Bayesian Spatial-temporal Model for Cardiac Congenital Anomalies and Ambient Air Pollution Risk Assessment.

We introduce a Bayesian spatial-temporal hierarchical multivariate probit regression model that identifies weeks during the first trimester of pregnancy which are impactful in terms of cardiac congenital anomaly development. The model is able to consider multiple pollutants and a multivariate cardiac anomaly grouping outcome jointly while allowing the critical windows to vary in a continuous manner across time and space. We utilize a dataset of numerical chemical model output which contains information regarding multiple species of PM2.5. Our introduction of an innovative spatial-temporal semiparametric prior distribution for the pollution risk effects allows for greater flexibility to identify critical weeks during pregnancy which are missed when more standard models are applied. The multivariate kernel stick-breaking prior is extended to include space and time simultaneously in both the locations and the masses in order to accommodate complex data settings. Simulation study results suggest that our prior distribution has the flexibility to outperform competitor models in a number of data settings. When applied to the geo-coded Texas birth data, weeks 3, 7 and 8 of the pregnancy are identified as being impactful in terms of cardiac defect development for multiple pollutants across the spatial domain.