A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution.
Bottom Line: These smooth random effects confound the effects of air pollution, which are also globally smooth.This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models.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.
Affiliation: School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK.Show MeSH
Related in: MedlinePlus
Mentions: Five hundred data sets are generated under each of the nine scenarios and the results are displayed in Figure3 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. The back dots in the figure display the RMSE values for all four models, while the vertical lines represents bootstrapped 95% uncertainty intervals based on 1000 bootstrapped samples. The figure shows that no single model exhibits the lowest RMSE values for all scenarios, as the LCAR model performs best in this regard for six scenarios and second best in the remaining three, while the LM model has the lowest values for three scenarios. The latter performs well when the magnitude of the localized structure is large (large M), which is likely to be because it induces localized smoothness only when there are substantial differences between neighboring random effects. In contrast, it performs on a par with the BYM model when the localized structure is less prominent, and is substantially worse than the LCAR model in these situations. The HH model performs consistently poorly relative to the other models, which is likely to be because although it induces spatial smoothing orthogonal to the covariates, the smoothing is global (each basis function is a globally smooth quantity) and does not allow adjacent areas to have very different values (step changes). The figure also illustrates the importance of choosing an appropriate model for spatial autocorrelation, as reductions in RMSE between the best and worst model range between 6.3% and 68.3% depending on the scenario. The differences between the models can also be substantial, as the bootstrapped 95% uncertainty intervals for the RMSE often do not overlap.
Affiliation: School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW, UK.