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The analysis of semi‐competing risks data using Archimedean copula models

Author

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  • Antai Wang
  • Ziyan Guo
  • Yilong Zhang
  • Jihua Wu

Abstract

In this paper, we derive the copula‐graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi‐competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion.

Suggested Citation

  • Antai Wang & Ziyan Guo & Yilong Zhang & Jihua Wu, 2024. "The analysis of semi‐competing risks data using Archimedean copula models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(1), pages 191-207, February.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:1:p:191-207
    DOI: 10.1111/stan.12311
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    References listed on IDEAS

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    1. Antai Wang & Krishnendu Chandra & Xieyang Jia, 2018. "The analysis of left truncated bivariate data using frailty models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 847-860, December.
    2. Antai Wang & Krishnendu Chandra & Ruihua Xu & Junfeng Sun, 2015. "The Identifiability of Dependent Competing Risks Models Induced by Bivariate Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 427-437, June.
    3. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
    4. Wang, Antai, 2014. "Properties of the marginal survival functions for dependent censored data under an assumed Archimedean copula," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 57-68.
    5. Lajmi Lakhal & Louis-Paul Rivest & Belkacem Abdous, 2008. "Estimating Survival and Association in a Semicompeting Risks Model," Biometrics, The International Biometric Society, vol. 64(1), pages 180-188, March.
    6. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
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