A Comparison of Bayesian Accelerated Failure Time Models with Spatially Varying Coefficients
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A Comparison of Bayesian Accelerated Failure Time Models with Spatially Varying Coefficients Guanyu Hu University of Missouri Columbia, Columbia, USA
Yishu Xue University of Connecticut, Storrs, USA
Fred Huffer Florida State University, Tallahassee, USA Abstract The accelerated failure time (AFT) model is a commonly used tool in analyzing survival data. In public health studies, data is often collected from medical service providers in different locations. Survival rates from different locations often present geographically varying patterns. In this paper, we focus on the accelerated failure time model with spatially varying coefficients. We compare three different types of priors for spatially varying coefficients. A model selection criterion, logarithm of the pseudo-marginal likelihood (LPML), is employed to assess the fit of the AFT model with different priors. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. Finally, we apply our modelto SEER data on prostate cancer in Louisiana and demonstrate the existence of spatially varying effects on survival rates from prostate cancer. AMS (2000) subject classification. Primary: 62N01; Secondary: 62H11 . Keywords and phrases. survival model.
Geographical pattern, prostate cancer, MCMC,
1 Introduction Patient data in public health studies is often collected on certain administrative divisions such as counties or provinces. Oftentimes, the patient group in different regions have similar characteristics yet exhibit different patterns of survival outcomes, which leads us to investigate the geographical variation of covariate effects. There is much recent work analyzing geographical patterns of survival data. For example, Henderson et al. (2002) used the proportional hazards
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model to model spatial variation in survival of leukemia patients in northwest England; Banerjee and Dey (2005) applied a spatial frailty model to infant mortality in Minnesota by using geostatistical or Gaussian Markov random field priors for the spatial component; Zhou et al. (2008) applied the conditional autoregressive (CAR) model in a parametric survival model to construct a joint spatial survival model for prostate cancer data, and Zhang and Lawson (2011) modeled the spatial random effects in an accelerated failure rate (AFT) model using the CAR prior. In all these works, spatial variation is modeled as spatial random effect, while the variation in the covariate effects for risk factors is not accounted for. From the spatially varying coefficients perspective, Gelfand et al. (2003) proposed a model that allows the coefficients in a regression model to vary at the local or subregional level by viewing them as realizations of a Gaussian process with a certain covariance structure that is decided by the relationship between spatial locations. Reich et al. (2010) & Boehm Vock et al. (2015) applied spatially varying coefficients in a generalized linear model to investigate the health effects of fine particulate matter components. An application of the sp
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