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Estimation of the association parameters in hierarchically clustered survival data by nested Archimedean copula functions

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  • Mirza Nazmul Hasan

    (Universiteit Hasselt
    Shahjalal University of Science and Technology)

  • Roel Braekers

    (Universiteit Hasselt)

Abstract

Statisticians are frequently confronted with highly complex data such as clustered data, missing data or censored data. In this manuscript, we consider hierarchically clustered survival data. This type of data arises when a sample consists of clusters, and each cluster has several, correlated sub-clusters containing various, dependent survival times. Two approaches are commonly used to analysis such data and estimate the association between the survival times within a cluster and/or sub-cluster. The first approach is by using random effects in a frailty model while a second approach is by using copula models. Hereby we assume that the joint survival function is described by a copula function evaluated in the marginal survival functions of the different individuals within a cluster. In this manuscript, we introduce a copula model based on a nested Archimedean copula function for hierarchical survival data, where both the clusters and sub-clusters are allowed to be moderate to large and varying in size. We investigate one-stage, two-stage and three-stage parametric estimation procedures for the association parameters in this model. In a simulation study we check the finite sample properties of these estimators. Furthermore we illustrate the methods on a real life data-set on Chronic Granulomatous Disease.

Suggested Citation

  • Mirza Nazmul Hasan & Roel Braekers, 2021. "Estimation of the association parameters in hierarchically clustered survival data by nested Archimedean copula functions," Computational Statistics, Springer, vol. 36(4), pages 2755-2787, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01094-3
    DOI: 10.1007/s00180-021-01094-3
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    References listed on IDEAS

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    1. Hofert, Marius & Pham, David, 2013. "Densities of nested Archimedean copulas," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 37-52.
    2. Renjun Ma, 2003. "Random effects Cox models: A Poisson modelling approach," Biometrika, Biometrika Trust, vol. 90(1), pages 157-169, March.
    3. 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.
    4. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    5. Hofert, Marius, 2011. "Efficiently sampling nested Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 57-70, January.
    6. Li, Yi & Lin, Xihong, 2006. "Semiparametric Normal Transformation Models for Spatially Correlated Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 591-603, June.
    7. Joanna H. Shih & Shou-En Lu, 2007. "Analysis of Failure Time Data with Multilevel Clustering, with Application to the Child Vitamin A Intervention Trial in Nepal," Biometrics, The International Biometric Society, vol. 63(3), pages 673-680, September.
    8. Yi Li & Ross L. Prentice & Xihong Lin, 2008. "Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data," Biometrika, Biometrika Trust, vol. 95(4), pages 947-960.
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