IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v24y2015i4p734-751.html
   My bibliography  Save this article

An algorithm for estimating survival under a copula-based dependent truncation model

Author

Listed:
  • T. Emura
  • K. Murotani

Abstract

Traditional analysis with truncated survival data has been developed under the assumption that the lifetime variable of interest is statistically independent of the truncation variable. However, empirical evidence has shown that the truncation variable may depend on the lifetime of interest in many real-world examples. The lack of independence can lead to seriously biased analysis. In this article, we revisit an existing estimation procedure for survival under a copula-based dependent truncation model. Here, the same estimating equation is adopted but a different algorithm to solve the equation is proposed. We compare the new algorithm with the existing one and discuss its theoretical and practical usefulness. Real data examples are analyzed for illustration. We implemented the proposed algorithm in an R “depend.truncation” package, available from CRAN. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • T. Emura & K. Murotani, 2015. "An algorithm for estimating survival under a copula-based dependent truncation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 734-751, December.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:4:p:734-751
    DOI: 10.1007/s11749-015-0432-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11749-015-0432-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11749-015-0432-8?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. E. Strzalkowska-Kominiak & W. Stute, 2013. "Empirical copulas for consecutive survival data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 688-714, November.
    2. 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.
    3. Lajmi Lakhal Chaieb & Louis-Paul Rivest & Belkacem Abdous, 2006. "Estimating survival under a dependent truncation," Biometrika, Biometrika Trust, vol. 93(3), pages 655-669, September.
    4. Emura, Takeshi & Wang, Weijing, 2012. "Nonparametric maximum likelihood estimation for dependent truncation data based on copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 171-188.
    5. Takeshi Emura & Yoshihiko Konno, 2012. "Multivariate normal distribution approaches for dependently truncated data," Statistical Papers, Springer, vol. 53(1), pages 133-149, February.
    6. Emura, Takeshi & Chen, Yi-Hau, 2014. "Gene selection for survival data under dependent censoring: a copula-based approach," MPRA Paper 58043, University Library of Munich, Germany.
    7. 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.
    8. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    9. Emura, Takeshi & Wang, Weijing, 2010. "Testing quasi-independence for truncation data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 223-239, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    2. Bella Vakulenko‐Lagun & Jing Qian & Sy Han Chiou & Nancy Wang & Rebecca A. Betensky, 2022. "Nonparametric estimation of the survival distribution under covariate‐induced dependent truncation," Biometrics, The International Biometric Society, vol. 78(4), pages 1390-1401, December.
    3. Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    4. Jing Qian & Sy Han Chiou & Rebecca A. Betensky, 2022. "Transformation model based regression with dependently truncated and independently censored data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 395-416, March.
    5. Carla Moreira & Jacobo de Uña-Álvarez & Roel Braekers, 2021. "Nonparametric estimation of a distribution function from doubly truncated data under dependence," Computational Statistics, Springer, vol. 36(3), pages 1693-1720, September.
    6. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.
    7. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Chiou, Sy Han & Qian, Jing & Mormino, Elizabeth & Betensky, Rebecca A., 2018. "Permutation tests for general dependent truncation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 308-324.
    9. Jing Qian & Rebecca A. Betensky, 2023. "Nonparametric bounds for the survivor function under general dependent truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 327-357, March.
    10. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    11. Lior Rennert & Sharon X. Xie, 2022. "Cox regression model under dependent truncation," Biometrics, The International Biometric Society, vol. 78(2), pages 460-473, June.

    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. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    2. Emura, Takeshi & Konno, Yoshihiko, 2012. "A goodness-of-fit test for parametric models based on dependently truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2237-2250.
    3. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    5. Chiou, Sy Han & Qian, Jing & Mormino, Elizabeth & Betensky, Rebecca A., 2018. "Permutation tests for general dependent truncation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 308-324.
    6. Emura, Takeshi & Wang, Weijing, 2012. "Nonparametric maximum likelihood estimation for dependent truncation data based on copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 171-188.
    7. Jing Qian & Rebecca A. Betensky, 2023. "Nonparametric bounds for the survivor function under general dependent truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 327-357, March.
    8. Emura, Takeshi & Hsu, Jiun-Huang, 2020. "Estimation of the Mann–Whitney effect in the two-sample problem under dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    9. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
    10. Carla Moreira & Jacobo de Uña-Álvarez & Roel Braekers, 2021. "Nonparametric estimation of a distribution function from doubly truncated data under dependence," Computational Statistics, Springer, vol. 36(3), pages 1693-1720, September.
    11. Lior Rennert & Sharon X. Xie, 2022. "Cox regression model under dependent truncation," Biometrics, The International Biometric Society, vol. 78(2), pages 460-473, June.
    12. Jing Qian & Sy Han Chiou & Rebecca A. Betensky, 2022. "Transformation model based regression with dependently truncated and independently censored data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 395-416, March.
    13. Pao-Sheng Shen, 2011. "Testing quasi-independence for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 753-761.
    14. Emura, Takeshi & Wang, Weijing, 2009. "Testing Quasi-independence for Truncation Data," MPRA Paper 58582, University Library of Munich, Germany.
    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. Bella Vakulenko‐Lagun & Jing Qian & Sy Han Chiou & Nancy Wang & Rebecca A. Betensky, 2022. "Nonparametric estimation of the survival distribution under covariate‐induced dependent truncation," Biometrics, The International Biometric Society, vol. 78(4), pages 1390-1401, December.
    17. Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    18. Emura, Takeshi & Shiu, Shau-Kai, 2014. "Estimation and model selection for left-truncated and right-censored lifetime data with application to electric power transformers analysis," MPRA Paper 57528, University Library of Munich, Germany.
    19. 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.
    20. Lo Simon M.S. & Wilke Ralf A., 2014. "A Regression Model for the Copula-Graphic Estimator," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 21-46, January.

    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:testjl:v:24:y:2015:i:4:p:734-751. 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.