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

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    7. 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).
    8. Lior Rennert & Sharon X. Xie, 2022. "Cox regression model under dependent truncation," Biometrics, The International Biometric Society, vol. 78(2), pages 460-473, June.
    9. 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.
    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. 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.

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