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Nonparametric estimation for competing risks survival data subject to left truncation and interval censoring

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  • Pao-sheng Shen

    (Tunghai University)

Abstract

In this article, we consider nonparametric estimation of the cumulative incidence function (CIF) for left-truncated and interval-censored competing risks (LT-ICC) data. To reduce the bias of the pseudo-likelihood estimator (PLE) of CIF in the literature, we proposed two alternative estimators. The first estimator, called the modified PLE (MPLE), is obtained based on the modified NPMLE of F(t). The second estimator, called the modified maximum likelihood estimator (MMLE), is derived using modified likelihood functions for LT-ICC data, where the left endpoints of the intervals for left-censored observations with failure type j are the maximum of left-truncated variables and the estimated left endpoint of the support of the observations. Simulation studies show that the MPLE and MMLE are less biased than the PLE for most of the cases considered and their standard deviations are significantly smaller than that of the PLE.

Suggested Citation

  • Pao-sheng Shen, 2022. "Nonparametric estimation for competing risks survival data subject to left truncation and interval censoring," Computational Statistics, Springer, vol. 37(1), pages 29-42, March.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:1:d:10.1007_s00180-021-01111-5
    DOI: 10.1007/s00180-021-01111-5
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    References listed on IDEAS

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    1. Pao-Sheng Shen, 2020. "Correction to: Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 893-894, October.
    2. Pao-Sheng Shen, 2020. "Nonparametric estimators of survival function under the mixed case interval-censored model with left truncation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 624-637, July.
    3. Anton Schick & Qiqing Yu, 2000. "Consistency of the GMLE with Mixed Case Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 45-55, March.
    4. Scheike, Thomas H. & Zhang, Mei-Jie, 2011. "Analyzing Competing Risk Data Using the R timereg Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i02).
    5. Michael G. Hudgens & Glen A. Satten & Ira M. Longini, 2001. "Nonparametric Maximum Likelihood Estimation for Competing Risks Survival Data Subject to Interval Censoring and Truncation," Biometrics, The International Biometric Society, vol. 57(1), pages 74-80, March.
    6. Michael G. Hudgens, 2005. "On nonparametric maximum likelihood estimation with interval censoring and left truncation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 573-587, September.
    7. Lu Mao & D. Y. Lin, 2017. "Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 573-587, March.
    8. Sangbum Choi & Xuelin Huang, 2014. "Maximum likelihood estimation of semiparametric mixture component models for competing risks data," Biometrics, The International Biometric Society, vol. 70(3), pages 588-598, September.
    9. M. Mahdizadeh & E. Strzalkowska-Kominiak, 2017. "Resampling based inference for a distribution function using censored ranked set samples," Computational Statistics, Springer, vol. 32(4), pages 1285-1308, December.
    10. Junru Ren & Wenhao Gui, 2021. "Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution," Computational Statistics, Springer, vol. 36(1), pages 479-513, March.
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