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Laplace approximation approach for frailty survival models
Journal of the Korean Data & Information Science Society 2018;29:1679-85
Published online November 30, 2018
© 2018 Korean Data and Information Science Society.

Il Do Ha1 · Geon Ho Cho2

1Department of Statistics, Pukyong National University
2Division of Cosmetic Science and Technology, Daegu Haany University
Correspondence to: Professor, Department of Statistics, Pukyong National University, Busan 608-737, Korea. E-mail:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2017R1E1A1A03070747).
Received October 17, 2018; Revised November 17, 2018; Accepted November 20, 2018.
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.
For multivariate or correlated survival data semi-parametric frailty models with nonparametric baseline hazards, extensions of Cox's (1972) proportional hazards models, has been often used. The marginal likelihood has been usually used for the inferences, but it often requires the computation of dicult integration in integrating out the frailty terms. In this paper we propose a Laplace approximation approach based on hierarchical likelihood for the frailty models. The proposed method is demonstrated via simulation study and two well-known real data sets. In particular, the simulation results show that our method is better than standard h-likelihood method in terms of bias.
Keywords : Frailty models, hierarchical likelihood, Laplace approximation, multivariate survival data.