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Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach

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  • Xiaodong Luo
  • Wei Yann Tsai

Abstract

To estimate the lifetime distribution of right-censored length-biased data, we propose a pseudo-partial likelihood approach that allows us to derive two nonparametric estimators. With its closed-form estimators and explicit limiting variances, this approach retains the simplicity of conditional analysis, and has only a small efficiency loss compared with the unconditional analysis. Under some regularity conditions, we show that the two estimators are uniformly consistent and converge weakly to Gaussian processes. A simulation study demonstrates that the proposed estimators have satisfactory finite-sample performance. Application to an Alzheimer's disease study is reported. Copyright 2009, Oxford University Press.

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  • Xiaodong Luo & Wei Yann Tsai, 2009. "Nonparametric estimation for right-censored length-biased data: a pseudo-partial likelihood approach," Biometrika, Biometrika Trust, vol. 96(4), pages 873-886.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:873-886
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    File URL: http://hdl.handle.net/10.1093/biomet/asp064
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    Citations

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    Cited by:

    1. 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.
    2. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    3. Gongjun Xu & Tony Sit & Lan Wang & Chiung-Yu Huang, 2017. "Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1571-1586, October.
    4. 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.
    5. Yu-Jen Cheng & Mei-Cheng Wang, 2012. "Estimating Propensity Scores and Causal Survival Functions Using Prevalent Survival Data," Biometrics, The International Biometric Society, vol. 68(3), pages 707-716, September.
    6. 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.
    7. Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2015. "Double Bias: Estimation of Causal Effects from Length-Biased Samples in the Presence of Confounding," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 69-89, May.
    8. 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.
    9. 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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