Daniels Michael J, Dominici Francesca, Zeger Scott
Department of Statistics, University of Florida, Gainesville, Florida 32611, USA.
Epidemiology. 2004 Jan;15(1):57-62. doi: 10.1097/01.ede.0000092721.00997.f7.
Multi-site time series studies of the association of air pollution with mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating short-term effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and to estimate pooled air pollution effects while taking into account both within-site statistical uncertainty and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, and highly correlated predictors) make the modeling of all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined.In this paper, we investigate the impact of variance underestimation on the pooled relative rate estimate. We focused on two-stage normal-normal hierarchical models and on underestimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation did not affect the pooled estimate substantially. However, the pooled estimate was somewhat sensitive to variance underestimation when the number of sites was small and underestimation was severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results (including meta-analyses), and they can easily be extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity, Mortality and Air Pollution Study. We found that variance underestimation as large as 40% had little effect on the national average.
空气污染与死亡率和发病率关联的多地点时间序列研究在文献中占据显著地位，是估算空气污染对健康短期影响的综合方法。分层模型通常用于整合特定地点的信息，并在考虑地点内统计不确定性和地点间异质性的同时估算汇总的空气污染影响。在一个地点内，空气污染和健康的时间序列数据特征（微小的污染影响、缺失数据以及高度相关的预测因子）使得对所有不确定性来源进行建模具有挑战性。一个潜在后果是低估了要汇总的特定地点效应的统计方差。在本文中，我们研究方差低估对汇总相对率估计的影响。我们聚焦于两阶段正态 - 正态分层模型以及第一阶段统计方差的低估情况。通过数学考量和模拟研究，我们发现方差低估对汇总估计的影响不大。然而，当地点数量较少且低估严重时，汇总估计对方差低估有些敏感。这些模拟结果适用于任何用于整合特定地点结果信息的两阶段正态 - 正态分层模型（包括荟萃分析），并且可以轻松扩展到更一般的分层形式。我们还研究了方差低估对《国家发病率、死亡率与空气污染研究》中全国平均相对率估计的影响。我们发现高达40%的方差低估对全国平均值影响不大。
