title: Bayesian hierarchical modelling of noisy spatial rates on a modestly large and discontinuous irregular lattice.
abstract: We present Bayesian hierarchical spatial model development motivated from a recent analysis of noisy small area response rate data, named the Booster data. The Booster data are postcode-level aggregates from a recent mail-out recruitment for a physical exercise intervention in deprived urban neighbourhoods in Sheffield, UK. Bayesian hierarchical Bernoulli-binomial spatial mixture zero-inflated Binomial models were developed for modelling overdispersion and for separation of systematic and random variations in the noisy and mostly low crude response rates. We present methods that enabled us to explore the underlying spatial rate variation, clustering of low or high response rate areas and neighbourhood characteristics that were associated with variations and patterns of invitation mail-outs, zero-response and response rates. Three spatial prior formulations, the intrinsic conditional autoregressive or (iCAR), the Besag-York-Mollié (BYM) and the modified BYM models, were explored for their performance on modelling sparse data on a modestly large and discontinuous irregular lattice. An in-depth Bayesian analysis of the Booster data is presented, with the resulting posterior estimation and inference implemented via Markov chain Monte Carlo simulation in WinBUGS. With increasing availability of spatial data referenced at fine spatial scales such as the postcode, the sparse-data situation and the Bayesian models and methods discussed herein should have considerable relevance to small area disease and health mapping and to spatial regression.
authors.affiliation: Epidemiology and Biostatistics, School of Population and Public Health, University of British Columbia, Vancouver, Canada British Columbia Child & Family Research Institute, Vancouver, Canada ying.macnab@ubc.ca.
authors.forename: Ying C
authors.initials: YC
authors.lastname: MacNab
authors.affiliation: Public Health GIS Unit, School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK.
authors.forename: Simon
authors.initials: S
authors.lastname: Read
authors.affiliation: Public Health GIS Unit, School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK.
authors.forename: Mark
authors.initials: M
authors.lastname: Strong
authors.affiliation: Public Health GIS Unit, School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK.
authors.forename: Tim
authors.initials: T
authors.lastname: Pearson
authors.affiliation: Public Health GIS Unit, School of Health and Related Research (ScHARR), University of Sheffield, Sheffield, UK.
authors.forename: Ravi
authors.initials: R
authors.lastname: Maheswaran
authors.affiliation: Section of Public Health, School of Health and Related Research(ScHARR), University of Sheffield, Sheffield, UK.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Goyder
mesh_terms: D001499:Bayes Theorem; D016000:Cluster Analysis; D008962:Models, Theoretical
keywords: BYM model; Bernoulli-binomial spatial mixture; Hierarchical models; discontinuous irregular lattice; intrinsic CAR; modified BYM model; postcode areas; public health intervention; response rate; zero-inflated binomial (ZIB) model