A Bayesian localized conditional autoregressive model for estimating the health effects of air pollution

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.

A Gaussian random field model for similarity-based smoothing in Bayesian disease mapping

“…The LCAR [52] model as the only model that does not take the neighborhoods as fixed but those emerge from real data, as a random quantity.…”

“…We examine their capabilities, drawbacks and developments. We also analyse the most recent developments in the field by showing the new LCAR model [52], which assumes local and not global smoothing, as do the BYM, MBYM and LLB. We present the MBYM model [59] and its advantages versus the BYM model.…”

“…As mentioned by Waller and Carlin [84] DM refers to a collection of methods extending SAE to directly utilize the spatial setting and assumed positive spatial correlation between observations. The data used are aggregated or averaged values at the small area level, representing disease incidence, prevalence or mortality rates, frequently not coming from surveys but coming from counts of disease cases from hospital admissions [52,59]), counts of cancer cases or cancer deaths [9,47,82]), and mortality data [20,59,60]). In our motivating example we use counts of disease cases from a survey.…”

“…The matrixW is treated by the LCAR model as a single random quantity, which avoids several problems identified by other authors (for more details see Lee et al [52], section 3.2). The authors [51] propose eliciting the set of candidate values ofW from data having a similar spatial structure as the response variable.…”

“…For the basis classification category a good example is presented in English et al [25] in which the area was redefined in grids of 0.5 miles and neighbours chosen were the immediate north, south, east, and west of each particular gridpoint. A good example of the estimated adjacency matrix is the one used in the LCAR model [52].…”