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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
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    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.
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