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Width-scaled confidence bands for survival functions

Author

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  • McKeague, Ian W.
  • Zhao, Yichuan

Abstract

A popular simultaneous confidence band for survival functions is the equal precision band of Nair [1984. Confidence bands for survival functions with censored data: a comparative study. Technometrics 26, 265-275] This band is found by adjusting the level of Wald-type pointwise confidence intervals centered on the Kaplan-Meier estimator. The present paper develops a complementary method of adjusting pointwise confidence intervals to produce a simultaneous band. Our approach is to scale the width, rather than the level, of the pointwise confidence intervals. The resulting adjustment of the pointwise band, called a width-scaled band, provides an attractive alternative to the equal precision band. Empirical likelihood-based width-scaled bands are studied in the one- and two-sample censored data settings. An example with real data is included.

Suggested Citation

  • McKeague, Ian W. & Zhao, Yichuan, 2006. "Width-scaled confidence bands for survival functions," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 327-339, February.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:4:p:327-339
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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.
    4. Gang Li & Ingrid Van Keilegom, 2002. "Likelihood Ratio Confidence Bands in Non–parametric Regression with Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 547-562, September.
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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. 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.
    4. Yang, Song & Zhao, Yichuan, 2007. "Testing treatment effect by combining weighted log-rank tests and using empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1385-1393, July.
    5. 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.
    6. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
    7. Yichuan Zhao & Ali Jinnah, 2012. "Inference for Cox’s regression models via adjusted empirical likelihood," Computational Statistics, Springer, vol. 27(1), pages 1-12, March.
    8. 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.
    9. 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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