Hierarchical likelihood approach for the Weibull frailty model

Abstract

In this article, the proportional hazard model with Weibull frailty, which is outside the range of the exponential family, is used for analysing the right-censored longitudinal survival data. Complex multidimensional integrals are avoided by using hierarchical likelihood to estimate the regression parameters and to predict the realizations of random effects. The adjusted profile hierarchical likelihood is adopted to estimate the parameters in frailty distribution, during which the first- and second-order methods are used. The simulation studies indicate that the regression-parameter estimates in the Weibull frailty model are accurate, which is similar to the gamma frailty and lognormal frailty models. Two published data sets are used for illustration.

Keywords:

• hierarchical likelihood
• Weibull frailty
• multivariate survival data
• profile likelihood

Acknowledgements

We sincerely thank Professor IL DO HA and the reviewer for their very careful reading and their insightful comments, which have led to a great improvement for this article.