Semiparametric Bayes Inference of Gap-Time Distribution with Recurrent Event Data

• Activity Number: 296 - Bayesian Biostatistical Applications
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): AKM Fazlur Rahman* and Edsel Aldea Pena
• Companies: University of Alabama at Birmingham and University of South Carolina
• Keywords: Bayes methods ; Gamma process ; Breslow-Aalen type estimator ; Gibbs sampling

Abstract

We consider semiparametric Bayes inference of the gap-time survivor function with the effect of covariates of a correlated recurrent event in the presence of censoring. A frailty model is considered to allow the association between inter-occurrence gap-times. We assume that for a subject or unit given the unobserved frailty variable W=w, the inter-occurrence gap-time {T_j, j>=1} are IID with some distribution function F(t|W=w). In our procedure, we assign a Gamma process prior on the baseline cumulative hazard function and parametric prior distributions on the finite dimensional parameters associated with covariates and frailty. We derive the conditional posterior distributions from the joint posterior distribution of the unknown parameters of interest and employ the Gibbs sampler techniques to obtain samples from the joint posterior distribution. Breslow-Aalen type estimator of the baseline cumulative hazard function is a special case of our developed estimator with the precision parameter of the Gamma process prior tends to zero. Simulation studies demonstrate the effectiveness of the developed method. The developed methodology is illustrated by Multiple Sclerosis data.