Modeling Air Pollution, Climate, and Health Data Using Bayesian Networks: A Case Study of the English Regions

Abstract

The link between pollution and health is commonly explored by trying to identify the dominant cause of pollution and its most significant effect on health outcomes. The use of multivariate features to describe exposure is less explored because investigating a large domain of scenarios is theoretically (i.e., interpretation of results) and technically (i.e., computational effort) challenging. In this work we explore the use of Bayesian Networks with a multivariate approach to identify the probabilistic dependence structure of the environment‐health nexus. This consists of environmental factors (topography and climate), exposure levels (concentration of outdoor air pollutants), and health outcomes (mortality rates). The information is collated with regard to a data‐rich study area: the English regions (UK), which incorporate environmental types that are different in character from urban to rural. We implemented a reproducible workflow in the R programming language to collate environment‐health data and analyze almost 50 millions of observations making use of a graphical model (Bayesian Network) and Big Data technologies. Results show that for pollution and weather variables the model tests well in sample but also has good predictive power when tested out of sample. This is facilitated by a training/testing split in the data along time and space dimension and suggests that the model generalizes well to new regions and time periods.

Learning Bayesian networks from big data with greedy search: computational complexity and efficient implementation

“…Year Zone Fig. 1 Conditional Linear Gaussian BN from Vitolo et al (2018). Yellow nodes are multinomial, blue nodes are Gaussian, and green nodes are conditional linear Gaussian.…”

“…We demonstrate the reductions in computational complexity we discussed in Sections 4.1 and 4.2 using the MEHRA data set from Vitolo et al (2018), which studied 50 million observations to explore the interplay between environmental factors, exposure levels to outdoor air pollutants, and health outcomes in the English regions of the United Kingdom between 1981 and 2014. The CLGBN learned in that paper is shown in Figure 1: it comprises 24 variables describing the concentrations of various air pollutants (O3, PM 2.5 , PM 10 , SO 2 , NO 2 , CO) measured in 162 monitoring stations, their geographical characteristics (latitude, longitude, latitude, region and zone type), weather (wind speed and direction, temperature, rainfall, solar radiation, boundary layer height), demography and mortality rates.…”

“…The original analysis was performed with the bnlearn R package (Scutari, 2010), and it was complicated by the fact that many of the variables describing the pollutants had significant amounts of missing data due to the lack of coverage in particular regions and years. Therefore, Vitolo et al (2018) learned the BN using the Structural EM algorithm (Friedman, 1997), which is an application of the Expectation-Maximisation algorithm (EM; Dempster et al, 1977) to BN structure learning that uses hill-climbing to implement the M step.…”

“…Furthermore, we measure the accuracy of network reconstruction using the Structural Hamming Distance Tsamardinos et al (SHD;2006), which measures the number of arcs that differ between the CPDAG representations of the equivalence classes of two network structures. In our case, those we learn from the simulated data and the original network structure from Vitolo et al (2018). All computations are performed with the bnlearn package in R 3.3.3 on a machine with two Intel Xeon CPU E5-2690 processors (16 cores) and 384GB of RAM.…”

“…Furthermore, we confirm the results from Chickering and Heckerman (2000) on network reconstruction accuracy. In Table 1 we report the sums of the SHDs between the network structures learned by BIC and that from Vitolo et al (2018), and the corresponding sum for the networks learned using PRED, for the considered sample sizes. Overall, we find that BIC results in 13 errors over the 30 learned DAGs, compared to 4 for (12).…”