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author:("ZHAO, louping")
1.  Spatially Dependent Polya Tree Modeling for Survival Data 
Biometrics  2010;67(2):391-403.
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.
doi:10.1111/j.1541-0420.2010.01468.x
PMCID: PMC3025072  PMID: 20731644
Breast cancer; Conditionally autoregressive (CAR) model; Log pseudo marginal likelihood (LPML); Mixture of Polya trees; Nonparametric modeling; Proportional hazards
2.  A Bayesian Semiparametric Temporally–Stratified Proportional Hazards Model with Spatial Frailties 
Bayesian analysis (Online)  2011;6(4):1-48.
Incorporating temporal and spatial variation could potentially enhance information gathered from survival data. This paper proposes a Bayesian semiparametric model for capturing spatio–temporal heterogeneity within the proportional hazards framework. The spatial correlation is introduced in the form of county–level frailties. The temporal effect is introduced by considering the stratification of the proportional hazards model, where the time–dependent hazards are indirectly modeled using a probability model for related probability distributions. With this aim, an autoregressive dependent tailfree process is introduced. The full Kullback–Leibler support of the proposed process is provided. The approach is illustrated using simulated and data from the Surveillance Epidemiology and End Results database of the National Cancer Institute on patients in Iowa diagnosed with breast cancer.
PMCID: PMC3255564  PMID: 22247752
Spatio–temporal modeling; Dependent processes; Tailfree processes; Breast cancer
3.  Mixtures of Polya trees for flexible spatial frailty survival modelling 
Biometrika  2009;96(2):263-276.
Summary
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.
doi:10.1093/biomet/asp014
PMCID: PMC2749263  PMID: 19779579
Areal data; Bayesian modelling; Breast cancer; Conditionally autoregressive model; Log pseudo marginal likelihood; Nonparametric modelling
4.  Mixtures of Polya trees for flexible spatial frailty survival modelling 
Biometrika  2009;96(2):263-276.
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.
doi:10.1093/biomet/asp014
PMCID: PMC2749263  PMID: 19779579
Areal data; Bayesian modelling; Breast cancer; Conditionally autoregressive model; Log pseudo marginal likelihood; Nonparametric modelling

Results 1-4 (4)