Spatio-temporal modeling of PM_2.5 concentrations with missing data problem: a case study in Beijing, China

One of the major challenges in conducting epidemiological studies of air pollution and health is the difficulty of estimating the degree of exposure accurately. Fine particulate matter (PM_2.5) concentrations vary in space and time, which are difficult to estimate in rural, suburban and smaller urban areas due to the sparsity of the ground monitoring network. Satellite retrieved aerosol optical depth (AOD) has been increasingly used as a proxy of ground PM_2.5 observations, although it suffers from non-trivial missing data problems. To address these issues, we developed a multi-stage statistical model in which daily PM_2.5 concentrations can be obtained with complete spatial coverage. The model consists of three stages–an inverse probability weighting scheme to correct non-random missing patterns of AOD values, a spatio-temporal linear mixed effect model to account for the spatially and temporally varying PM_2.5-AOD relationships, and a gap-filling model based on the integrated nested Laplace approximation-stochastic partial differential equations (INLA-SPDE). Good model performance was achieved from out-of-sample validation as shown in R² of 0.93 and root mean square error of 9.64 μg/m³. The results indicated that the multi-stage PM_2.5 prediction model proposed in the present study yielded highly accurate predictions, while gaining computational efficiency from the INLA-SPDE.