In this article we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 large U.S. cities included in the National Morbidity, Mortality and Air Pollution Study (NMMAPS) for the summers of 1987-1994. In the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP mortality associated with short-term exposure to summer ozone. In the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by taking into account the variability within and across cities. We perform the calculations with respect to several random effects distributions (normal, t-student, and mixture of normal), thus relaxing the common assumption of a two-stage normal-normal hierarchical model. We assess the sensitivity of the results to: (i) lag structure for ozone exposure; (ii) degree of adjustment for long-term trends; (iii) inclusion of other pollutants in the model; (iv) heat waves; (v) random effects distributions; and (vi) prior hyperparameters. On average across cities, we found that a 10ppb increase in summer ozone level over the previous week is associated with a 1.25 per cent increase in CVDRESP mortality (95 per cent posterior regions: 0.47, 2.03). The relative rate estimates are also positive and statistically significant at lags 0, 1 and 2. We found that associations between summer ozone and CVDRESP mortality are sensitive to the confounding adjustment for PM10, but are robust to: (i) the adjustment for long-term trends, other gaseous pollutants (NO2, SO2 and CO); (ii) the distributional assumptions at the second stage of the hierarchical model; and (iii) the prior distributions on all unknown parameters. Bayesian hierarchical distributed lag models and their application to the NMMAPS data allow us to estimate of an acute health effect associated with exposure to ambient air pollution in the last few days on average across several locations. The application of these methods and the systematic assessment of the sensitivity of findings to model assumptions provide important epidemiological evidence for future air quality regulations.

中文翻译：

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夏季臭氧暴露和心肺死亡率的贝叶斯分层分布滞后模型

在本文中，我们开发了贝叶斯分层分布滞后模型，用于估计夏季臭氧水平的每日变化与心血管和呼吸系统 (CVDRESP) 死亡率计数的每日变化之间的关联，这些关系包括在美国国家发病率、死亡率和空气污染研究 (NMMAPS) 中的 19 个美国大城市) 1987-1994 年的夏天。在第一阶段，我们定义了一个半参数分布式滞后泊松回归模型来估计与短期暴露于夏季臭氧相关的城市特定的 CVDRESP 死亡率相对率。在第二阶段，我们为真实的城市特定相对比率指定一类分布，以通过考虑城市内部和城市之间的可变性来估计整体影响。我们对几个随机效应分布（正态分布、t-student 和混合正态），从而放宽了两阶段正态-正态分层模型的共同假设。我们评估结果对以下方面的敏感性：(i) 臭氧暴露的滞后结构；(ii) 长期趋势的调整程度；(iii) 将其他污染物纳入模型；(iv) 热浪；(v) 随机效应分布；(vi) 先验超参数。平均而言，我们发现夏季臭氧水平比前一周增加 10ppb 与 CVDRESP 死亡率增加 1.25% 相关（95% 的后区：0.47、2.03）。相对速率估计值在滞后 0、1 和 2 处也是正数且具有统计显着性。我们发现夏季臭氧与 CVDRESP 死亡率之间的关联对 PM10 的混杂调整很敏感，但在以下方面是稳健的：(i) 长期趋势的调整，其他气态污染物（二氧化氮、二氧化硫和一氧化碳）；(ii) 分层模型第二阶段的分布假设；(iii) 所有未知参数的先验分布。贝叶斯分层分布式滞后模型及其在 NMMAPS 数据中的应用使我们能够估计与过去几天平均在多个地点暴露于环境空气污染相关的急性健康影响。这些方法的应用以及结果对模型假设的敏感性的系统评估为未来的空气质量监管提供了重要的流行病学证据。(iii) 所有未知参数的先验分布。贝叶斯分层分布式滞后模型及其在 NMMAPS 数据中的应用使我们能够估计与过去几天平均在多个地点暴露于环境空气污染相关的急性健康影响。这些方法的应用以及结果对模型假设的敏感性的系统评估为未来的空气质量监管提供了重要的流行病学证据。(iii) 所有未知参数的先验分布。贝叶斯分层分布式滞后模型及其在 NMMAPS 数据中的应用使我们能够估计与过去几天平均在多个地点暴露于环境空气污染相关的急性健康影响。这些方法的应用以及研究结果对模型假设的敏感性的系统评估为未来的空气质量监管提供了重要的流行病学证据。