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THE NPMLE of the joint distribution function with right-censored and masked competing risks data

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  • Qiqing Yu
  • Jiahui Li

Abstract

Even though the right-censored competing risks data with masked failure cause have been studied for 30 years, the asymptotic properties of the nonparametric maximum-likelihood estimator (NPMLE) of the joint distribution function with such data have never been studied. We show that the solution to the NPMLE is not unique, and the NPMLE proposed in the current literature is inconsistent. Moreover, we construct a consistent NPMLE and establish its asymptotic normality. It is a non-trivial example in the survival analysis context that there exist an inconsistent NPMLE as well as another consistent NPMLE with the same data and under the same model. Our proofs do not need the symmetry assumption made by almost all researchers on such data. We present simulation results on the consistent NPMLE and apply the NPMLE to a data set in medical research.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:753-764
    DOI: 10.1080/10485252.2012.695782
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    Cited by:

    1. 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.
    2. 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.

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