Statistical models used to estimate the spatio-temporal pattern in disease risk from areal unit data represent the risk surface for each time period with known covariates and a set of spatially smooth random effects. The latter act as a proxy for unm
easured spatial confounding, whose spatial structure is often characterised by a spatially smooth evolution between some pairs of adjacent areal units while other pairs exhibit large step changes. This spatial heterogeneity is not consistent with existing global smoothing models, in which partial correlation exists between all pairs of adjacent spatial random effects. Therefore we propose a novel space-time disease model with an adaptive spatial smoothing specification that can identify step changes. The model is motivated by a new study of respiratory and circulatory disease risk across the set of Local Authorities in England, and is rigorously tested by simulation to assess its efficacy. Results from the England study show that the two diseases have similar spatial patterns in risk, and exhibit a number of common step changes in the unmeasured component of risk between neighbouring local authorities.
Estimation of the long-term health effects of air pollution is a challenging task, especially when modelling small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial correlation struc
ture in these data, which is accounted for using random effects modelled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localised conditional autoregressive model is developed for the random effects. This localised model is flexible spatially, in the sense that it is not only able to model step changes in the random effects surface, but also is able to capture areas of spatial smoothness in the study region. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2010. The model shows substantial health effects of particulate matter air pollution and income deprivation, whose effects have been consistently attenuated by the currently available globally smooth models.
