Abstract
Multivariate survival data are characterized by the presence of correlation between event times within the same cluster. First, we build multi-dimensional copulas with flexible and possibly symmetric dependence structures for such data. In particular, clustered right-censored survival data are modeled using mixtures of max-infinitely divisible bivariate copulas. Second, these copulas are fit by a likelihood approach where the vast amount of copula derivatives present in the likelihood is approximated by finite differences. Third, we formulate conditions for clustered right-censored survival data under which an information criterion for model selection is either weakly consistent or consistent. Several of the familiar selection criteria are included. A set of four-dimensional data on time-to-mastitis is used to demonstrate the developed methodology.
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Acknowledgments
The authors wish to thank Dr. H. Laevens (Catholic University College Sint-Lieven, Sint-Niklaas, Belgium), for permission to use the mastitis data for this research. This work was supported by the IAP Research Network P6/03 of the Belgian State (Belgian Research Policy), by the Fund for Scientific Research Flanders and by KU Leuven grant GOA/12/14. For the simulations we used the infrastructure of the VSC - Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government – department EWI. The authors thank all the reviewers of this paper for the constructive remarks and questions that have led to a clearer presentation.
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Geerdens, C., Claeskens, G. & Janssen, P. Copula based flexible modeling of associations between clustered event times. Lifetime Data Anal 22, 363–381 (2016). https://doi.org/10.1007/s10985-015-9336-x
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DOI: https://doi.org/10.1007/s10985-015-9336-x