Spatially Dependent Polya Tree Modeling for Survival Data
Article first published online: 19 AUG 2010
© 2010, The International Biometric Society
Volume 67, Issue 2, pages 391–403, June 2011
How to Cite
Zhao, L. and Hanson, T. E. (2011), Spatially Dependent Polya Tree Modeling for Survival Data. Biometrics, 67: 391–403. doi: 10.1111/j.1541-0420.2010.01468.x
- Issue published online: 20 JUN 2011
- Article first published online: 19 AUG 2010
- Received March 2008. Revised May 2010. Accepted May 2010.
- Breast cancer;
- Conditionally autoregressive (CAR) model;
- Log pseudo marginal likelihood (LPML);
- Mixture of Polya trees;
- Nonparametric modeling;
- Proportional hazards
Summary With the proliferation of spatially oriented time-to-event data, spatial modeling in the survival context has received increased recent attention. A traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model, such as proportional hazards or accelerated failure time. We propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent Polya trees for the baseline survival in the proportional hazards model. Thanks to modern Markov chain Monte Carlo (MCMC) methods, this approach remains computationally feasible in a fully hierarchical Bayesian framework. We compare the spatially dependent mixture of Polya trees (MPT) approach to the traditional spatial frailty approach, and illustrate the usefulness of this method with an analysis of Iowan breast cancer survival data from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. Our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood (LPML), the deviance information criterion (DIC), and full sample score (FSS) statistics.