We calculated the between-pollutant Pearson correlations over time for each exposure estimation approach--and for each type of exposure error--to provide information on the collinearity of exposure estimates and exposure error that must be accounted for in a multipollutant model.
where [delta] is the exposure error, [X.sub.fine] is the exposure metric with the greater degree of refinement (i.e., increased spatial resolution or inclusion of weighting by population factors), var([x.sub.fine]) is the variance across days of [x.sub.fine], and P represents the model coefficients.
The goal of the present analysis was to examine exposure error and between-pollutant relationships and how these differ by pollutant pair and exposure metric.
Summary statistics for exposure error. The magnitude and spatial variability of the three types of normalized exposure error ([[DELTA].sub.spatial], [[delta].sub.population], and [[delta].sub.total]) across pollutants are presented in Figure 2A (see Supplemental Material, Figure S3A, for the full distribution).
To assess the potential for spatially differential exposure error, we compared the spatial variability of exposure errors across ZIP codes.
In one of the early papers on the topic of exposure error in studies of air pollution, Shy et al.
Because exposure measurement error may have substantial implications for interpreting epidemiologic studies on air pollution, particularly the time-series analyses, we developed one systematic conceptual formulation of the problem of exposure error in epidemiologic time-series studies of air pollution and considered the possible consequences for relative risk estimation.
The fundamental concepts of how exposure error can affect an epidemiologic study of pollution and health can be shown by considering the effects of exposure measurement error in a standard linear Gaussian regression model.
The degree of attenuation increases as the variance of the exposure error increases.