IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v31y2025i1d10.1007_s10985-024-09640-z.html
   My bibliography  Save this article

Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data

Author

Listed:
  • Sakie J. Arachchige

    (Mississippi State University)

  • Xinyuan Chen

    (Mississippi State University)

  • Qian M. Zhou

    (Mississippi State University)

Abstract

We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen YH (Lifetime Data Anal 18:36–57, 2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu H et al., (Commu Statistics-Theory Methods 51(22):7830–7845, 2021) . An R package PMLE4SCR is developed to implement our proposed method.

Suggested Citation

  • Sakie J. Arachchige & Xinyuan Chen & Qian M. Zhou, 2025. "Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(1), pages 52-75, January.
  • Handle: RePEc:spr:lifeda:v:31:y:2025:i:1:d:10.1007_s10985-024-09640-z
    DOI: 10.1007/s10985-024-09640-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-024-09640-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10985-024-09640-z?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yi‐Hau Chen, 2010. "Semiparametric marginal regression analysis for dependent competing risks under an assumed copula," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 235-251, March.
    2. Weijing Wang, 2003. "Estimating the association parameter for copula models under dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 257-273, February.
    3. Elif F. Acar & Radu V. Craiu & Fang Yao, 2011. "Dependence Calibration in Conditional Copulas: A Nonparametric Approach," Biometrics, The International Biometric Society, vol. 67(2), pages 445-453, June.
    4. Renke Zhou & Hong Zhu & Melissa Bondy & Jing Ning, 2016. "Semiparametric model for semi-competing risks data with application to breast cancer study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 456-471, July.
    5. Hong Zhu & Yu Lan & Jing Ning & Yu Shen, 2021. "Semiparametric copula-based regression modeling of semi-competing risks data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(22), pages 7830-7845, September.
    6. Jin‐Jian Hsieh & Weijing Wang & A. Adam Ding, 2008. "Regression analysis based on semicompeting risks data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 3-20, February.
    7. Donglin Zeng & D. Y. Lin, 2006. "Efficient estimation of semiparametric transformation models for counting processes," Biometrika, Biometrika Trust, vol. 93(3), pages 627-640, September.
    8. 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.
    9. Abegaz, Fentaw & Gijbels, Irène & Veraverbeke, Noël, 2012. "Semiparametric estimation of conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 43-73.
    10. Limin Peng & Jason P. Fine, 2007. "Regression Modeling of Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 63(1), pages 96-108, 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. Fei Jiang & Sebastien Haneuse, 2017. "A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 112-129, March.
    2. Chia-Hui Huang, 2019. "Mixture regression models for the gap time distributions and illness–death processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 168-188, January.
    3. Xifen Huang & Jinfeng Xu & Hao Guo & Jianhua Shi & Wenjie Zhao, 2022. "An MM Algorithm for the Frailty-Based Illness Death Model with Semi-Competing Risks Data," Mathematics, MDPI, vol. 10(19), pages 1-13, October.
    4. Jing Yang & Limin Peng, 2018. "Estimating cross quantile residual ratio with left-truncated semi-competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 652-674, October.
    5. 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.
    6. Huazhen Lin & Ling Zhou & Chunhong Li & Yi Li, 2014. "Semiparametric transformation models for semicompeting survival data," Biometrics, The International Biometric Society, vol. 70(3), pages 599-607, September.
    7. Annalisa Orenti & Patrizia Boracchi & Giuseppe Marano & Elia Biganzoli & Federico Ambrogi, 2022. "A pseudo-values regression model for non-fatal event free survival in the presence of semi-competing risks," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 709-727, September.
    8. 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.
    9. Zhao, XiaoBing & Zhou, Xian, 2010. "Applying copula models to individual claim loss reserving methods," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 290-299, April.
    10. Peng, Mengjiao & Xiang, Liming & Wang, Shanshan, 2018. "Semiparametric regression analysis of clustered survival data with semi-competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 53-70.
    11. Renke Zhou & Hong Zhu & Melissa Bondy & Jing Ning, 2016. "Semiparametric model for semi-competing risks data with application to breast cancer study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 456-471, July.
    12. Qui Tran & Kelley M. Kidwell & Alex Tsodikov, 2018. "A joint model of cancer incidence, metastasis, and mortality," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 385-406, July.
    13. Zongwu Cai & Guannan Liu & Wei Long & Xuelong Luo, 2024. "Semiparametric Conditional Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202401, University of Kansas, Department of Economics, revised Jan 2024.
    14. repec:kan:wpaper:202105 is not listed on IDEAS
    15. Guannan Liu & Wei Long & Bingduo Yang & Zongwu Cai, 2022. "Semiparametric estimation and model selection for conditional mixture copula models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 287-330, March.
    16. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    17. Yang Li & Hao Liu & Xiaoshen Wang & Wanzhu Tu, 2022. "Semi‐parametric time‐to‐event modelling of lengths of hospital stays," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1623-1647, November.
    18. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    19. Ding, A. Adam, 2010. "Identifiability conditions for covariate effects model on survival times under informative censoring," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 911-915, June.
    20. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    21. Sangbum Choi & Xuelin Huang, 2014. "Maximum likelihood estimation of semiparametric mixture component models for competing risks data," Biometrics, The International Biometric Society, vol. 70(3), pages 588-598, September.

    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:spr:lifeda:v:31:y:2025:i:1:d:10.1007_s10985-024-09640-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.