  This paper presents an approach to estimating the health effects of an
environmental hazard. The approach is general in nature, but is applied here to
the case of air pollution. It uses a computer model involving ambient pollution
and temperature inputs, to simulate the exposures experienced by individuals in
an urban area, whilst incorporating the mechanisms that determine exposures.
The output from the model comprises a set of daily exposures for a sample of
individuals from the population of interest. These daily exposures are
approximated by parametric distributions, so that the predictive exposure
distribution of a randomly selected individual can be generated. These
distributions are then incorporated into a hierarchical Bayesian framework
(with inference using Markov Chain Monte Carlo simulation) in order to examine
the relationship between short-term changes in exposures and health outcomes,
whilst making allowance for long-term trends, seasonality, the effect of
potential confounders and the possibility of ecological bias.
  The paper applies this approach to particulate pollution (PM$_{10}$) and
respiratory mortality counts for seniors in greater London ($\geq$65 years)
during 1997. Within this substantive epidemiological study, the effects on
health of ambient concentrations and (estimated) personal exposures are
compared.
