A hierarchical modelling approach to assess multi pollutant effects in time-series studies

Abstract

When assessing the short-term effect of air pollution on health outcomes, it is common practice to consider one pollutant at a time, due to their high correlation. Multi pollutant methods have been recently proposed, mainly consisting of collapsing the different pollutants into air quality indexes or clustering the pollutants and then evaluating the effect of each cluster on the health outcome. A major drawback of such approaches is that it is not possible to evaluate the health impact of each pollutant. In this paper we propose the use of the Bayesian hierarchical framework to deal with multi pollutant concentrations in a two-component model: a pollutant model is specified to estimate the 'true' concentration values for each pollutant and then such concentration is linked to the health outcomes in a time-series perspective. Through a simulation study we evaluate the model performance and we apply the modelling framework to investigate the effect of six pollutants on cardiovascular mortality in Greater London in 2011-2012.

Fig 1. Graphical representation of the modelling frameworks.

(a) shows the proposed two component model: the left hand side represents the pollutant component, while the right hand side the health component. The latent concentration for each pollutant and day, μ_pt, obtained from the pollutant component enters the health model as predictor. The specification of the link between μ_pt and λ_t makes the difference between H2M and H2Mjoint. In the former the uncertainty from μ_pt goes forward into the health model, but there is no feedback from O_t; in the latter the uncertainty goes forward, while at the same time information from the mortality count O_t can influence back μ_pt. (b) shows the ME model: the pollutant component is not there and the measured pollutant concentration Y_pt is now directly linked to λ_t. For both (a) and (b) the circles denote latent random variables, while the rectangles are observed quantities; single rectangles are random variables, while double rectangles enter the model as data and are not characterised by a probability distribution i.e. the Y_t in (b).

Fig 2. 95% posterior credible intervals for β under ME, H2M and H2Mjoint.

The H2Ms show smaller levels of uncertainty, as this influence the coefficients from the pollutant estimates as well as from the health model itself. At the same time the ME model shows a larger bias in the estimates, due to the measurement error, while H2Mjoint model shows a median estimate virtually equal to the true values, suggesting how the feedback from the outcome can play a role in reducing the corresponding bias.