  Understanding the role of time-varying pollution mixtures on human health is
critical as people are simultaneously exposed to multiple pollutants during
their lives. For vulnerable sub-populations who have well-defined exposure
periods (e.g., pregnant women), questions regarding critical windows of
exposure to these mixtures are important for mitigating harm. We extend
Critical Window Variable Selection (CWVS) to the multipollutant setting by
introducing CWVS for Mixtures (CWVSmix), a hierarchical Bayesian method that
combines smoothed variable selection and temporally correlated weight
parameters to (i) identify critical windows of exposure to mixtures of
time-varying pollutants, (ii) estimate the time-varying relative importance of
each individual pollutant and their first order interactions within the
mixture, and (iii) quantify the impact of the mixtures on health. Through
simulation, we show that CWVSmix offers the best balance of performance in each
of these categories in comparison to competing methods. Using these approaches,
we investigate the impact of exposure to multiple ambient air pollutants on the
risk of stillbirth in New Jersey, 2005-2014. We find consistent elevated risk
in gestational weeks 2, 16-17, and 20 for non-Hispanic Black mothers, with
pollution mixtures dominated by ammonium (weeks 2, 17, 20), nitrate (weeks 2,
17), nitrogen oxides (weeks 2, 16), PM2.5 (week 2), and sulfate (week 20). The
method is available in the R package CWVSmix.
