search for


Comparison of copula model and frailty model for correlated survival data
Journal of the Korean Data & Information Science Society 2019;30:551-62
Published online May 31, 2019;
© 2019 Korean Data and Information Science Society.

Sookhee Kwon1 · Il Do Ha2

12Department of Statistics, Pukyong National University
Correspondence to: Professor, Department of Statistics, Pukyong National University, Busan 48513, Korea.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science & ICT (No.NRF-2017R1E1A1A03070747).
Received April 6, 2019; Revised May 9, 2019; Accepted May 10, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copula model and frailty model have been widely used for analyzing correlated or multivariate survival data. However, both models are different because copula model is marginal whereas frailty model is conditional. In this paper, we compare the behaviors of both models for correlated survival data with various cluster sizes. We explain how to fit both models using recent R packages, and compare the results of fitting both models via simulation study and two real data. In particular, we found out that the results from both models are more different as the strength of correlation among survival times increases.
Keywords : Copula model, correlated survival data, frailty model, hierarchical likelihood, marginal likelihood.