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Nonparametric estimation for length-biased and right-censored data

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  • Chiung-Yu Huang
  • Jing Qin

Abstract

This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory. Copyright 2011, Oxford University Press.

Suggested Citation

  • Chiung-Yu Huang & Jing Qin, 2011. "Nonparametric estimation for length-biased and right-censored data," Biometrika, Biometrika Trust, vol. 98(1), pages 177-186.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:177-186
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    File URL: http://hdl.handle.net/10.1093/biomet/asq069
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    Cited by:

    1. Chi Hyun Lee & Jing Ning & Yu Shen, 2018. "Analysis of restricted mean survival time for length†biased data," Biometrics, The International Biometric Society, vol. 74(2), pages 575-583, June.
    2. Yi Xiong & W. John Braun & X. Joan Hu, 2021. "Estimating duration distribution aided by auxiliary longitudinal measures in presence of missing time origin," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 388-412, July.
    3. Ahmadi, Jafar & Doostparast, Mahdi & Parsian, Ahmad, 2012. "Estimation with left-truncated and right censored data: A comparison study," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1391-1400.
    4. Shi, Jianhua & Ma, Huijuan & Zhou, Yong, 2018. "The nonparametric quantile estimation for length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 150-158.
    5. Xuerong Chen & Yeqian Liu & Jianguo Sun & Yong Zhou, 2016. "Semiparametric Quantile Regression Analysis of Right-censored and Length-biased Failure Time Data with Partially Linear Varying Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 921-938, December.
    6. Arup Bose & Santanu Dutta, 2022. "Kernel based estimation of the distribution function for length biased data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 269-287, April.
    7. Ma, Huijuan & Zhang, Feipeng & Zhou, Yong, 2015. "Composite estimating equation approach for additive risk model with length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 45-53.
    8. Chengbo Li & Yong Zhou, 2021. "The estimation for the general additive–multiplicative hazard model using the length-biased survival data," Statistical Papers, Springer, vol. 62(1), pages 53-74, February.
    9. Yifan He & Yong Zhou, 2020. "Nonparametric and semiparametric estimators of restricted mean survival time under length-biased sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 761-788, October.
    10. Shi, Jianhua & Chen, Xiaoping & Zhou, Yong, 2015. "The strong representation for the nonparametric estimator of length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 49-57.
    11. Jacobo Uña-Álvarez, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 414-418, September.
    12. Kwun Chuen Gary Chan, 2017. "Acceleration of Expectation-Maximization algorithm for length-biased right-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 102-112, January.
    13. Zhang, Feipeng & Peng, Heng & Zhou, Yong, 2016. "Composite partial likelihood estimation for length-biased and right-censored data with competing risks," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 160-176.
    14. Zhang, Feipeng & Yang, Jiejing & Ye, Min, 2020. "A nonparametric maximum likelihood estimation for biased-sampling data with zero-inflated truncation," Economics Letters, Elsevier, vol. 194(C).

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