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Empirical likelihood for the difference of two survival functions under right censorship

Author

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  • Shen, Junshan
  • He, Shuyuan

Abstract

For right censored data, empirical likelihood method is used to construct the confidence band for the difference of two survival functions. The empirical log-likelihood ratio is derived and its asymptotic distribution is obtained. Simulation studies show that the likelihood confidence band based on the empirical likelihood method performed better than that of the Hall-Wellner type band in terms of the coverage accuracy, especially for small size of observation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:2:p:169-181
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Subramanian, Sundarraman, 2022. "Simultaneous confidence bands for survival functions from twice censorship," Statistics & Probability Letters, Elsevier, vol. 186(C).
    6. 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.
    7. 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.

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