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Investigating the correlation structure of quadrivariate udder infection times through hierarchical Archimedean copulas

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  • Leen Prenen

    (Universiteit Hasselt)

  • Roel Braekers

    (Universiteit Hasselt)

  • Luc Duchateau

    (Universiteit Gent)

Abstract

The correlation structure imposed on multivariate time to event data is often of a simple nature, such as in the shared frailty model where pairwise correlations between event times in a cluster are all the same. In modeling the infection times of the four udder quarters clustered within the cow, more complex correlation structures are possibly required, and if so, such more complex correlation structures give more insight in the infection process. In this article, we will choose a marginal approach to study more complex correlation structures, therefore leaving the modeling of marginal distributions unaffected by the association parameters. The dependency of failure times will be induced through copula functions. The methods are shown for (mixtures of) the Clayton copula, but can be generalized to mixtures of Archimedean copulas for which the nesting conditions are met (McNeil in J Stat Comput Simul 6:567–581, 2008; Hofert in Comput Stat Data Anal 55:57–70, 2011).

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  • Leen Prenen & Roel Braekers & Luc Duchateau, 2018. "Investigating the correlation structure of quadrivariate udder infection times through hierarchical Archimedean copulas," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 719-742, October.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:4:d:10.1007_s10985-017-9411-6
    DOI: 10.1007/s10985-017-9411-6
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    References listed on IDEAS

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    1. Duchateau, Luc & Janssen, Paul & Lindsey, Patrick & Legrand, Catherine & Nguti, Rosemary & Sylvester, Richard, 2002. "The shared frailty model and the power for heterogeneity tests in multicenter trials," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 603-620, September.
    2. 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.
    3. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
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    Cited by:

    1. Mirza Nazmul Hasan & Roel Braekers, 2022. "Modelling the association in bivariate survival data by using a Bernstein copula," Computational Statistics, Springer, vol. 37(2), pages 781-815, April.

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