In clustered survival data, the dependence among individual survival times within a cluster has usually been described using copula models and frailty models. In this paper we propose a profile likelihood approach for semiparametric copula models with different cluster sizes. We also propose a likelihood ratio method based on profile likelihood for testing the absence of association parameter (i.e. test of independence) under the copula models, leading to the boundary problem of the parameter space. For this purpose, we show via simulation study that the proposed likelihood ratio method using an asymptotic chi-square mixture distribution performs well as sample size increases. We compare the behaviors of the two models using the profile likelihood approach under a semiparametric setting. The proposed method is demonstrated using two well-known data sets.
Bibliographical noteFunding Information:
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).
- Copula models
- marginal likelihood
- profile likelihood
- random effect
- semi-parametric frailty models