Abstract
Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled 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 localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. 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 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models.
Highlights
Quantification of the health effects of air pollution is an important problem of considerable public interest, both in terms of its financial and health impact
To contain the required flexibility, the localized conditional autoregressive (LCAR) prior captures localized residual spatial autocorrelation by allowing random effects in geographically adjacent areas to be autocorrelated or conditionally independent, and we show that this prior distribution can have realizations at both spatial smoothing extremes, namely global smoothness and independence
Five hundred data sets are generated under each of the nine scenarios and the results are displayed in Figure 3 and Table 1, which, respectively, summarize the root mean square error (RMSE) of the estimated regression parameter and the coverage and widths of the 95% uncertainty intervals
Summary
Quantification of the health effects of air pollution is an important problem of considerable public interest, both in terms of its financial and health impact. Thereby imposing an estimated equivalent health cost of £19 billion” (DEFRA Air Quality Subject Group, 2010). These estimates are based on large numbers of epidemiological studies, which have quantified the impact of both short-term and long-term exposure. Ecological small-area study designs have been used, including Elliott et al (2007), Lee, Ferguson, and Mitchell (2009), Haining et al (2010), and Greven, Dominici, and Zeger (2011) While these studies cannot assess the causal health effects of air pollution due to their ecological design, they are quick and cheap to implement, and they contribute to, and independently corroborate, the body of evidence about the long-term population level impact of air pollution.
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