Semiparametric Bayesian analysis of accelerated failure time models with cluster structures

Abstract

In this paper, we develop a Bayesian semiparametric accelerated failure time model for survival data with cluster structures. Our model allows distributional heterogeneity across clusters and accommodates their relationships through a density ratio approach. Moreover, a nonparametric mixture of Dirichlet processes prior is placed on the baseline distribution to yield full distributional flexibility. We illustrate through simulations that our model can greatly improve estimation accuracy by effectively pooling information from multiple clusters, while taking into account the heterogeneity in their random error distributions. We also demonstrate the implementation of our method using analysis of Mayo Clinic Trial in Primary Biliary Cirrhosis.

Bayesian Analysis for Random Effects Models

“…where β is a vector of p-dim regression coefficients of interest and ε ij are independent random errors following the distribution with density f i . [7] posed an exponential tilt on the distributions of error terms to incorporate the cluster heterogeneity. That is,…”

“…: Thus, θ i represents the parametric random effects in the model. Li et al [7] place the DPM prior on the baseline density f 1 to develop a set of procedures which improves estimation efficiency through information pooling.…”

“…The extended random effects models, termed semiparametric random effects models, improve statistical performance with added interpretability. Bayesian techniques, which provide a convenient means to model non-Gaussian distributions, have recently been proposed for semiparametric random effects model in a variety of settings ( [7,8], among others).…”