  Environmental epidemiologic studies routinely utilize aggregate health
outcomes to estimate effects of short-term (e.g., daily) exposures that are
available at increasingly fine spatial resolutions. However, areal averages are
typically used to derive population-level exposure, which cannot capture the
spatial variation and individual heterogeneity in exposures that may occur
within the spatial and temporal unit of interest (e.g., within day or ZIP
code). We propose a general modeling approach to incorporate within-unit
exposure heterogeneity in health analyses via exposure quantile functions.
Furthermore, by viewing the exposure quantile function as a functional
covariate, our approach provides additional flexibility in characterizing
associations at different quantile levels. We apply the proposed approach to an
analysis of air pollution and emergency department (ED) visits in Atlanta over
four years. The analysis utilizes daily ZIP code-level distributions of
personal exposures to four traffic-related ambient air pollutants simulated
from the Stochastic Human Exposure and Dose Simulator. Our analyses find that
effects of carbon monoxide on respiratory and cardiovascular disease ED visits
are more pronounced with changes in lower quantiles of the population-level
exposure. Software for implement is provided in the R package nbRegQF.
