Bobb Jennifer F, Dominici Francesca, Peng Roger D
Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115.
Department of Biostatistics, Johns Hopkins School of Public Health, Baltimore, MD 21205.
J R Stat Soc Ser C Appl Stat. 2013 May;62(3):451-72. doi: 10.1111/rssc.12006.
Hierarchical models (HM) have been used extensively in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for other pollutants and other time-varying factors. Recently, Environmental Protection Agency (EPA) has called for research quantifying health effects of simultaneous exposure to many air pollutants. However, straightforward application of HM in this context is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters. Here we introduce as a general statistical approach for analyzing correlated data with many nuisance parameters. For reduced HM we first calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants), and we then specify a flexible random-effect distribution directly on this parameter. Simulation studies show that the reduced HM performs comparably to the full HM in many scenarios, and even performs better in some cases, particularly when the multivariate random-effect distribution of the full HM is misspecified. Methods are applied to estimate relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during 1999-2005.
分层模型（HM）已广泛应用于空气污染与健康的多地点时间序列研究中，以估计单一污染物经其他污染物及其他随时间变化因素调整后的健康影响。最近，美国环境保护局（EPA）呼吁开展研究，量化同时接触多种空气污染物的健康影响。然而，在这种情况下直接应用HM面临挑战，因为需要在高维干扰参数向量上指定随机效应分布。在此，我们引入一种作为分析具有许多干扰参数的相关数据的通用统计方法。对于简化的HM，我们首先计算感兴趣参数的积分似然（例如，因同时接触多种高浓度污染物导致的额外死亡人数），然后直接在该参数上指定灵活的随机效应分布。模拟研究表明，在许多情况下，简化的HM与完整的HM表现相当，甚至在某些情况下表现更好，特别是当完整HM的多元随机效应分布指定错误时。所提出的方法用于估计1999 - 2005年期间美国51个县同时接触高水平颗粒物和臭氧与心血管疾病住院的相对风险。
