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A copula model for dependent competing risks

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  • Simon M. S. Lo
  • Ralf Wilke

Abstract

Many popular estimators for duration models require independent competing risks or independent censoring. In contrast, copula based estimators are also consistent in presence of dependent competing risks. In this paper we suggest a computationally convenient extension of the Copula Graphic Estimator (Zheng and Klein, 1995) to a model with more than two dependent competing risks. We analyse the applicability of this estimator by means of simulations and real world unemployment duration data from Germany. We obtain evidence that our estimator yields nice results if the dependence structure is known and that it is a powerful tool for the assessment of the relevance of (in-)dependence assumptions in applied duration research.

Suggested Citation

  • Simon M. S. Lo & Ralf Wilke, 2009. "A copula model for dependent competing risks," Discussion Papers 09/01, University of Nottingham, School of Economics.
    • Handle: RePEc:not:notecp:09/01
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    References listed on IDEAS

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    1. repec:iab:iabfme:200704(en is not listed on IDEAS
    2. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460, Elsevier.
    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. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    5. Wilke, Ralf A. & Lo, Simon M. S. & Arntz, Melanie, 2007. "Bounds Analysis of Competing Risks: A Nonparametric Evaluation of the Effect of Unemployment Benefits on Imigration in Germany," ZEW Discussion Papers 07-049, ZEW - Leibniz Centre for European Economic Research.
    6. Zimmer, David M. & Trivedi, Pravin K., 2006. "Using Trivariate Copulas to Model Sample Selection and Treatment Effects: Application to Family Health Care Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 63-76, January.
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    Citations

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    Cited by:

    1. Richard Arnold & Stefanka Chukova & Yu Hayakawa, 2016. "Failure distributions in multicomponent systems with imperfect repairs," Journal of Risk and Reliability, , vol. 230(1), pages 4-17, February.
    2. 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.
    3. 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.
    4. Melanie Arntz & Simon Lo & Ralf Wilke, 2014. "Bounds analysis of competing risks: a non-parametric evaluation of the effect of unemployment benefits on migration," Empirical Economics, Springer, vol. 46(1), pages 199-228, February.
    5. Kim, Dongwoo, 2023. "Partially identifying competing risks models: An application to the war on cancer," Journal of Econometrics, Elsevier, vol. 234(2), pages 536-564.
    6. 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.
    7. Nhan Huynh & Mike Ludkovski, 2021. "Joint Models for Cause-of-Death Mortality in Multiple Populations," Papers 2111.06631, arXiv.org.
    8. 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).
    9. 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).
    10. Arntz, Melanie & Lo, Simon M. S. & Wilke, Ralf A., 2008. "Bounds analysis of competing risks : a nonparametric evaluation of the effect of unemployment benefits on migration in Germany (Revised version of the FDZ Methodenbericht No. 04/2007)," FDZ Methodenreport 200806_en, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
    11. Dabrowska Dorota M., 2012. "Estimation in a Semi-Markov Transformation Model," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-62, June.
    12. Mossialos, Elias & Lear, Julia, 2012. "Balancing economic freedom against social policy principles: EC competition law and national health systems," Health Policy, Elsevier, vol. 106(2), pages 127-137.
    13. Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    14. Yicheng Zhou & Zhenzhou Lu & Yan Shi & Kai Cheng, 2019. "The copula-based method for statistical analysis of step-stress accelerated life test with dependent competing failure modes," Journal of Risk and Reliability, , vol. 233(3), pages 401-418, June.
    15. Lo, Simon M.S. & Stephan, Gesine & Wilke, Ralf, 2012. "Estimating the Latent Effect of Unemployment Benefits on Unemployment Duration," IZA Discussion Papers 6650, Institute of Labor Economics (IZA).
    16. Dimitrova, Dimitrina S. & Haberman, Steven & Kaishev, Vladimir K., 2013. "Dependent competing risks: Cause elimination and its impact on survival," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 464-477.
    17. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    18. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.
    19. Simon M.S. Lo & Ralf A. Wilke, 2011. "Identifiability and estimation of the sign of a covariate effect in the competing risks model," Discussion Papers 11/03, University of Nottingham, School of Economics.

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    More about this item

    Keywords

    Archimedean copula; dependent censoring; unemployment duration;
    All these keywords.

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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