Population Health Research Institute and MRC-PHE Centre for Environment and Health, St George's, University of London, Cranmer Terrace, Tooting, London, SW17 0RE, UK.
Department of Hygiene, Epidemiology and Medical Statistics, Medical School, National and Kapodistrian University of Athens, Athens, Greece.
Environ Health. 2019 Feb 14;18(1):13. doi: 10.1186/s12940-018-0432-8.
Spatio-temporal models are increasingly being used to predict exposure to ambient outdoor air pollution at high spatial resolution for inclusion in epidemiological analyses of air pollution and health. Measurement error in these predictions can nevertheless have impacts on health effect estimation. Using statistical simulation we aim to investigate the effects of such error within a multi-level model analysis of long and short-term pollutant exposure and health.
Our study was based on a theoretical sample of 1000 geographical sites within Greater London. Simulations of "true" site-specific daily mean and 5-year mean NO and PM concentrations, incorporating both temporal variation and spatial covariance, were informed by an analysis of daily measurements over the period 2009-2013 from fixed location urban background monitors in the London area. In the context of a multi-level single-pollutant Poisson regression analysis of mortality, we investigated scenarios in which we specified: the Pearson correlation between modelled and "true" data and the ratio of their variances (model versus "true") and assumed these parameters were the same spatially and temporally.
In general, health effect estimates associated with both long and short-term exposure were biased towards the null with the level of bias increasing to over 60% as the correlation coefficient decreased from 0.9 to 0.5 and the variance ratio increased from 0.5 to 2. However, for a combination of high correlation (0.9) and small variance ratio (0.5) non-trivial bias (> 25%) away from the null was observed. Standard errors of health effect estimates, though unaffected by changes in the correlation coefficient, appeared to be attenuated for variance ratios > 1 but inflated for variance ratios < 1.
While our findings suggest that in most cases modelling errors result in attenuation of the effect estimate towards the null, in some situations a non-trivial bias away from the null may occur. The magnitude and direction of bias appears to depend on the relationship between modelled and "true" data in terms of their correlation and the ratio of their variances. These factors should be taken into account when assessing the validity of modelled air pollution predictions for use in complex epidemiological models.
时空模型越来越多地被用于以高空间分辨率预测环境户外空气污染暴露情况，以便纳入空气污染与健康的流行病学分析中。然而，这些预测中的测量误差可能会对健康效应估计产生影响。我们旨在通过多水平模型分析长期和短期污染物暴露与健康之间的关系，利用统计模拟来研究这种误差的影响。
我们的研究基于大伦敦地区 1000 个地理点的理论样本。基于对伦敦地区固定位置城市背景监测器在 2009-2013 年期间的每日测量数据的分析，模拟了“真实”的特定地点每日平均和 5 年平均的 NO 和 PM 浓度，同时纳入了时间变化和空间协方差。在多水平单污染物泊松回归分析死亡率的背景下，我们研究了以下情况：模拟数据与“真实”数据之间的皮尔逊相关系数以及它们方差比（模型与“真实”），并假设这些参数在空间和时间上是相同的。
一般来说，长期和短期暴露与健康效应估计值都偏向于零，随着相关系数从 0.9 降低到 0.5，方差比从 0.5 增加到 2，偏差水平增加到 60%以上。然而，对于高相关系数（0.9）和小方差比（0.5）的组合，观察到了明显偏离零的非零偏差（>25%）。健康效应估计值的标准误差不受相关系数变化的影响，但对于方差比大于 1 的情况，标准误差似乎会被低估，而对于方差比小于 1 的情况，标准误差则会被高估。
虽然我们的研究结果表明，在大多数情况下，建模误差会导致效应估计值向零值衰减，但在某些情况下，可能会出现明显偏离零值的偏差。偏差的大小和方向似乎取决于模型数据与“真实”数据之间的关系，包括它们的相关性和方差比。在评估模型化空气污染预测在复杂流行病学模型中的有效性时，应考虑这些因素。
