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Model-based likelihood ratio confidence intervals for survival functions

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  • Subramanian, Sundarraman

Abstract

We introduce an adjusted likelihood ratio procedure for computing pointwise confidence intervals for survival functions from censored data. The test statistic, scaled by a ratio of two variance quantities, is shown to converge to a chi-squared distribution with one degree of freedom. The confidence intervals are seen to be a neighborhood of a semiparametric survival function estimator and are shown to have correct empirical coverage. Numerical studies also indicate that the proposed intervals have smaller estimated mean lengths in comparison to the ones that are produced as a neighborhood of the Kaplan–Meier estimator. We illustrate our method using a lung cancer data set.

Suggested Citation

  • Subramanian, Sundarraman, 2012. "Model-based likelihood ratio confidence intervals for survival functions," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 626-635.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:626-635
    DOI: 10.1016/j.spl.2011.11.028
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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. Dikta, Gerhard & Kvesic, Marsel & Schmidt, Christian, 2006. "Bootstrap Approximations in Model Checks for Binary Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 521-530, June.
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    Cited by:

    1. 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.
    2. Bhattacharya, Rianka & Subramanian, Sundarraman, 2014. "Two-sample location–scale estimation from semiparametric random censorship models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 25-38.
    3. Shoubhik Mondal & Sundarraman Subramanian, 2016. "Simultaneous confidence bands for Cox regression from semiparametric random censorship," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 122-144, January.
    4. Mondal, Shoubhik & Subramanian, Sundarraman, 2014. "Model assisted Cox regression," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 281-303.
    5. 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.

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