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

A Scalar-on-Quantile-Function Approach for Estimating Short-term Health Effects of Environmental Exposures