Performing studies on the risks of environmental hazards on human health requires accurate estimates of exposures that might be experienced by the populations at risk. Often there will be missing data and in many epidemiological studies, the locations and times of exposure measurements and health data do not match. To a large extent this will be due to the health and exposure data having arisen from completely different data sources and not as the result of a carefully designed study, leading to problems of both 'change of support' and 'misaligned data'. In such cases, a direct comparison of the exposure and health outcome is often not possible without an underlying model to align the two in the spatial and temporal domains. The Bayesian approach provides the natural framework for such models; however, the large amounts of data that can arise from environmental networks means that inference using Markov Chain Monte Carlo might not be computationally feasible in this setting. Here we adapt the integrated nested Laplace approximation to implement spatio-temporal exposure models. We also propose methods for the integration of large-scale exposure models and health analyses. It is important that any model structure allows the correct propagation of uncertainty from the predictions of the exposure model through to the estimates of risk and associated confidence intervals. The methods are demonstrated using a case study of the levels of black smoke in the UK, measured over several decades, and respiratory mortality.
Keywords: Air pollution; Bayesian modelling; Health risks; INLA; Spatio–temporal models.