Exploring Bias in a Generalized Additive Model for Spatial Air Pollution Data

During the past few years, the generalized additive model (GAM) has become a standard tool for epidemiologic analysis exploring the effect of air pollution on population health. Recently, the use of the GAM has been extended from time-series data to spatial data. Still more recently, it has been suggested that the use of GAMs to analyze time-series data results in air pollution risk estimates being biased upward and that concurvity in the time-series data results in standard error estimates being biased downward. We show that concurvity in spatial data can lead to underestimation of the standard error of the estimated air pollution effect, even when using an asymptotically unbiased standard error estimator. We also show that both the magnitude and direction of the bias in the air pollution effect depend, at least in part, on the nature of the concurvity. We argue that including a nonparametric function of location in a GAM for spatial epidemiologic data can be expected to result in concurvity. As a result, we recommend caution in using the GAM to analyze this type of data.