the difference of quantiles under censorship," Statistical Papers, Springer, vol. 48(3), pages 437-457, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Yichuan & Zhao, Meng, 2011. "Empirical likelihood for the contrast of two hazard functions with right censoring," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 392-401, March.
    2. Subramanian, Sundarraman, 2022. "Simultaneous confidence bands for survival functions from twice censorship," Statistics & Probability Letters, Elsevier, vol. 186(C).
    3. Zhou, Mai & Zhu, Shihong, 2015. "Empirical likelihood confidence band for the difference of survival functions under proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 228-235.
    4. Zhao, Meng & Zhao, Yichuan & McKeague, Ian W., 2015. "Empirical likelihood inference for the odds ratio of two survival functions under right censoring," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 304-312.
    5. Shihong Zhu & Yifan Yang & Mai Zhou, 2015. "A note on the empirical likelihood confidence band for hazards ratio with covariate adjustment," Biometrics, The International Biometric Society, vol. 71(3), pages 859-563, September.
    6. Nubyra Ahmed & Sundarraman Subramanian, 2016. "Semiparametric simultaneous confidence bands for the difference of survival functions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 504-530, October.
    7. Junshan Shen & Shuyuan He, 2007. "Empirical likelihood for the difference of quantiles under censorship," Statistical Papers, Springer, vol. 48(3), pages 437-457, September.
    8. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    9. Shen, Junshan & He, Shuyuan, 2006. "Empirical likelihood for the difference of two survival functions under right censorship," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 169-181, January.
    10. McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
    11. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    12. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    13. Robert Drake & Apratim Guha, 2014. "A mutual information-based k -sample test for discrete distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 2011-2027, September.
    14. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    15. Junshan Shen & Shuyuan He, 2008. "Empirical likelihood confidence intervals for hazard and density functions under right censorship," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 575-589, September.
    16. Bin Dong & David E. Matthews, 2012. "Empirical Likelihood for Cumulative Hazard Ratio Estimation with Covariate Adjustment," Biometrics, The International Biometric Society, vol. 68(2), pages 408-418, June.
    17. Subramanian, Sundarraman, 2016. "Bootstrap likelihood ratio confidence bands for survival functions under random censorship and its semiparametric extension," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 58-81.
    18. Jimin Lee & Seunggeun Hyun, 2011. "Confidence bands for the difference of two survival functions under the additive risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 785-797, February.
    19. Sundarraman Subramanian, 2020. "Function-based hypothesis testing in censored two-sample location-scale models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 183-213, January.
    20. Cheng, Guang & Zhao, Yichuan & Li, Bo, 2012. "Empirical likelihood inferences for the semiparametric additive isotonic regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 172-182.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:254-263. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.