Spatiotemporal Exposure Prediction with Penalized Regression

Exposure to ambient air pollution is a global health burden, and assessing its relationships to health effects requires predicting concentrations of ambient pollution over time and space. We propose a spatiotemporal penalized regression model that provides high predictive accuracy and greater computation speed than competing approaches. This model uses overfitting and time-smoothing penalties to provide accurate predictions when there are large amounts of temporal missingness in the data. When compared to spatial-only and spatiotemporal universal kriging models in simulations, our model performs similarly under most conditions and can outperform the others when temporal missingness in the data is high. As the number of spatial locations in a data set increases, the computation time of our penalized regression model is more scalable than either of the compared methods. We demonstrate our model using total particulate matter mass (PM2.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{2.5}$$\end{document} and PM10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{{10}}$$\end{document}) and using sulfate and silicon component concentrations. For total mass, our model has lower cross-validated RMSE than the spatial-only universal kriging method, but not the spatiotemporal version. For the component concentrations, which are less frequently observed, our model outperforms both of the other approaches, showing 15% and 13% improvements over the spatiotemporal universal kriging method for sulfate and silicon. The computational speed of our model also allows for the use of nonparametric bootstrap for measurement error correction, a valuable tool in two-stage health effects models. Supplementary materials accompanying this paper appear online.