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Frailty models and copulas: similarities and differences

Author

Listed:
  • Klara Goethals
  • Paul Janssen
  • Luc Duchateau

Abstract

Copulas and frailty models are important tools to model bivariate survival data. Equivalence between Archimedean copula models and shared frailty models, e.g. between the Clayton-Oakes copula model and the shared gamma frailty model, has often been claimed in the literature. In this note we show that, in both the models, there is indeed a well-known equivalence between the copula functions; the modeling of the marginal survival functions, however, is quite different. The latter fact leads to different joint survival functions.

Suggested Citation

  • Klara Goethals & Paul Janssen & Luc Duchateau, 2008. "Frailty models and copulas: similarities and differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1071-1079.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:9:p:1071-1079
    DOI: 10.1080/02664760802271389
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    Citations

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    Cited by:

    1. Dongdong Li & X. Joan Hu & Mary L. McBride & John J. Spinelli, 2020. "Multiple event times in the presence of informative censoring: modeling and analysis by copulas," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 573-602, July.
    2. Alan Kimber & Shah-Jalal Sarker, 2012. "A covariance-based test for shared frailty in multivariate lifetime data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2509-2522, August.
    3. Ma, Ling & Hu, Tao & Sun, Jianguo, 2016. "Cox regression analysis of dependent interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 79-90.
    4. Leen Prenen & Roel Braekers & Luc Duchateau, 2017. "Extending the Archimedean copula methodology to model multivariate survival data grouped in clusters of variable size," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 483-505, March.
    5. Akim Adekpedjou & Sophie Dabo‐Niang, 2021. "Semiparametric estimation with spatially correlated recurrent events," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1097-1126, December.
    6. Eleanderson Campos & Roel Braekers & Devanil J. Souza & Lucas M. Chaves, 2021. "Factor copula models for right-censored clustered survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 499-535, July.
    7. Brito, Éder S. & Tomazella, Vera L.D. & Ferreira, Paulo H., 2022. "Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    8. José Romeo & Nelson Tanaka & Antonio Pedroso-de-Lima & Victor Salinas-Torres, 2013. "Large sample properties for a class of copulas in bivariate survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 997-1015, November.
    9. Tao Sun & Yi Liu & Richard J. Cook & Wei Chen & Ying Ding, 2019. "Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 546-568, July.
    10. Jose S. Romeo & Renate Meyer & Diego I. Gallardo, 2018. "Bayesian bivariate survival analysis using the power variance function copula," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 355-383, April.
    11. Zhao, Xiaobing & Zhou, Xian, 2012. "Estimation of medical costs by copula models with dynamic change of health status," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 480-491.
    12. Hideatsu Tsukahara, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 287-289, August.
    13. Candida Geerdens & Gerda Claeskens & Paul Janssen, 2016. "Copula based flexible modeling of associations between clustered event times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 363-381, July.
    14. Paul Embrechts & Marius Hofert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 263-270, August.
    15. Paul Janssen & Luc Duchateau, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 271-275, August.
    16. Tshilidzi Benedicta Mulaudzi & Yehenew Getachew Kifle & Roel Braekers, 2023. "A Shared Frailty Model for Left-Truncated and Right-Censored Under-Five Child Mortality Data in South Africa," Stats, MDPI, vol. 6(4), pages 1-11, October.

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