IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v78y2024i1p191-207.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12311
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12311?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
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    5. 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.
    6. 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.
    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. Jacobo Uña-Álvarez & Noël Veraverbeke, 2013. "Generalized copula-graphic estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 343-360, June.
    2. 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.
    3. Menggang Yu & Constantin T. Yiannoutsos, 2015. "Marginal and Conditional Distribution Estimation from Double-sampled Semi-competing Risks Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 87-103, March.
    4. Lo, Simon M.S. & Wilke, Ralf A. & Emura, Takeshi, 2024. "A semiparametric model for the cause-specific hazard under risk proportionality," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    5. Heuchenne, Cedric & Laurent, Stephane & Legrand, Catherine & Van Keilegom, Ingrid, 2011. "Likelihood based inference for semi-competing risks," LIDAM Discussion Papers ISBA 2011022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Hsieh, Jin-Jian & Hsu, Chia-Hao, 2018. "Estimation of the survival function with redistribution algorithm under semi-competing risks data," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 1-6.
    8. Erica Brittain & Dean Follmann & Song Yang, 2008. "Dynamic Comparison of Kaplan–Meier Proportions: Monitoring a Randomized Clinical Trial with a Long-Term Binary Endpoint," Biometrics, The International Biometric Society, vol. 64(1), pages 189-197, March.
    9. Ebrahimi, Nader & Molefe, Daniel, 2003. "Survival function estimation when lifetime and censoring time are dependent," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 101-132, October.
    10. Paul Janssen & Noël Veraverbeke, 2024. "Nonparametric estimation of univariate and bivariate survival functions under right censoring: a survey," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(3), pages 211-245, April.
    11. Schwarz, Maik & Jongbloed, Geurt & Van Keilegom, Ingrid, 2012. "On the identifiability of copulas in bivariate competing risks models," LIDAM Discussion Papers ISBA 2012032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    13. Li, Gang & Sun, Yanqing, 2000. "A simulation-based goodness-of-fit test for survival data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 403-410, May.
    14. Myrthe D’Haen & Ingrid Van Keilegom & Anneleen Verhasselt, 2025. "Quantile regression under dependent censoring with unknown association," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(2), pages 253-299, April.
    15. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 673-682, December.
    16. Sun, Liuquan & Zhou, Yong, 1998. "Sequential confidence bands for densities under truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 31-41, September.
    17. Yang, Song, 1996. "Weighted empiricals and the product-limit estimator in the multiplicative hazard and time transfer regression model," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 17-24, September.
    18. Su, Pei-Fang & Chi, Yunchan & Li, Chung-I & Shyr, Yu & Liao, Yi-De, 2011. "Analyzing survival curves at a fixed point in time for paired and clustered right-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1617-1628, April.
    19. Thomas DeLeire & Shakeeb Khan & Christopher Timmins, 2013. "Roy Model Sorting And Nonrandom Selection In The Valuation Of A Statistical Life," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(1), pages 279-306, February.
    20. Yu-Mei Chang & Chun-Shu Chen & Pao-Sheng Shen, 2012. "A jackknife-based versatile test for two-sample problems with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 267-277, April.

    More about this item

    Statistics

    Access and download statistics

    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:bla:stanee:v:78:y:2024:i:1:p:191-207. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.