  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
concentration in a two-component model: a pollutant model is specified to
estimate the `true' concentration values for if your 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.
