7 8 These were then controlled for in the second stage of the statistical analysis (see below). Information about the age structure of wards was obtained from the Office of National Statistics’ www.selleckchem.com/products/Imatinib(STI571).html mid-2010 estimates (obtained from the Warwickshire Observatory website).9 The representative statistical value of ‘percentage (%) of population above age 50’ was used as an indicator of wards with a higher proportion of older people. Information about social deprivation was obtained from the English Indices of Deprivation

published by the Department for Communities and Local Government.10 The index of multiple deprivation (IMD) averaged across each ward was used as an indicator of the level of deprivation within the wards of Warwickshire. The information on crude observed air pollution level distribution, heart failure hospital admission rates and mortality rates were then represented on maps of Warwickshire (figure 1). Figure 1 Warwickshire

map with 2010 air quality index (all components of air pollution combined) displayed by ward (left) Warwickshire map with number of heart failure hospital admissions per 1000 population between 2005 and 2013 displayed by ward (centre) and … Statistical analysis To account for spatial autocorrelation in observed heart failure hospital admission and mortality rates at the ward level in Warwickshire we applied a unified approach to account for possible air pollution effects of environmental risk factors. This

was achieved using a geoadditive semiparametric mixed model. The model employed a fully Bayesian approach using Markov Chain Monte Carlo (MCMC) techniques for inference and model checking.11 12 Response variables were defined as the count (per 1000 population) of heart failure morbidity or mortality in a ward (Poisson model): yi |ηi,δ ∼ B(ηi,δ) for a binomial formulation. (Poisson model): 1 for a binomial formulation and a geoadditive semiparametric predictor µi=h(ηi): 2 where h is a known response function with a poison link function, f1 ,…, fp are non-linear smoothed effects of the metrical covariates (time in years), and fspat (si) is the effect of the spatial covariate si Carfilzomib ∈1 ,…,S labelling the ward in Warwickshire. Regression models with predictors such as those in equation 2 are sometimes referred to as geoadditive models. P-spline priors were assigned to the functions f1,…,fp, non-informative priors were used for fixed effects parameters and a Markov random field prior was used for fspat (si). More detailed information about the modelling approach can be found elsewhere.11 13 The standard measure of effect was the posterior mean (PM) and 95% credible region (CR). The analysis was carried out using V.2.0.1 of the BayesX software package, which permits Bayesian inference based on MCMC simulation techniques.