A Spatially-Varying Distributed Lag Model with Application to an Air Pollution and Term Low Birth Weight Study
Distributed lag models have been used to identify and estimate critical periods of exposure to air pollution during pregnancy (i.e., critical exposure windows) in studies of pregnancy outcomes. However, the majority of previous work in this area has ignored the possibility of spatial variability in the lagged health effect parameters and has instead assumed that these parameters were constant across the discrete geographic areas included in the study. To relax this assumption, we develop SpGPCW (Spatially-varying Gaussian Process model for Critical Windows) and use it to investigate geographic variability in the association between term low birth weight (gestational age ? 37 weeks, birth
weight < 2,500 grams) and average weekly concentrations of ozone and particulate matter less than 2.5 micrometers in aerodynamic diameter (PM2:5) during pregnancy. We evaluated birth records from the Raleigh-Durham-Chapel Hill Combined Statistical Area of North Carolina for the years 2005-2008. SpGPCW is designed to accommodate areal level spatial correlation between lagged health effect parameters, temporal smoothness in estimation across pregnancy, and collapses to the standard Gaussian process method for critical window estimation in the absence spatial variability in risk. Through simulation and real data application, we show the consequences of ignoring spatial variability in the lagged health effect parameters, investigate the use of an existing Bayesian model comparison technique as a method for determining the presence of spatial variability, and explore the impact of air pollution exposure on term low birth weight. We find that exposure to PM2:5 during late first and early second trimester is associated with elevated term low birth weight risk in selected counties and that ignoring the spatial variability in the lagged health effect parameters results in null associations during these periods. An R package (SpGPCW) is developed to implement the new method.