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An improved nonparametric estimator of sub-distribution function for bivariate competing risk models

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  • Emura, Takeshi
  • Kao, Fan-Hsuan
  • Michimae, Hirofumi

Abstract

For competing risks data, it is of interest to estimate the sub-distribution function of a particular failure event, which is the failure probability in the presence of competing risks. However, if multiple failure events per subject are available, estimation procedures become challenging even for the bivariate case. In this paper, we consider nonparametric estimation of a bivariate sub-distribution function, which has been discussed in the related literature. Adopting a decision-theoretic approach, we propose a new nonparametric estimator which improves upon an existing estimator. We show theoretically and numerically that the proposed estimator has smaller mean square error than the existing one. The consistency of the proposed estimator is also established. The usefulness of the estimator is illustrated by the salamander data and mouse data.

Suggested Citation

  • Emura, Takeshi & Kao, Fan-Hsuan & Michimae, Hirofumi, 2014. "An improved nonparametric estimator of sub-distribution function for bivariate competing risk models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 229-241.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:229-241
    DOI: 10.1016/j.jmva.2014.08.009
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    References listed on IDEAS

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    3. Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
    4. Takeshi Emura & Yi-Hau Chen & Hsuan-Yu Chen, 2012. "Survival Prediction Based on Compound Covariate under Cox Proportional Hazard Models," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-12, October.
    5. Emura, Takeshi & Chen, Yi-Hau & Chen, Hsuan-Yu, 2012. "Survival prediction based on compound covariate under cox proportional hazard models," MPRA Paper 41149, University Library of Munich, Germany.
    6. P. Sankaran & Ansa Antony, 2009. "Non-parametric estimation of lifetime distribution of competing risk models when censoring times are missing," Statistical Papers, Springer, vol. 50(2), pages 339-361, March.
    7. Michael G. Akritas & Ingrid Van Keilegom, 2003. "Estimation of bivariate and marginal distributions with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 457-471, May.
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    1. Emura, Takeshi & Lai, Ching-Chieh & Sun, Li-Hsien, 2023. "Change point estimation under a copula-based Markov chain model for binomial time series," Econometrics and Statistics, Elsevier, vol. 28(C), pages 120-137.

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