Assessing the impact of differential measurement error on estimates of fine particle mortality

In air pollution epidemiology, error in measurements of correlated pollutants has been advanced as a reason to distrust regressions that find statistically significant weak associations. Much of the related debate in the literature and elsewhere has been qualitative. To promote quantitative evaluation of such errors, this paper develops an air pollution time-series model based on correlations among unit-normal variables. Assuming there are no other sources of bias present, the model shows the expected amount of relative bias in the regression coefficients of a bivariate regression of coarse and fine particulate matter measurements on daily mortality. The model only requires information on instrumental error and spatial variability, along with the observed regression coefficients and information on the true fine-course correlation. Analytical results show that if one pollutant is truly more harmful than the other, then it must be measured more precisely than the other in order not to bias the ratio of the fine and course regression coefficients. Utilizing published data, a case study of the Harvard Six-Cities study illustrates use of the model and emphasizes the need for data on spatial variability across the study area. Current epidemiology time-series regressions can use this model to address the general concern of correlated pollutants with differing measurement errors.