Controlling for localised spatio-temporal autocorrelation in long-term air pollution and health studies

Estimating the long-term health impact of air pollution using an ecological spatio-temporal study design is a challenging task, due to the presence of residual spatio-temporal autocorrelation in the health counts after adjusting for the covariate effects. This autocorrelation is commonly modelled by a set of random effects represented by a Gaussian Markov random field (GMRF) prior distribution, as part of a hierarchical Bayesian model. However, GMRF models typically assume the random effects are globally smooth in space and time, and thus are likely to be collinear to any spatially and temporally smooth covariates such as air pollution. Such collinearity leads to poor estimation performance of the estimated fixed effects, and motivated by this epidemiological problem, this paper proposes new GMRF methodology to allow for localised spatio-temporal smoothing. This means random effects that are either geographically or temporally adjacent are allowed to be autocorrelated or conditionally independent, which allows more flexible autocorrelation structures to be represented. This increased flexibility results in improved fixed effects estimation compared with global smoothing models, which is evidenced by our simulation study. The methodology is then applied to the motivating study investigating the long-term effects of air pollution on respiratory ill health in Greater Glasgow, Scotland between 2007 and 2011.