Multivariate Parametric Spatiotemporal Models for County Level Breast Cancer Survival Data

Abstract

Abstract. In clustered survival settings where the clusters correspond to geographic regions, biostatisticians are increasingly turning to models with spatially distributed random effects. These models begin with spatially oriented frailty terms, but may also include further region-level terms in the parametrization of the baseline hazards or various covariate effects (as in a spatially-varying coefficients model). In this paper, we propose a multivariate conditionally autoregressive (MCAR) model as a mixing distribution for these random effects, as a way of capturing correlation across both the regions and the elements of the random effect vector for any particular region. We then extend this model to permit analysis of temporal cohort effects, where we use the term ''temporal cohort'' to mean a group of subjects all of whom were diagnosed with the disease of interest (and thus, entered the study) during the same time period (say, calendar year). We show how our spatiotemporal model may be efficiently fit in a hierarchical Bayesian framework implemented using Markov chain Monte Carlo (MCMC) computational techniques. We illustrate our approach in the context of county-level breast cancer data from 22 annual cohorts of women living in the state of Iowa, as recorded by the Surveillance, Epidemiology, and End Results (SEER) database. Hierarchical model comparison using the Deviance Information Criterion (DIC), as well as maps of the fitted county-level effects, reveal the benefit of our approach.

Linking process to pattern: estimating spatiotemporal dynamics of a wildlife epidemic from cross‐sectional data

“…Hierarchical Bayesian models have become a very popular approach for examining spatial data in general, and hierarchical Bayesian spatial frailty models (Banerjee et al 2003, Jin andCarlin 2005) are a natural extension to spatially referenced event time data. To date, hierarchical Bayesian spatial frailty models have been applied to longitudinal data where subjects have been identified and followed over time, and event times are observed exactly.…”

Neighborhood Dependence in Bayesian Spatial Models

“…See Best, Richardson, and Thomson (2005) for a comparison between different Bayesian spatial models. Starting from basic disease mapping techniques, spatial Bayesian models have developed into space–time generalized linear models (Knorr‐Held and Besag 1998; Sun et al 2000; MacNab and Dean, 2001; Martinez‐Beneito, Lopez‐Quilez, and Botella‐Rocamora, 2008; Silva et al 2008), spatial survival models (Carlin and Banerjee, 2003; Jin and Carlin, 2005; Diva, Dey, and Banerjee, 2008), spatially varying parameters models (Assunção, Potter, and Cavenaghi, 2002; Assunção, 2003; Gelfand et al . 2003), and generalized additive models (Fahrmeir and Lang, 2001).…”

On Selecting Spatial-Temporal Autologistic Regression Models for Binary Lattice Data

“…Spatial-temporal models are important tools for the analysis of spatial data collected repeatedly over time and have been applied to a wide range of problems, including modeling patterns in lung cancer [1], breast cancer [2], birth defects [3], and West Nile virus [4]; see also Cressie [5], Rue and Held [6], and Schabenberger and Gotway [7]. In particular, for binary data that are observed on a spatial lattice over time, spatial-temporal autologistic regression models relate binary responses to covariates while accounting for spatial and temporal dependence simultaneously [8,9].…”