Bayesian latent variable modelling in studies of air pollution and health

This paper describes the use of Bayesian latent variable models in the context of studies investigating the short-term effects of air pollution on health. Traditional Poisson or quasi-likelihood regression models used in this area assume that consecutive outcomes are independent (although the latter allows for overdispersion), which in many studies may be an untenable assumption as temporal correlation is to be expected. We compare this traditional approach with two Bayesian latent process models, which acknowledge the possibility of short-term autocorrelation. These include an autoregressive model that has previously been used in air pollution studies and an alternative based on a moving average structure that we describe here. A simulation study assesses the performance of these models when there are different forms of autocorrelation in the data. Although estimated risks are largely unbiased, the results show that assuming independence can produce confidence intervals that are too narrow. Failing to account for the additional uncertainty which may be associated with (positive) correlation can result in confidence/credible intervals being too narrow and thus lead to incorrect conclusions being made about the significance of estimated risks. The methods are illustrated within a case study of the effects of short-term exposure to air pollution on respiratory mortality in the elderly in London, between 1997 and 2003.