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Abstract:
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Mixtures of Polya trees offer a very flexible, nonparametric approach for modeling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at a point (geostatistical) or areal (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 thanks to modern Markov chain Monte Carlo methods. We illustrate the usefulness of 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 previous, competing methods that impose unrealistic parametric assumptions, ignore spatial association, or both.
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