Measurement error in a multi-level analysis of air pollution and health: a simulation study

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 NO₂ and PM₁₀ 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.