Non-parametric Bayesian analysis of clustered survival data

Abstract

Clustered survival data are often modelled with frailty models which incorporate frailties to model the cluster specific heterogeneity and the dependence between observations in the same cluster. For the analysis of the frailty models, we propose Bayesian modelling with beta process prior on the cumulative hazard function and describe the details of the posterior computation. We demonstrate the method with two data sets using three different frailty distributions: gamma, log-normal and log-logistic distributions. We also empirically demonstrate the difficulty in checking the assumed frailty distribution with the posterior sample of the frailties.

Keywords:

• clustered data
• proportional hazard model
• beta process

2000 Mathematics Subject Classification :

• 62N01
• 62G99

Acknowledgements

This work was supported by Korea Research Foundation Grant (KRF-2004-041-C00065).