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Prediction of random effects with misspecified AFT random effect models
Journal of the Korean Data & Information Science Society 2022;33:919-26
Published online September 30, 2022;
© 2022 Korean Data and Information Science Society.

Lin Hao1 · Il Do Ha2

12Department of Statistics, Pukyong National University
Correspondence to: This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2020R1F1A1A01056987).
1 Graduate Student, Department of Statistics, Pukyong National University, Busan 48513, Korea
2 Professor, Department of Statistics, Pukyong National University, Busan 48513, Korea. E-mail:
Received August 19, 2022; Revised September 1, 2022; Accepted September 7, 2022.
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.
The accelerated failure time (AFT) model with random effects has been widely used for clustered or correlated time-to-event data as an alternative to frailty model which is the Cox’s proportional hazards model with random effects. The AFT random effect model usually assumes a normal distribution for random effect distribution. It is well known that the estimated regression parameters in the AFT model are robust against various violations of the assumed model. However, the impact of prediction (or estimation) of random effect, when the assumed normal random effect is misspecified, has been relatively less studied. In this paper, we investigate the impact of misspecification of normal random effect distribution on the prediction of random effect under the AFT random effect model. Here, the random effect is estimated using the hierarchical likelihood (h-likelihood) which is useful for the inference of random effects. The proposed method is demonstrated using simulation studies and a real data set.
Keywords : AFT model, h-likelihood, prediction, random effect, survival data.