A Spatial Copula Approach to Fully Bayesian Nonparametric Survival Analysis

• Activity Number: 608
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Haiming Zhou*+ and Timothy Hanson and Roland Knapp
• Companies: and University of South Carolina and University of California
• Keywords: Dependent Dirichlet process ; Gaussian spatial copula ; spatial survival data ; point referenced spatial ; full scale approximation ; delayed rejection

Abstract

Modeling for spatially correlated survival data is receiving increased attention in biomedical and epidemiologic studies. We propose a novel class of Gaussian spatial copula models for point referenced spatially correlated right-censored survival data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a Dependent Dirichlet process (DDP) prior on the random mixing measure, and their joint distribution is obtained by the Gaussian copula model with a spatial correlation structure. A major feature of the proposed approach is that it provides a rich class of spatial models where survival curves can be estimated without imposing the ubiquitous proportional hazards assumption and the spatial dependence is modeled simultaneously. In view of the inverse of high-dimensional spatial correlation matrices, we adopt the full scale approximation that can capture both large- and the small-scale spatial dependence. An efficient Markov chain Monte Carlo (MCMC) algorithm with delayed rejection is proposed for posterior computation. The methods are evaluated through simulations and applied to an study on amphibian declines.