Using spline models to estimate the varying health risks from air pollution across Scotland.

The health risks associated with long-term exposure to air pollution are often estimated from small-area data by regressing the numbers of disease cases in each small area against air pollution concentrations and other covariates. The majority of studies in this field only estimate a single health risk for the entire region, whereas in fact the risks in each small area may vary because of differences in the exposure level and the extent to which the population are vulnerable to disease. This paper proposes a natural cubic spline model for estimating these varying health risks, which allows the risks to depend (potentially) non-linearly on additional risk factors. The methods are implemented within a Bayesian setting, with inference based on Markov chain Monte Carlo simulation. The approach is illustrated by presenting a study based in Scotland, which investigates the relationship between PM (10) concentrations and respiratory related hospital admissions.