Two-stage Bayesian model to evaluate the effect of air pollution on chronic respiratory diseases using drug prescriptions

A scalable two-stage Bayesian approach accounting for exposure measurement error in environmental epidemiology

Accounting for exposure measurement errors has been recognized as a crucial problem in environmental epidemiology for over two decades. Bayesian hierarchical models offer a coherent probabilistic framework for evaluating associations between environmental exposures and health effects, which take into account exposure measurement errors introduced by uncertainty in the estimated exposure as well as spatial misalignment between the exposure and health outcome data. While two-stage Bayesian analyses are often regarded as a good alternative to fully Bayesian analyses when joint estimation is not feasible, there has been minimal research on how to properly propagate uncertainty from the first-stage exposure model to the second-stage health model, especially in the case of a large number of participant locations along with spatially correlated exposures. We propose a scalable two-stage Bayesian approach, called a sparse multivariate normal (sparse MVN) prior approach, based on the Vecchia approximation for assessing associations between exposure and health outcomes in environmental epidemiology. We compare its performance with existing approaches through simulation. Our sparse MVN prior approach shows comparable performance with the fully Bayesian approach, which is a gold standard but is impossible to implement in some cases. We investigate the association between source-specific exposures and pollutant (nitrogen dioxide [NO2])-specific exposures and birth weight of full-term infants born in 2012 in Harris County, Texas, using several approaches, including the newly developed method.

A Bayesian framework for incorporating exposure uncertainty into health analyses with application to air pollution and stillbirth

Studies of the relationships between environmental exposures and adverse health outcomes often rely on a two-stage statistical modeling approach, where exposure is modeled/predicted in the first stage and used as input to a separately fit health outcome analysis in the second stage. Uncertainty in these predictions is frequently ignored, or accounted for in an overly simplistic manner when estimating the associations of interest. Working in the Bayesian setting, we propose a flexible kernel density estimation (KDE) approach for fully utilizing posterior output from the first stage modeling/prediction to make accurate inference on the association between exposure and health in the second stage, derive the full conditional distributions needed for efficient model fitting, detail its connections with existing approaches, and compare its performance through simulation. Our KDE approach is shown to generally have improved performance across several settings and model comparison metrics. Using competing approaches, we investigate the association between lagged daily ambient fine particulate matter levels and stillbirth counts in New Jersey (2011-2015), observing an increase in risk with elevated exposure 3 days prior to delivery. The newly developed methods are available in the R package KDExp.

Delivering spatially comparable inference on the risks of multiple severities of respiratory disease from spatially misaligned disease count data

Population-level disease risk varies between communities, and public health professionals are interested in mapping this spatial variation to monitor the locations of high-risk areas and the magnitudes of health inequalities. Almost all of these risk maps relate to a single severity of disease outcome, such as hospitalization, which thus ignores any cases of disease of a different severity, such as a mild case treated in a primary care setting. These spatially-varying risk maps are estimated from spatially aggregated disease count data, but the set of areal units to which these disease counts relate often varies by severity. Thus, the statistical challenge is to provide spatially comparable inference from multiple sets of spatially misaligned disease count data, and an additional complexity is that the spatial extents of the areal units for some severities are partially unknown. This paper thus proposes a novel spatial realignment approach for multivariate misaligned count data, and applies it to the first study delivering spatially comparable inference for multiple severities of the same disease. Inference is via a novel spatially smoothed data augmented MCMC algorithm, and the methods are motivated by a new study of respiratory disease risk in Scotland in 2017.

Quantifying the impact of air pollution on Covid-19 hospitalisation and death rates in Scotland

Better understanding the risk factors that exacerbate Covid-19 symptoms and lead to worse health outcomes is vitally important in the public health fight against the virus. One such risk factor that is currently under investigation is air pollution concentrations, with some studies finding statistically significant effects while other studies have found no consistent associations. The aim of this paper is to add to this global evidence base on the potential association between air pollution concentrations and Covid-19 hospitalisations and deaths, by presenting the first study on this topic at the small-area scale in Scotland, United Kingdom. Our study is one of the most comprehensive to date in terms of its temporal coverage, as it includes all hospitalisations and deaths in Scotland between 1st March 2020 and 31st July 2021. We quantify the effects of air pollution on Covid-19 outcomes using a small-area spatial ecological study design, with inference using Bayesian hierarchical models that allow for the residual spatial correlation present in the data. A key advantage of our study is its extensive sensitivity analyses, which examines the robustness of the results to our modelling assumptions. We find clear evidence that PM_2.5 concentrations are associated with hospital admissions, with a 1 μgm−3 increase in concentrations being associated with between a 7.4% and a 9.3% increase in hospitalisations. In addition, we find some evidence that PM_2.5 concentrations are associated with deaths, with a 1 μgm−3 increase in concentrations being associated with between a 2.9% and a 10.3% increase in deaths.

Readmission Prediction for Patients with Heterogeneous Medical History: A Trajectory-Based Deep Learning Approach

Hospital readmission refers to the situation where a patient is re-hospitalized with the same primary diagnosis within a specific time interval after discharge. Hospital readmission causes $26 billion preventable expenses to the U.S. health systems annually and often indicates suboptimal patient care. To alleviate those severe financial and health consequences, it is crucial to proactively predict patients’ readmission risk. Such prediction is challenging because the evolution of patients’ medical history is dynamic and complex. The state-of-the-art studies apply statistical models which use static predictors in a period, failing to consider patients’ heterogeneous medical history. Our approach – Trajectory-BAsed DEep Learning (TADEL) – is motivated to tackle the deficiencies of the existing approaches by capturing dynamic medical history. We evaluate TADEL on a five-year national Medicare claims dataset including 3.6 million patients per year over all hospitals in the United States, reaching an F1 score of 87.3% and an AUC of 88.4%. Our approach significantly outperforms all the state-of-the-art methods. Our findings suggest that health status factors and insurance coverage are important predictors for readmission. This study contributes to IS literature and analytical methodology by formulating the trajectory-based readmission prediction problem and developing a novel deep-learning-based readmission risk prediction framework. From a health IT perspective, this research delivers implementable methods to assess patients’ readmission risk and take early interventions to avoid potential negative consequences.

Modeling Antimicrobial Prescriptions in Scotland: A Spatiotemporal Clustering Approach

In 2016, the British government acknowledged the importance of reducing antimicrobial prescriptions to avoid the long-term harmful effects of overprescription. Prescription needs are highly dependent on the factors that have a spatiotemporal component, such as bacterial outbreaks and urban densities. In this context, density-based clustering algorithms are flexible tools to analyze data by searching for group structures and therefore identifying peer groups of GPs with similar behavior. The case of Scotland presents an additional challenge due to the diversity of population densities under the area of study. We propose here a spatiotemporal clustering approach for modeling the behavior of antimicrobial prescriptions in Scotland. Particularly, we consider the density-based spatial clustering of applications with noise algorithm (DBSCAN) due to its ability to include both spatial and temporal data. We extend this approach into two directions. For the temporal analysis, we use dynamic time warping to measure the dissimilarity between time series while taking into account effects such as seasonality. For the spatial component, we propose a new way of weighting spatial distances with continuous weights derived from a Kernel density estimation-based process. This makes our approach suitable for cases with different local densities, which presents a well-known challenge for the original DBSCAN. We apply our approach to antibiotic prescription data in Scotland, demonstrating how the findings can be used to compare antimicrobial prescription behavior within a group of similar peers and detect regions of extreme behaviors.

Compositional and Bayesian inference analysis of the concentrations of air pollutants in Catalonia, Spain

While most countries have networks of stations for monitoring pollutant concentrations, they do not cover the whole territory continuously. Therefore, to be able to carry out a spatial and temporal study, the predictions for air pollution from unmeasured sites and time periods need to be used. The objective of this study is to predict the air pollutant concentrations of PM₁₀, O₃, NO₂, SO₂ and CO in sites throughout Catalonia (Spain) and time periods without a monitoring station. Compositional data (CoDa) studies the relative importance of pollutants. A novel feature in this article is combining CoDa with an indicator of total pollution. Predictions are then made using a combination of spatio-temporal models and the Bayesian Laplace Integrated Approach (INLA) inference method. The most relevant results obtained indicate that the log-ratio between NO₂ and O₃ has the highest variance and the best predictive accuracy in time and space. Total pollution levels are second in variance but have low spatial predictive accuracy. Third in variance is the low temporal accuracy found in the log-ratio between SO₂ and the remaining pollutants. Globally, the combination of CoDa and the INLA method is suitable for making effective spatio-temporal predictions of air pollutants.

Multivariate Spatial Prediction of Air Pollutant Concentrations with INLA

Estimates of daily air pollution concentrations with complete spatial and temporal coverage are important for supporting epidemiologic studies and health impact assessments. While numerous approaches have been developed for modeling air pollution, they typically only consider each pollutant separately. We describe a spatial multipollutant data fusion model that combines monitoring measurements and chemical transport model simulations that leverages dependence between pollutants to improve spatial prediction. For the contiguous United States, we created a data product of daily concentration for 12 pollutants (CO, NOx, NO₂, SO₂, O₃, PM₁₀, and PM_2.5 species EC, OC, NO₃, NH₄, SO₄) during the period 2005 to 2014. Out-of-sample prediction showed good performance, particularly for daily PM_2.5 species EC (R² = 0.64), OC (R² = 0.75), NH₄ (R² = 0.84), NO₃ (R2 = 0.73), and SO₄ (R² = 0.80). By employing the integrated nested Laplace approximation (INLA) for Bayesian inference, our approach also provides model-based prediction error estimates. The daily data product at 12km spatial resolution will be publicly available immediately upon publication. To our knowledge this is the first publicly available data product for major PM_2.5 species and several gases at this spatial and temporal resolution.

Ambient air pollution and cardiovascular disease rate an ANN modeling: Yazd-Central of Iran

This study was aimed to investigate the air pollutants impact on heart patient's hospital admission rates in Yazd for the first time. Modeling was done by time series, multivariate linear regression, and artificial neural network (ANN). During 5 years, the mean concentrations of PM₁₀, SO₂, O₃, NO₂, and CO were 98.48 μg m^-3, 8.57 ppm, 19.66 ppm, 18.14 ppm, and 4.07 ppm, respectively. The total number of cardiovascular disease (CD) patients was 12,491, of which 57% and 43% were related to men and women, respectively. The maximum correlation of air pollutants was observed between CO and PM₁₀ (R = 0.62). The presence of SO₂ and NO₂ can be dependent on meteorological parameters (R = 0.48). Despite there was a positive correlation between age and CD (p = 0.001), the highest correlation was detected between SO₂ and CD (R = 0.4). The annual variation trend of SO₂, NO₂, and CO concentrations was more similar to the variations trend in meteorological parameters. Moreover, the temperature had also been an effective factor in the O₃ variation rate at lag = 0. On the other hand, SO₂ has been the most effective contaminant in CD patient admissions in hospitals (R = 0.45). In the monthly database classification, SO₂ and NO₂ were the most prominent factors in the CD (R = 0.5). The multivariate linear regression model also showed that CO and SO₂ were significant contaminants in the number of hospital admissions (R = 0.46, p = 0.001) that both pollutants were a function of air temperature (p = 0.002). In the ANN nonlinear model, the 14, 12, 10, and 13 neurons in the hidden layer were formed the best structure for PM, NO₂, O₃, and SO₂, respectively. Thus, the R_all rate for these structures was 0.78-0.83. In these structures, according to the autocorrelation of error in lag = 0, the series are stationary, which makes it possible to predict using this model. According to the results, the artificial neural network had a good ability to predict the relationship between the effect of air pollutants on the CD in a 5 years' time series.

Bayesian variable selection for the Cox regression model with spatially varying coefficients with applications to Louisiana respiratory cancer data

The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first and then applying an Markov chain Monte Carlo algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real dataset on respiratory cancer in Louisiana from the Surveillance, Epidemiology, and End Results (SEER) program.

Estimating ambient air pollutant levels in Suzhou through the SPDE approach with R-INLA

Spatio-temporal models of ambient air pollution can be used to predict pollutant levels across a geographical region. These predictions may then be used as estimates of exposure for individuals in analyses of the health effects of air pollution. Integrated nested Laplace approximations is a method for Bayesian inference, and a fast alternative to Markov chain Monte Carlo methods. It also facilitates the SPDE approach to spatial modelling, which has been used for modelling of air pollutant levels, and is available in the R-INLA package for the R statistics software. Covariates such as meteorological variables may be useful predictors in such models, but covariate misalignment must be dealt with. This paper describes a flexible method used to estimate pollutant levels for six pollutants in Suzhou, a city in China with dispersed air pollutant monitors and weather stations. A two-stage approach is used to address misalignment of weather covariate data.

Spatial Analysis of Ambient Air Pollution and Cardiovascular Disease (CVD) Hospitalization Across Sweden

The associations of multiple pollutants and cardiovascular disease (CVD) morbidity, and the spatial variations of these associations have not been nationally studied in Sweden. The main aim of this study was, thus, to spatially analyze the associations between ambient air pollution (black carbon, carbon monoxide, particulate matter (both <10 µm and <2.5 µm in diameter) and Sulfur oxides considered) and CVD admissions while controlling for neighborhood deprivation across Sweden from 2005 to 2010. Annual emission estimates across Sweden along with admission records for coronary heart disease, ischemic stroke, atherosclerotic and aortic disease were obtained and aggregated at Small Areas for Market Statistics level. Global associations were analyzed using global Poisson regression and spatially autoregressive Poisson regression models. Spatial non-stationarity of the associations was analyzed using Geographically Weighted Poisson Regression. Generally, weak but significant associations were observed between most of the air pollutants and CVD admissions. These associations were non-homogeneous, with more variability in the southern parts of Sweden. Our study demonstrates significant spatially varying associations between ambient air pollution and CVD admissions across Sweden and provides an empirical basis for developing healthcare policies and intervention strategies with more emphasis on local impacts of ambient air pollution on CVD outcomes in Sweden.

Population-weighted exposure to air pollution and COVID-19 incidence in Germany

Many countries have enforced social distancing to stop the spread of COVID-19. Within countries, although the measures taken by governments are similar, the incidence rate varies among areas (e.g., counties, cities). One potential explanation is that people in some areas are more vulnerable to the coronavirus disease because of their worsened health conditions caused by long-term exposure to poor air quality. In this study, we investigate whether long-term exposure to air pollution increases the risk of COVID-19 infection in Germany. The results show that nitrogen dioxide (NO 2 ) is significantly associated with COVID-19 incidence, with a 1 μ g  m - 3 increase in long-term exposure to NO 2 increasing the COVID-19 incidence rate by 5.58% (95% credible interval [CI]: 3.35%, 7.86%). This result is consistent across various models. The analyses can be reproduced and updated routinely using public data sources and shared R code.

The Effect of Corona Virus Lockdown on Air Pollution: Evidence from the City of Brescia in Lombardia Region (Italy)

After the outbreak of Corona virus pandemic in Italy, the government has taken extraordinary measures, including a national lockdown, to prevent the spread of the infection. This extraordinary situation has led to a reduction in air pollution levels measured in the whole Po Valley, usually known as one of the most polluted areas in Europe in terms of particulate matter (PM) and nitrogen dioxide (NO 2 ) concentrations. The main aim of this paper is to evaluate the effectiveness of the lockdown on the air quality improvement. In particular, an interrupted time series modelling approach is employed to test if a significant change in the level and the trend of the pollutant time series has occurred after the lockdown measure. The case study regards the city of Brescia (Northern Italy) and focuses on the comparison of the period before (January 1st-March 7th, 2020) and after (March 8th-March 27th, 2020) the lockdown. By adjusting for meteorology and Sunday effect, the results show that a significant change in air quality occurring in the post intervention period was observed only for a single NO 2 station located in a heavy traffic zone. In particular, the estimate of the time series slope, i.e. the expected change in the concentration associated with a time unit increase, decreases from -0.25 to -1.67 after the lockdown. For the remaining stations, no significant change was found in the concentration time series when comparing the two periods. This confirms the complexity of air pollutant concentration dynamics for the considered area, which is not merely related to emission sources but depends also on other factors as, for example, (micro and macro) meteorological conditions and the chemical and physical processes in the atmosphere, which are all independent of the lockdown measure.

Application of spatial analysis to investigate contribution of VOCs to photochemical ozone creation

This study was concerned with the temporal analysis of benzene, toluene, ethylbenzene, xylenes (BTEXs), and ozone in Rochester, New York, between 2012 and 2018. Additionally, the influence of ozone precursors (e.g., BTEXs and NO₂) and meteorological variables (e.g., relative humidity (RH), temperature along with wind speed) on ozone dispersion was investigated in the eastern half of the USA using the integrated nested Laplace approximation and stochastic partial differential equation (INLA-SPDE). The benzene variability at seasonal scale was characterized by higher values during the cold seasons. On the contrary, the long-term temporal trend of ozone depicted a repetitive cyclic behavior while an episode, with values exceeding 5 μg/m³, was detected associated with benzene in 2015. The spatial analysis by INLA-SPDE indicated that 1,3,5-trimethylbenzene and benzene were the key ozone precursors influencing ozone formation. It was demonstrated that increase of temperature had a considerable impact on ozone build-up whereas the increment of RH leads to decrease in ambient values of ozone. The amounts of root mean squared error (RMSE), mean absolute error (MAE), and bias for the validation data (e.g., 32 samples) were 0.005, 0.004, and 0.0008, exhibiting a reasonable out-of-sample forecasting by the INLA-SPDE model. The distribution map of ozone highlighted a hot spot in the state of Florida.

Estimating the health impact of air pollution in Scotland, and the resulting benefits of reducing concentrations in city centres

Air pollution continues to be a key health issue in Scotland, despite recent improvements in concentrations. The Scottish Government published the Cleaner Air For Scotland strategy in 2015, and will introduce Low Emission Zones (LEZs) in the four major cities (Aberdeen, Dundee, Edinburgh and Glasgow) by 2020. However, there is no epidemiological evidence quantifying the current health impact of air pollution in Scotland, which this paper addresses. Additionally, we estimate the health benefits of reducing concentrations in city centres where most LEZs are located. We focus on cardio-respiratory disease and total non-accidental mortality outcomes, linking them to concentrations of both particulate (PM₁₀ and PM_2.5) and gaseous (NO₂ and NO_x) pollutants. Our two main findings are that: (i) all pollutants exhibit significant associations with respiratory disease but not cardiovascular disease; and (ii) reducing concentrations in city centres with low resident populations only provides a small health benefit.

Multivariate space-time modelling of multiple air pollutants and their health effects accounting for exposure uncertainty

The long-term health effects of air pollution are often estimated using a spatio-temporal ecological areal unit study, but this design leads to the following statistical challenges: (1) how to estimate spatially representative pollution concentrations for each areal unit; (2) how to allow for the uncertainty in these estimated concentrations when estimating their health effects; and (3) how to simultaneously estimate the joint effects of multiple correlated pollutants. This article proposes a novel 2-stage Bayesian hierarchical model for addressing these 3 challenges, with inference based on Markov chain Monte Carlo simulation. The first stage is a multivariate spatio-temporal fusion model for predicting areal level average concentrations of multiple pollutants from both monitored and modelled pollution data. The second stage is a spatio-temporal model for estimating the health impact of multiple correlated pollutants simultaneously, which accounts for the uncertainty in the estimated pollution concentrations. The novel methodology is motivated by a new study of the impact of both particulate matter and nitrogen dioxide concentrations on respiratory hospital admissions in Scotland between 2007 and 2011, and the results suggest that both pollutants exhibit substantial and independent health effects.

A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale.

Quantifying the impact of current and future concentrations of air pollutants on respiratory disease risk in England

BACKGROUND

Estimating the long-term health impact of air pollution in a spatio-temporal ecological study requires representative concentrations of air pollutants to be constructed for each geographical unit and time period. Averaging concentrations in space and time is commonly carried out, but little is known about how robust the estimated health effects are to different aggregation functions. A second under researched question is what impact air pollution is likely to have in the future.

METHODS

We conducted a study for England between 2007 and 2011, investigating the relationship between respiratory hospital admissions and different pollutants: nitrogen dioxide (NO2); ozone (O3); particulate matter, the latter including particles with an aerodynamic diameter less than 2.5 micrometers (PM2.5), and less than 10 micrometers (PM10); and sulphur dioxide (SO2). Bayesian Poisson regression models accounting for localised spatio-temporal autocorrelation were used to estimate the relative risks (RRs) of pollution on disease risk, and for each pollutant four representative concentrations were constructed using combinations of spatial and temporal averages and maximums. The estimated RRs were then used to make projections of the numbers of likely respiratory hospital admissions in the 2050s attributable to air pollution, based on emission projections from a number of Representative Concentration Pathways (RCP).

RESULTS

NO2 exhibited the largest association with respiratory hospital admissions out of the pollutants considered, with estimated increased risks of between 0.9 and 1.6% for a one standard deviation increase in concentrations. In the future the projected numbers of respiratory hospital admissions attributable to NO2 in the 2050s are lower than present day rates under 3 Representative Concentration Pathways (RCPs): 2.6, 6.0, and 8.5, which is due to projected reductions in future NO2 emissions and concentrations.

CONCLUSIONS

NO2 concentrations exhibit consistent substantial present-day health effects regardless of how a representative concentration is constructed in space and time. Thus as concentrations are predicted to remain above limits set by European Union Legislation until the 2030s in parts of urban England, it will remain a substantial health risk for some time.