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There is growing evidence in the epidemiologic literature of the relationshipbetween air pollution and adverse health outcomes. Prediction of individual airpollution exposure in the Environmental Protection Agency (EPA) fundedMulti-Ethnic Study of Atheroscelerosis and Air Pollution (MESA Air) studyrelies on a flexible spatio-temporal prediction model that integrates land-useregression with kriging to account for spatial dependence in pollutantconcentrations. Temporal variability is captured using temporal trendsestimated via modified singular value decomposition and temporally varyingspatial residuals. This model utilizes monitoring data from existing regulatorynetworks and supplementary MESA Air monitoring data to predict concentrationsfor individual cohort members. In general, spatio-temporal models are limitedin their efficacy for large data sets due to computational intractability. Wedevelop reduced-rank versions of the MESA Air spatio-temporal model. To do so,we apply low-rank kriging to account for spatial variation in the mean processand discuss the limitations of this approach. As an alternative, we representspatial variation using thin plate regression splines. We compare theperformance of the outlined models using EPA and MESA Air monitoring data forpredicting concentrations of oxides of nitrogen (NO$_x$)-a pollutant of primaryinterest in MESA Air-in the Los Angeles metropolitan area via cross-validated$R^2$. Our findings suggest that use of reduced-rank models can improvecomputational efficiency in certain cases. Low-rank kriging and thin plateregression splines were competitive across the formulations considered,although TPRS appeared to be more robust in some settings.

Reduced-rank spatio-temporal modeling of air pollution concentrations in the Multi-Ethnic Study of Atherosclerosis and Air Pollution