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Hierarchical Bivariate Time Series Models: A Combined Analysis of the Effects of Particulate Matter on Morbidity and Mortality

机译:分层双变量时间序列模型:颗粒物对发病率和死亡率的影响的组合分析

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摘要

In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (PM10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mortality and morbidity for 10 metropolitan areas in the United States from 1986 to 1993. We postulate that these time series should be related through a shared relationship with PM10.At the first stage of the hierarchy, we fit two seemingly unrelated Poisson regression models to produce city-specific estimates of the log relative rates of mortality and morbidity associated with exposure to PM10 within each location. The sample covariance matrix of the estimated log relative rates is obtained using a novel generalized estimating equation approach that takes into account the correlation between the mortality and morbidity time series. At the second stage, we combine information across locations to estimate overall log relative rates of mortality and morbidity and variation of the rates across cities.Using the combined information across the 10 locations we find that a 10 mu g/m3 increase in average PM10 at the current day and previous day is associated with a 0:26% increase in mortality (95% posterior interval -0:37; 0:65), and a 0:71% increase in hospital admissions (95% posterior interval 0:35; 0:99). The log relative rates of mortality and morbidity have a similar degree of heterogeneity across cities: the posterior means of the between-city standard deviations of the mortality and morbidity air pollution effects are 0:42 (95% interval 0:05; 1:18), and 0:31 (95% interval 0:10; 0:89), respectively. The city-specific log relative rates of mortality and morbidity are estimated to have very low correlation, but the uncertainty in the correlation is very substantial (posterior mean = 0:20; 95% interval -0:89; 0:98).With the parameter estimates from the model, we can predict the hospitalization log relative rate for a new city for which hospitalization data are unavailable, using that cityu27s estimated mortality relative rate. We illustrate this prediction using New York as an example.
机译:在本文中,我们开发了一个分层的双变量时间序列模型,以表征空气动力学直径(PM10)小于10微米的颗粒物与心血管疾病的死亡率和住院率之间的关系。该模型应用于1986年至1993年美国10个大都市地区的死亡率和发病率的时间序列数据。我们假设这些时间序列应该通过与PM10的共享关系来关联。在层次结构的第一阶段,我们对两个看似无关的Poisson回归模型进行拟合,以得出每个地点与PM10暴露相关的死亡率和发病率的对数相对死亡率的城市估计值。使用新颖的广义估计方程方法获得估计对数相对比率的样本协方差矩阵,该方法考虑了死亡率和发病时间序列之间的相关性。在第二阶段,我们结合各个地区的信息来估算死亡率和发病率的总体对数相对比率以及各个城市间的比率变化,利用这10个地区的综合信息,我们发现在10个州的平均PM10增长了10克/立方米。当前和前一天的死亡率增加0:26%(后间隔95%-0:37; 0:65),住院人数增加0:71%(后间隔95%以后0:35) ; 0:99)。对数死亡率和发病率相对比率在城市之间具有相似程度的异质性:死亡率和发病率空气污染影响的城市间标准差的后验均值为0:42(95%区间为0:05; 1:18 )和0:31(95%间隔0:10; 0:89)。据估计,特定城市的对数死亡率和发病率的相对比率具有非常低的相关性,但相关性的不确定性非常大(后均值= 0:20; 95%区间-0:89; 0:98)。根据模型中的参数估计值,我们可以使用该城市的估计死亡率相对率来预测没有可用住院数据的新城市的住院记录相对率。我们以纽约为例说明了这一预测。

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