Laplace approximation approach for frailty survival models

Abstract

For multivariate or correlated survival data semi-parametric frailty models with non-parametric 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 difficult 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.