Exposure and measurement contributions to estimates of acute air pollution effects

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Abstract
Air pollution health effect studies are intended to estimate the effect of a pollutant on a health outcome. The definition of this effect depends upon the study design, disease model parameterization, and the type of analysis. Further limitations are imposed by the nature of exposure and our ability to measure it. We define a plausible exposure model for air pollutants that are relatively nonreactive and discuss how exposure varies. We discuss plausible disease models and show how their parameterizations are affected by different exposure partitions and by different study designs. We then discuss a measurement model conditional on ambient concentrations and incorporate this into the disease model. We use simulation studies to show the impact of a range of exposure model assumptions on estimation of the health effect in the ecologic time series design. This design only uses information from the time-varying ambient source exposure. When ambient and nonambient sources are independent, exposure variation due to nonambient source exposures behaves like Berkson measurement error and does not bias the effect estimates. Variation in the population attenuation of ambient concentrations over time does bias the estimates with the bias being either positive or negative depending upon the association of this parameter with ambient pollution. It is not realistic to substitute measured average personal exposures into time series studies because so much of the variation in personal exposures comes from nonambient sources that do not contribute information in the time series design. We conclude that general statements about the implications of measurement error need to be conditioned on the health effect study design and the health effect parameter to be estimated.