  Distributed lag models are useful in environmental epidemiology as they allow
the user to investigate critical windows of exposure, defined as the time
period during which exposure to a pollutant adversely affects health outcomes.
Recent studies have focused on estimating the health effects of a large number
of environmental exposures, or an environmental mixture, on health outcomes. In
such settings, it is important to understand which environmental exposures
affect a particular outcome, while acknowledging the possibility that different
exposures have different critical windows. Further, in the studies of
environmental mixtures, it is important to identify interactions among
exposures, and to account for the fact that this interaction may occur between
two exposures having different critical windows. Exposure to one exposure early
in time could cause an individual to be more or less susceptible to another
exposure later in time. We propose a Bayesian model to estimate the temporal
effects of a large number of exposures on an outcome. We use spike-and-slab
priors and semiparametric distributed lag curves to identify important
exposures and exposure interactions, and discuss extensions with improved power
to detect harmful exposures. We then apply these methods to estimate the
effects of exposure to multiple air pollutants during pregnancy on birthweight
from vital records in Colorado.
