Bayesian adaptive and interpretable functional regression for exposure profiles

Pollutant exposure during gestation is a known and adverse factor for birth and health outcomes. However, the links between prenatal air pollution exposures and educational outcomes are less clear, in particular the critical windows of susceptibility during pregnancy. Using a large cohort of students in North Carolina, we study the link between prenatal daily $\mbox{PM}_{2.5}$ exposure and 4th end-of-grade reading scores. We develop and apply a locally adaptive and highly scalable Bayesian regression model for scalar responses with functional and scalar predictors. The proposed model pairs a B-spline basis expansion with dynamic shrinkage priors to capture both smooth and rapidly-changing features in the regression surface. The model is accompanied by a new decision analysis approach for functional regression that extracts the critical windows of susceptibility and guides the model interpretations. These tools help to identify and address broad limitations with the interpretability of functional regression models. Simulation studies demonstrate more accurate point estimation, more precise uncertainty quantification, and far superior window selection than existing approaches. Leveraging the proposed modeling, computational, and decision analysis framework, we conclude that prenatal $\mbox{PM}_{2.5}$ exposure during early and late pregnancy is most adverse for 4th end-of-grade reading scores.