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Author Zhao, Luping
Title Mixtures of polya trees for flexible spatial survival modeling
book jacket
Descript 108 p
Note Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0036
Thesis (Ph.D.)--University of Minnesota, 2008
With the proliferation of spatially oriented time-to-event data, spatial modeling has received dramatically increased attention. The traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor. We introduce a flexible nonparametric mixture of Polya trees (MPT) prior to the spatial frailty models within three competing survival settings -- proportional hazards (PH), accelerated failure time (AFT), and proportional odds (PO). We then extend our working structure from spatially oriented time-to-event data to both spatially and temporally indexed time-to-event data Besides the spatial pattern, temporal cohort effects are also an interest of analyses for subjects who were diagnosed with the disease of interest (and thus, entered the study) during different time periods, e.g. calendar year. We develop semiparametric hierarchical Bayesian frailty models that conditionally follow a PH assumption to capture both spatial and temporal associations. A mixture of dependent Polya trees prior is developed as a flexible nonparametric approach. The dependency structure explicitly models evolution in baseline survival under a conditionally PH assumption. We also propose a new methodology to capture the spatial pattern other than the traditional spatial frailty method. The proposed PH model assumes a mixture of spatially dependent Polya trees prior based on Markov random fields for the baselines. Specifically, the logit transformed MPT conditional probabilities follow a proper conditional autoregressive (CAR) prior at each pair of companion sets in the partition defining the tailfree process. Thanks to modern Markov chain Monte Carlo (MCMC) methods; the proposed approaches remain computationally feasible in a fully hierarchical Bayesian framework. We illustrate the usefulness of our proposed methods with analyses of three spatially oriented breast cancer survival data from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. Our results indicate appreciable advantages for the proposed approaches over traditional alternatives according to Log pseudo marginal likelihood (LPML), deviance information criterion (DIC), and full sample score (FSS) statistics
School code: 0130
Host Item Dissertation Abstracts International 69-01B
Subject Biology, Biostatistics
Alt Author University of Minnesota
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