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Simultaneous confidence bands for survival functions from twice censorship

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  • Subramanian, Sundarraman

Abstract

When a failure time observation is right censored, it is not observed beyond a random right threshold. When a possibly right censored observation is further susceptible to a random left threshold, a twice censored observation results. Patilea and Rolin have proposed product limit estimators for survival functions from twice censored data. Simultaneous confidence bands (SCBs) for survival functions from twice censored data are constructed in a way that mimics the approach that Hollander, McKeague and Yang pursued for random right censoring. Their nonparametric likelihood ratio function is adjusted, providing the basis for constructing the SCBs. The critical value needed for the SCBs is obtained using the bootstrap, for which asymptotic justification is provided. The SCBs align nicely as “neighborhoods” of the Patilea–Rolin nonparametric survival function estimator, in much the same way the likelihood ratio SCBs under random censoring are the “neighborhoods” of the Kaplan–Meier estimator. A simulation study supports the effectiveness of the proposed method. An illustration is given using synthetic data.

Suggested Citation

  • Subramanian, Sundarraman, 2022. "Simultaneous confidence bands for survival functions from twice censorship," Statistics & Probability Letters, Elsevier, vol. 186(C).
  • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000797
    DOI: 10.1016/j.spl.2022.109494
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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. Subramanian, Sundarraman, 2021. "Median regression from twice censored data," Statistics & Probability Letters, Elsevier, vol. 168(C).
    4. 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.
    5. McKeague Ian W. & Zhao Yichuan, 2006. "Comparing Distribution Functions via Empirical Likelihood," The International Journal of Biostatistics, De Gruyter, vol. 1(1), pages 1-20, January.
    6. 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.
    7. Pao-sheng Shen, 2011. "Nonparametric estimators of the survival function with twice censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1207-1219, December.
    8. 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.
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