| In environmental health studies air pollution measurements from the closest monitor are commonly used as a proxy for personal exposure. This technique assumes that air pollution concentrations are spatially homogeneous in the neighborhoods associated with the monitors and consequently introduces measurement error into a model. To model the relationship between maternal exposure to air pollution and birth weight, we build a hierarchical model that accounts for the associated measurement error. We allow four possible scenarios, with increasing flexibility, for capturing this uncertainty. In the two simplest cases, we specify one model with a constant variance term and another with a variance component that allows the uncertainty in the exposure measurements to increase as the distance between maternal residence and the location of the closest monitor increases. In the remaining two models, we introduce spatial dependence in these errors using spatial processes in the form of random effects models. We detail the specification for the exposure measure to reflect the sparsity of monitoring sites and discuss the issue of quantifying exposure over the course of a pregnancy. The model is illustrated using Bayesian hierarchical modeling techniques that relate pregnancy outcomes from the North Carolina Detailed Birth Records to air pollution data from the U.S. Environmental Protection Agency. |
