The issue of measurement error is unavoidable in epidemiologic studies of air pollution . Although methods for dealing with this measurement error have been proposed [2, 3] and applied to air pollution epidemiology specifically [4, 5], the issue remains a central concern in the field . Because large-scale time-series studies often use single central monitoring sites to characterize community exposure to ambient concentrations , uncertainties arise regarding the extent to which these monitors are representative of exposure. Zeger et al.  identify three components of measurement error: (1) the difference between individual exposures and average personal exposure, (2) the difference between average personal exposure and ambient levels, and (3) the difference between measured and true ambient concentrations. While the former two components of error can have a sizeable impact on epidemiologic findings that address etiologic questions of health effects and personal exposure, it is the third component that is particularly relevant in time-series studies that address questions of the health benefits of ambient regulation .
Prior studies have suggested that the impact of measurement error on time-series health studies differs depending upon the type of error introduced [[8, 10, 11]]. Two distinctly different types of error have been identified. One type is classical error, in which measurements, Z
, vary randomly about true concentrations,
; this can be considered the case for instrument error associated with ambient monitors. That is, instrument error is independent of the true ambient level, such that
. Moreover, the variation in the measurements, Z
, is expected to be greater than the variation in the true values,
. Therefore, classical error is expected to attenuate the effect estimate in time-series epidemiologic studies. In contrast, under a Berkson error framework, the true ambient,
, varies randomly about the measurement, Z
. This might be the case, for example, of a measured population average over the study area with true individual ambient levels varying randomly about this population average measurement. In this case, measurement error is independent of the measured population average ambient; that is,
. Furthermore, the measurement, Z
, is less variable than the true ambient level,
. A purely Berkson error is expected to yield an unbiased effect estimate, provided that the true dose-response is linear .
Several studies have investigated the impact of error type on regression models. The simultaneous impact of classical and Berkson errors in a parametric regression estimating radon exposure has been investigated  and error type has been assessed in a semiparametric Bayesian setting looking at exposure to radiation from nuclear testing [13, 14]; however, no study to date has comprehensively assessed the impact of error type across multiple pollutants for instrument imprecision and spatial variability in a time-series context.
Error type depends on the relationship between the distribution of measurements and the distribution of true values. Because true relevant exposure in environmental epidemiologic studies is not known exactly, determination of error type is challenging; thus, here we examine the impact of error modelled as two distinctly different types: classical and Berkson. First, we examine monitor data to assess whether error is better modelled on a logged or unlogged basis. Typically, researchers investigating error type have added error on an unlogged basis (e.g. [8, 11]); however, air pollution data are more often lognormal due to atmospheric dynamics and concentration levels that are never less than zero. It is plausible that true ambient exposures are distributed lognormally about a population average as well; therefore, measurement error may be best described as additive error on the log scale. We investigate the combined error from two sources that have been previously identified as relevant in time-series studies: (1) instrument precision error and (2) error due to spatial variability . We limit our scope to ambient levels of pollutants measured in accordance with regulatory specifications, disregarding spatial microscale variability, such as near roadway concentrations, as well as temporal microscale variability, such as that associated with meteorological events on sub-hour time scales. Here, building on a previously developed model for the amount of error associated with selected ambient air pollutants , we quantitatively assess the effect of error type on the impacts of measurement error on epidemiologic results from an ongoing study of air pollution and emergency department visits in Atlanta.