IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v22y2016i1d10.1007_s10985-014-9308-6.html
   My bibliography  Save this article

A consistent NPMLE of the joint distribution function with competing risks data under the dependent masking and right-censoring model

Author

Listed:
  • Jiahui Li

    (SUNY
    Celgene Corporation)

  • Qiqing Yu

    (SUNY)

Abstract

Dinse (Biometrics, 38:417–431, 1982) provides a special type of right-censored and masked competing risks data and proposes a non-parametric maximum likelihood estimator (NPMLE) and a pseudo MLE of the joint distribution function $$F$$ F with such data. However, their asymptotic properties have not been studied so far. Under the extention of either the conditional masking probability (CMP) model or the random partition masking (RPM) model (Yu and Li, J Nonparametr Stat 24:753–764, 2012), we show that (1) Dinse’s estimators are consistent if $$F$$ F takes on finitely many values and each point in the support set of $$F$$ F can be observed; (2) if the failure time is continuous, the NPMLE is not uniquely determined, and the standard approach (which puts weights only on one element in each observed set) leads to an inconsistent NPMLE; (3) in general, Dinse’s estimators are not consistent even under the discrete assumption; (4) we construct a consistent NPMLE. The consistency is given under a new model called dependent masking and right-censoring model. The CMP model and the RPM model are indeed special cases of the new model. We compare our estimator to Dinse’s estimators through simulation and real data. Simulation study indicates that the consistent NPMLE is a good approximation to the underlying distribution for moderate sample sizes.

Suggested Citation

  • Jiahui Li & Qiqing Yu, 2016. "A consistent NPMLE of the joint distribution function with competing risks data under the dependent masking and right-censoring model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 63-99, January.
    • Handle: RePEc:spr:lifeda:v:22:y:2016:i:1:d:10.1007_s10985-014-9308-6
    DOI: 10.1007/s10985-014-9308-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-014-9308-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10985-014-9308-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sanjib Basu & Ananda Sen & Mousumi Banerjee, 2003. "Bayesian analysis of competing risks with partially masked cause of failure," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 77-93, January.
    2. B. Reiser & I. Guttman & Dennis K. J. Lin & Frank M. Guess & John S. Usher, 1995. "Bayesian Inference for Masked System Lifetime Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 79-90, March.
    3. Qiqing Yu & G. Wong & Hao Qin & Jiaping Wang, 2012. "Random partition masking model for censored and masked competing risks data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 69-85, February.
    4. 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.
    5. Wong, George Y. C. & Yu, Qiqing, 1999. "Generalized MLE of a Joint Distribution Function with Multivariate Interval-Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 155-166, May.
    6. Qiqing Yu & Jiahui Li, 2012. "THE NPMLE of the joint distribution function with right-censored and masked competing risks data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 753-764.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pavlides, Marios G. & Wellner, Jon A., 2012. "Nonparametric estimation of multivariate scale mixtures of uniform densities," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 71-89.
    2. Kuo, Lynn & Yang, Tae Young, 2000. "Bayesian reliability modeling for masked system lifetime data," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 229-241, April.
    3. Daniel Nevo & Reiko Nishihara & Shuji Ogino & Molin Wang, 2018. "The competing risks Cox model with auxiliary case covariates under weaker missing-at-random cause of failure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 425-442, July.
    4. Kozumi, Hideo, 2004. "Posterior analysis of latent competing risk models by parallel tempering," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 441-458, June.
    5. Louzada, Francisco & Roman, Mari & Cancho, Vicente G., 2011. "The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2516-2524, August.
    6. Chanseok Park & Min Wang, 2024. "Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm," Mathematics, MDPI, vol. 12(11), pages 1-17, June.
    7. Halina Frydman & Michael Szarek, 2009. "Nonparametric Estimation in a Markov “Illness–Death” Process from Interval Censored Observations with Missing Intermediate Transition Status," Biometrics, The International Biometric Society, vol. 65(1), pages 143-151, March.
    8. Basu, Sanjib & Ebrahimi, Nader, 2008. "A note on a transformation under censoring with application to partial least squares regression," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1161-1164, August.
    9. David B. Dunson & Gregg E. Dinse, 2002. "Bayesian Models for Multivariate Current Status Data with Informative Censoring," Biometrics, The International Biometric Society, vol. 58(1), pages 79-88, March.
    10. Lu Mao & Dan-Yu Lin & Donglin Zeng, 2017. "Semiparametric regression analysis of interval-censored competing risks data," Biometrics, The International Biometric Society, vol. 73(3), pages 857-865, September.
    11. Wang, Yong, 2008. "Dimension-reduced nonparametric maximum likelihood computation for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2388-2402, January.
    12. Audrey Boruvka & Richard J. Cook, 2015. "A Cox-Aalen Model for Interval-censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 414-426, June.
    13. Gürler, Ülkü & Deniz Yenigün, C., 2011. "Full and conditional likelihood approaches for hazard change-point estimation with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2856-2870, October.
    14. Tamalika Koley & Anup Dewanji, 2019. "Revisiting Non-Parametric Maximum Likelihood Estimation of Current Status Data with Competing Risks," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 39-59, June.
    15. Yuet-Yee Wong, Linda & Yu, Qiqing, 2007. "A bivariate interval censorship model for partnership formation," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 370-383, February.
    16. 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.
    17. Li, Chenxi, 2016. "Cause-specific hazard regression for competing risks data under interval censoring and left truncation," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 197-208.
    18. Michael G. Hudgens & Marloes H. Maathuis & Peter B. Gilbert, 2007. "Nonparametric Estimation of the Joint Distribution of a Survival Time Subject to Interval Censoring and a Continuous Mark Variable," Biometrics, The International Biometric Society, vol. 63(2), pages 372-380, June.
    19. Ebrahimi, Nader & Shehadeh, Mahmoud, 2015. "Assessing the reliability of components with micro- and nano-structures when they are part a multi-scale system," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 13-20.
    20. Yu, Shaohua & Yu, Qiqing & Wong, George Y.C., 2006. "Consistency of the generalized MLE of a joint distribution function with multivariate interval-censored data," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 720-732, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:lifeda:v:22:y:2016:i:1:d:10.1007_s10985-014-9308-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.