Inference from ecological models: Estimating the relative risk of stroke from air pollution exposure using small area data

Maheswaran et al. (2006) analysed the effect of outdoor modelled NOx levels, classified into quintiles, on stroke mortality using a Poisson Bayesian hierarchical model with spatial random effects. An association was observed between higher levels of NOx and stroke mortality at the small area (enumeration district) level.
As this model is framed in an ecological perspective, the relative risk estimates suffer from ecological bias. In this paper we use a different model specification based on Jackson et al. (2008), modelling the number of cases of mortality due to stroke as a binomial random variable where p(i) is the probability of dying from stroke in area i. The within-area variation in outdoor modelled NOx levels is used to determine the proportion of the population in area i falling into each of the five exposure categories in order to estimate the probability of an individual dying from stroke given the kth level of NOx exposure assuming a homogeneous effect across the study region. The inclusion of within-area variability in an ecological regression model has been demonstrated to help reduce the ecological bias ([Jackson et al., 2006] and [Jackson et al., 2008]). Revised estimates of relative risk are obtained and compared with previous estimates.