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.

翻译：环境流行病学研究通常利用聚合健康结局来估计短期（如每日）暴露的健康效应，这些暴露数据可达到越来越精细的空间分辨率。然而，通常采用区域平均值推导人群水平暴露量，这无法捕捉研究时空单元内（如日内或邮政编码区）可能发生的暴露空间变异和个体异质性。我们提出一种通用建模方法，通过暴露分位数函数将单元内暴露异质性纳入健康分析。进一步地，通过将暴露分位数函数视为函数型协变量，我们的方法在表征不同分位数水平的关联性时提供了额外灵活性。我们将该方法应用于亚特兰大四年间空气污染与急诊就诊关系的分析中。该分析利用随机人体暴露与剂量模拟器模拟得到的四种交通相关环境空气污染物的每日邮政编码级个人暴露分布数据。研究发现，一氧化碳对呼吸系统和心血管疾病急诊就诊的影响随人群暴露低分位数变化更为显著。实现该方法的软件已收录于R包nbRegQF。