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Estimation of the long-term health effects of air pollution is a challengingtask, especially when modelling small-area disease incidence data in anecological study design. The challenge comes from the unobserved underlyingspatial correlation structure in these data, which is accounted for usingrandom effects modelled by a globally smooth conditional autoregressive model.These smooth random effects confound the effects of air pollution, which arealso globally smooth. To avoid this collinearity a Bayesian localisedconditional autoregressive model is developed for the random effects. Thislocalised model is flexible spatially, in the sense that it is not only able tomodel step changes in the random effects surface, but also is able to captureareas of spatial smoothness in the study region. This methodologicaldevelopment allows us to improve the estimation performance of the covariateeffects, compared to using traditional conditional auto-regressive models.These results are established using a simulation study, and are thenillustrated with our motivating study on air pollution and respiratory illhealth in Greater Glasgow, Scotland in 2010. The model shows substantial healtheffects of particulate matter air pollution and income deprivation, whoseeffects have been consistently attenuated by the currently available globallysmooth models.

A Bayesian localised conditional auto-regressive model for estimating the health effects of air pollution