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Nonparametric quantile inference with competing–risks data

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  • L. Peng
  • J. P. Fine

Abstract

A conceptually simple quantile inference procedure is proposed for cause-specific failure probabilities with competing risks data. The quantiles are defined using the cumulative incidence function, which is intuitively meaningful in the competing–risks set–up. We establish the uniform consistency and weak convergence of a nonparametric estimator of this quantile function. These results form the theoretical basis for extensions of standard one–sample and two–sample quantile inference for independently censored data. This includes the construction of confidence intervals and bands for the quantile function, and two–sample tests. Simulation studies and a real data example illustrate the practical utility of the methodology. Copyright 2007, Oxford University Press.

Suggested Citation

  • L. Peng & J. P. Fine, 2007. "Nonparametric quantile inference with competing–risks data," Biometrika, Biometrika Trust, vol. 94(3), pages 735-744.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:735-744
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    File URL: http://hdl.handle.net/10.1093/biomet/asm059
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    Citations

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    Cited by:

    1. Bo Wei & Limin Peng & Mei‐Jie Zhang & Jason P. Fine, 2021. "Estimation of causal quantile effects with a binary instrumental variable and censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 559-578, July.
    2. Soni, Pooja & Dewan, Isha & Jain, Kanchan, 2012. "Nonparametric estimation of quantile density function," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3876-3886.
    3. Zhang, Feipeng & Tan, Zhong, 2015. "A new nonparametric quantile estimate for length-biased data with competing risks," Economics Letters, Elsevier, vol. 137(C), pages 10-12.
    4. P. Sankaran & N. Midhu, 2016. "Testing exponentiality using mean residual quantile function," Statistical Papers, Springer, vol. 57(1), pages 235-247, March.
    5. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    6. Peng Liu & Yixin Wang & Yong Zhou, 2015. "Quantile residual lifetime with right-censored and length-biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 999-1028, October.
    7. Lee, Minjung & Han, Junhee, 2016. "Covariate-adjusted quantile inference with competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 57-63.
    8. Julien Worms & Rym Worms, 2018. "Extreme value statistics for censored data with heavy tails under competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 849-889, October.
    9. S. R. Haile & J.-H. Jeong & X. Chen & Y. Cheng, 2016. "A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2239-2253, September.
    10. Sankaran, P.G. & Unnikrishnan Nair, N. & Sreedevi, E.P., 2010. "A quantile based test for comparing cumulative incidence functions of competing risks models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 886-891, May.
    11. Li, Ruosha & Peng, Limin, 2014. "Varying coefficient subdistribution regression for left-truncated semi-competing risks data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 65-78.

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