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Nonparametric estimation of the cumulative incidence function for doubly-truncated and interval-censored competing risks data

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  • Pao-sheng Shen

    (Tunghai University)

Abstract

Interval sampling is widely used for collection of disease registry data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated data if the failure time can be observed exactly and doubly truncated and interval censored (DTIC) data if the failure time is known only to lie within an interval. In this article, we consider nonparametric estimation of the cumulative incidence functions (CIF) using doubly-truncated and interval-censored competing risks (DTIC-C) data obtained from interval sampling scheme. Using the approach of Shen (Stat Methods Med Res 31:1157–1170, 2022b), we first obtain the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of failure time ignoring failure types. Using the NPMLE, we proposed nonparametric estimators of the CIF with DTIC-C data and establish consistency of the proposed estimators. Simulation studies show that the proposed estimator performs well for finite sample size.

Suggested Citation

  • Pao-sheng Shen, 2025. "Nonparametric estimation of the cumulative incidence function for doubly-truncated and interval-censored competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(1), pages 76-101, January.
    • Handle: RePEc:spr:lifeda:v:31:y:2025:i:1:d:10.1007_s10985-024-09641-y
    DOI: 10.1007/s10985-024-09641-y
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    References listed on IDEAS

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    1. Moreira, C. & de Uña-Álvarez, J. & Meira-Machado, L., 2016. "Nonparametric regression with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 294-307.
    2. Balakrishnan, N. & Mitra, Debanjan, 2012. "Left truncated and right censored Weibull data and likelihood inference with an illustration," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4011-4025.
    3. Moreira, Carla & Van Keilegom, Ingrid, 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," LIDAM Reprints ISBA 2013018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Qiqing Yu, 2023. "The generalised MLE with truncated interval-censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(2), pages 266-282, April.
    5. Pao-sheng Shen, 2013. "Regression analysis of interval censored and doubly truncated data with linear transformation models," Computational Statistics, Springer, vol. 28(2), pages 581-596, April.
    6. Hong Zhu & Mei-Cheng Wang, 2014. "Nonparametric inference on bivariate survival data with interval sampling: association estimation and testing," Biometrika, Biometrika Trust, vol. 101(3), pages 519-533.
    7. 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.
    8. Carla Moreira & Jacobo de Uña-Álvarez, 2010. "Bootstrapping the NPMLE for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 567-583.
    9. 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.
    10. 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.
    11. Carla Moreira & Jacobo Uña-Álvarez & Ingrid Keilegom, 2014. "Goodness-of-fit tests for a semiparametric model under random double truncation," Computational Statistics, Springer, vol. 29(5), pages 1365-1379, October.
    12. Moreira, C. & Van Keilegom, I., 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 107-123.
    13. J Xiao & M G Hudgens, 2019. "On nonparametric maximum likelihood estimation with double truncation," Biometrika, Biometrika Trust, vol. 106(4), pages 989-996.
    14. Moreira, Carla & de Una-Alvarez, Jacobo & Van Keilegom, Ingrid, 2014. "Goodness-of-fit tests for a semiparametric model under random double truncation," LIDAM Reprints ISBA 2014039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. 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).
    16. Hong Zhu & Mei-Cheng Wang, 2012. "Analysing bivariate survival data with interval sampling and application to cancer epidemiology," Biometrika, Biometrika Trust, vol. 99(2), pages 345-361.
    17. Moreira, Carla & de Uña-Álvarez, Jacobo & Crujeiras, Rosa M., 2010. "DTDA: An R Package to Analyze Randomly Truncated Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 37(i07).
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