Adaptive predictive principal components for modeling multivariate air pollution

Abstract

Air pollution monitoring locations are typically spatially misaligned with locations of participants in a cohort study, so to analyze pollution-health associations, exposures must be predicted at subject locations. For a pollution measure like PM_2.5 (fine particulate matter) comprised of multiple chemical components, the predictive principal component analysis (PCA) algorithm derives a low-dimensional representation of component profiles for use in health analyses. Geographic covariates and spatial splines help determine the principal component loadings of the pollution data to give improved prediction accuracy of the principal component scores. While predictive PCA can accommodate pollution data of arbitrary dimension, it is currently limited to a small number of pre-selected geographic covariates. We propose an adaptive predictive PCA algorithm, which automatically identifies a combination of covariates that is most informative in choosing the principal component directions in the pollutant space. We show that adaptive predictive PCA improves the accuracy of multi-pollutant exposure predictions at subject locations.

Keywords: Multicomponent pollution; dimension reduction; partial least squares; prediction; spatial misalignment.

Figure 1:

For one simulated dataset with uncorrelated covariates: PC1 loadings for the 15 pollutant constituents. There is one bar for each pollutant.

Figure 2:

The first component of covariate loadings for predictive PCA, and for adaptive predictive PCA for pollutant PC1: for the simulation scenario with uncorrelated covariates. Note the difference in the axis scales: bottom figure axis maximum is greater than 0.2.

Figure 3:

For one simulated dataset with uncorrelated covariates: Observed vs. predicted pollutant PC1 scores. The lines are 1–1 lines.

Figure 4:

Loadings for first 4 pollutant PCs using the adaptive predictive PCA method on IMPROVE 2014 data.

Figure 5:

Scores for first 4 pollutant PCs using the adaptive predictive PCA method on IMPROVE 2014 data.

Figure 6:

PC1: Scatterplots of prediction of pollutant PC scores doing leave one out cross validation for IMPROVE 2014 data. The lines are 1–1 lines.

Figure 7:

PC2: Scatterplots of prediction of pollutant PC scores doing leave one out cross validation for IMPROVE 2014 data. The lines are 1–1 lines.

Figure 8:

PC3: Scatterplots of prediction of pollutant PC scores doing leave one out cross validation for IMPROVE 2014 data. The lines are 1–1 lines.

Figure 9:

PC4: Scatterplots of prediction of pollutant PC scores doing leave one out cross validation for IMPROVE 2014 data. The lines are 1–1 lines.