Bayesian Semiparametric Inference for Frailty Model Using Levy Process Priors with Example

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Avik Halder*+ and Glen Takahara
• Companies: Queen's University and Queen's University
• Keywords: Levy process ; Cumulative hazard function ; Frailty model ; Beta-Dirichlet process ; Event history data

Abstract

Lee and Kim (2003) first proposed the use of a Levy process prior for Bayesian inference of the cumulative hazard function in a proportional hazard model. We extend this model by incorporating a frailty component for heterogeneity among the cumulative intensity processes for different subjects. The Levy process prior generalizes that used by Sinha (1993) and Sinha et al.(1998), who do consider frailty models. It is assumed that random effects are Gamma with mean one and unknown variance ?. We characterize the joint posterior and use blocked Gibbs sampling for sampling from the joint posterior. We first choose Beta process as a special case of Levy process then compared our result with Aslanidou et.al (1998)'s Bayesian analysis of cumulative hazard function in a frailty model (assuming frailty as Gamma with mean one and variance ? ) where they had martingale structured prior process. We will provide some simulation results. Kim et al.(2012) proposed beta-Dirichlet process priors for Bayesian inference of cumulative hazard functions in a event history data analysis. We will propose a new algorithm to generate sample paths from beta-Dirichlet process and then use it for data analysis.