Recent studies of associations between environmental exposures and health outcomes have shifted toward estimating the effect of simultaneous exposure to multiple chemicals. Summary index methods, such as the weighted quantile sum and quantile g-computation, are now commonly used to analyze environmental exposure mixtures in a broad range of applications. These methods provide a simple and interpretable framework for quantifying mixture effects. However, when data arise from a large geographical study region, it may be unreasonable to expect a common mixture effect. In this work, we explore the use of a recently developed spatially varying coefficient model based on Bayesian additive regression trees to estimate spatially heterogeneous mixture effects using quantile g-computation. We conducted simulation studies to evaluate the method's performance. We then applied this model to an analysis of multiple ambient air pollutants and birthweight in Georgia, USA from 2005-2016. We find evidence of county-level spatially varying mixture associations, where for 17 of 159 counties in Georgia, elevated concentrations of a mixture of PM2.5, nitrogen dioxide, sulfur dioxide, ozone, and carbon monoxide were associated with a reduction in birthweight by as much as -16.65 grams (95% credible interval: -33.93, -0.40) per decile increase in all five air pollutants.

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