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Biometrika Advance Access published online on April 27, 2009
Biometrika, doi:10.1093/biomet/asp014
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© 2009 Biometrika Trust

Article

Mixtures of Polya trees for flexible spatial frailty survival modelling

Luping Zhao

Eli Lilly & Company, Indianapolis, Indiana 46285, U.S.A. zhao0117{at}umn.edu

Timothy E. Hanson and Bradley P. Carlin

Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. hans0058{at}umn.edu carli002{at}umn.edu

Received for publication 1 August 2007. Revision received 1 September 2008.
  Abstract

Mixtures of Polya trees offer a very flexible nonparametric approach for modelling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at the point level or at the lattice level. In this paper, we combine these two aspects within three competing survival models, obtaining a data analytic approach that remains computationally feasible in a fully hierarchical Bayesian framework using Markov chain Monte Carlo methods. We illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the Surveillance, Epidemiology and End Results program of the National Cancer Institute. Our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions, ignore spatial association or both.

Key Words: Areal data • Bayesian modelling • Breast cancer • Conditionally autoregressive model • Log pseudo marginal likelihood • Nonparametric modelling


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