Bayesian 2-Stage Space-Time Mixture Modeling With Spatial Misalignment of the Exposure in Small Area Health Data

A Bayesian multistage spatio-temporally dependent model for spatial clustering and variable selection

In spatio-temporal epidemiological analysis, it is of critical importance to identify the significant covariates and estimate the associated time-varying effects on the health outcome. Due to the heterogeneity of spatio-temporal data, the subsets of important covariates may vary across space and the temporal trends of covariate effects could be locally different. However, many spatial models neglected the potential local variation patterns, leading to inappropriate inference. Thus, this article proposes a flexible Bayesian hierarchical model to simultaneously identify spatial clusters of regression coefficients with common temporal trends, select significant covariates for each spatial group by introducing binary entry parameters and estimate spatio-temporally varying disease risks. A multistage strategy is employed to reduce the confounding bias caused by spatially structured random components. A simulation study demonstrates the outperformance of the proposed method, compared with several alternatives based on different assessment criteria. The methodology is motivated by two important case studies. The first concerns the low birth weight incidence data in 159 counties of Georgia, USA, for the years 2007 to 2018 and investigates the time-varying effects of potential contributing covariates in different cluster regions. The second concerns the circulatory disease risks across 323 local authorities in England over 10 years and explores the underlying spatial clusters and associated important risk factors.

Multi-pollutant case-crossover models of all-cause and cause-specific mortality and hospital admissions by age group in 47 Canadian cities

Most of the existing epidemiological studies have investigated adverse health effects of multiple air pollutants for a limited number of cities, thus the evidence of the health impacts is limited and it is challenging to compare these results because of different modeling approaches and potential publication bias. In this paper, we expand the number of Canadian cities, with the use of the most recent available health data. A multi-pollutant model in a case-crossover design is used to investigate the short-term impacts of air pollution on various health outcomes in 47 Canadian main cities, comparing three age groups (all-age, senior (age 66+), non-senior). The main findings are that a 14 ppb increase of O₃ was associated with a 0.17%-2.78% (0.62%-1.46%) increase in the odds of all-age respiratory mortality (hospitalization). A 12.8 ppb increase of NO₂ was associated with a 0.57%-1.47% (0.68%-1.86%) increase in the odds of all-age (non-senior) respiratory hospitalization. A 7.6 μgm^-3 increase of PM_2.5 was associated with a 0.19%-0.69% (0.33%-1.1%) increase in the odds of all-age (non-senior) respiratory hospitalization.

Investigating the spatio-temporal variation of hepatitis A in Korea using a Bayesian model

Hepatitis A is a water-borne infectious disease that frequently occurs in unsanitary environments. However, paradoxically, those who have spent their infancy in a sanitary environment are more susceptible to hepatitis A because they do not have the opportunity to acquire natural immunity. In Korea, hepatitis A is prevalent because of the distribution of uncooked seafood, especially during hot and humid summers. In general, the transmission of hepatitis A is known to be dynamically affected by socioeconomic, environmental, and weather-related factors and is heterogeneous in time and space. In this study, we aimed to investigate the spatio-temporal variation of hepatitis A and the effects of socioeconomic and weather-related factors in Korea using a flexible spatio-temporal model. We propose a Bayesian Poisson regression model coupled with spatio-temporal variability to estimate the effects of risk factors. We used weekly hepatitis A incidence data across 250 districts in Korea from 2016 to 2019. We found spatial and temporal autocorrelations of hepatitis A indicating that the spatial distribution of hepatitis A varied dynamically over time. From the estimation results, we noticed that the districts with large proportions of males and foreigners correspond to higher incidences. The average temperature was positively correlated with the incidence, which is in agreement with other studies showing that the incidences in Korea are noticeable in spring and summer due to the increased outdoor activity and intake of stale seafood. To the best of our knowledge, this study is the first to suggest a spatio-temporal model for hepatitis A across the entirety of Korean. The proposed model could be useful for predicting, preventing, and controlling the spread of hepatitis A.

Spatiotemporal high-resolution prediction and mapping: methodology and application to dengue disease

Dengue disease has become a major public health problem. Accurate and precise identification, prediction and mapping of high-risk areas are crucial elements of an effective and efficient early warning system in countering the spread of dengue disease. In this paper, we present the fusion area-cell spatiotemporal generalized geoadditive-Gaussian Markov random field (FGG-GMRF) framework for joint estimation of an area-cell model, involving temporally varying coefficients, spatially and temporally structured and unstructured random effects, and spatiotemporal interaction of the random effects. The spatiotemporal Gaussian field is applied to determine the unobserved relative risk at cell level. It is transformed to a Gaussian Markov random field using the finite element method and the linear stochastic partial differential equation approach to solve the "big n" problem. Sub-area relative risk estimates are obtained as block averages of the cell outcomes within each sub-area boundary. The FGG-GMRF model is estimated by applying Bayesian Integrated Nested Laplace Approximation. In the application to Bandung city, Indonesia, we combine low-resolution area level (district) spatiotemporal data on population at risk and incidence and high-resolution cell level data on weather variables to obtain predictions of relative risk at subdistrict level. The predicted dengue relative risk at subdistrict level suggests significant fine-scale heterogeneities which are not apparent when examining the area level. The relative risk varies considerably across subdistricts and time, with the latter showing an increase in the period January-July and a decrease in the period August-December.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10109-021-00368-0.

Joint space-time Bayesian disease mapping via quantification of disease risk association

Alzheimer's disease is an increasingly prevalent neurological disorder with no effective therapies. Thus, there is a need to characterize the progression of Alzheimer's disease risk in order to preclude its inception in patients. Characterizing Alzheimer's disease risk can be accomplished at the population-level by the space-time modeling of Alzheimer's disease incidence data. In this paper, we develop flexible Bayesian hierarchical models which can borrow risk information from conditions antecedent to Alzheimer's disease, such as mild cognitive impairment, in an effort to better characterize Alzheimer's disease risk over space and time. From an application of these models to real-world Alzheimer's disease and mild cognitive impairment spatiotemporal incidence data, we found that our novel models provided improved model goodness of fit, and via a simulation study, we demonstrated the importance of diagnosing the label-switching problem for our models as well as the importance of model specification in order to best capture the contribution of time in modeling Alzheimer's disease risk.

Using Latent Class Modeling to Jointly Characterize Economic Stress and Multipollutant Exposure

BACKGROUND

Work is needed to better understand how joint exposure to environmental and economic factors influence cancer. We hypothesize that environmental exposures vary with socioeconomic status (SES) and urban/rural locations, and areas with minority populations coincide with high economic disadvantage and pollution.

METHODS

To model joint exposure to pollution and SES, we develop a latent class mixture model (LCMM) with three latent variables (SES Advantage, SES Disadvantage, and Air Pollution) and compare the LCMM fit with K-means clustering. We ran an ANOVA to test for high exposure levels in non-Hispanic black populations. The analysis is at the census tract level for the state of North Carolina.

RESULTS

The LCMM was a better and more nuanced fit to the data than K-means clustering. Our LCMM had two sublevels (low, high) within each latent class. The worst levels of exposure (high SES disadvantage, low SES advantage, high pollution) are found in 22% of census tracts, while the best levels (low SES disadvantage, high SES advantage, low pollution) are found in 5.7%. Overall, 34.1% of the census tracts exhibit high disadvantage, 66.3% have low advantage, and 59.2% have high mixtures of toxic pollutants. Areas with higher SES disadvantage had significantly higher non-Hispanic black population density (NHBPD; P < 0.001), and NHBPD was higher in areas with higher pollution (P < 0.001).

CONCLUSIONS

Joint exposure to air toxins and SES varies with rural/urban location and coincides with minority populations.

IMPACT

Our model can be extended to provide a holistic modeling framework for estimating disparities in cancer survival.See all articles in this CEBP Focus section, "Environmental Carcinogenesis: Pathways to Prevention."

An Introductory Framework for Choosing Spatiotemporal Analytical Tools in Population-Level Eco-Epidemiological Research

Spatiotemporal visualization and analytical tools (SATs) are increasingly being applied to risk-based surveillance/monitoring of adverse health events affecting humans, animals, and ecosystems. Different disciplines use diverse SATs to address similar research questions. The juxtaposition of these diverse techniques provides a list of options for researchers who are new to population-level spatial eco-epidemiology. Here, we are conducting a narrative review to provide an overview of the multiple available SATs, and introducing a framework for choosing among them when addressing common research questions across disciplines. The framework is comprised of three stages: (a) pre-hypothesis testing stage, in which hypotheses regarding the spatial dependence of events are generated; (b) primary hypothesis testing stage, in which the existence of spatial dependence and patterns are tested; and (c) secondary-hypothesis testing and spatial modeling stage, in which predictions and inferences were made based on the identified spatial dependences and associated covariates. In this step-wise process, six key research questions are formulated, and the answers to those questions should lead researchers to select one or more methods from four broad categories of SATs: (T1) visualization and descriptive analysis; (T2) spatial/spatiotemporal dependence and pattern recognition; (T3) spatial smoothing and interpolation; and (T4) geographic correlation studies (i.e., spatial modeling and regression). The SATs described here include both those used for decades and also other relatively new tools. Through this framework review, we intend to facilitate the choice among available SATs and promote their interdisciplinary use to support improving human, animal, and ecosystem health.

A Bayesian space-time model for clustering areal units based on their disease trends

Population-level disease risk across a set of non-overlapping areal units varies in space and time, and a large research literature has developed methodology for identifying clusters of areal units exhibiting elevated risks. However, almost no research has extended the clustering paradigm to identify groups of areal units exhibiting similar temporal disease trends. We present a novel Bayesian hierarchical mixture model for achieving this goal, with inference based on a Metropolis-coupled Markov chain Monte Carlo ((MC)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$^3$\end{document}) algorithm. The effectiveness of the (MC)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$^3$\end{document} algorithm compared to a standard Markov chain Monte Carlo implementation is demonstrated in a simulation study, and the methodology is motivated by two important case studies in the United Kingdom. The first concerns the impact on measles susceptibility of the discredited paper linking the measles, mumps, and rubella vaccination to an increased risk of Autism and investigates whether all areas in the Scotland were equally affected. The second concerns respiratory hospitalizations and investigates over a 10 year period which parts of Glasgow have shown increased, decreased, and no change in risk.

Space-Time Relationship between Short-Term Exposure to Fine and Coarse Particles and Mortality in a Nationwide Analysis of Korea: A Bayesian Hierarchical Spatio-Temporal Model

Previous studies have shown an association between mortality and ambient air pollution in South Korea. However, these studies may have been subject to bias, as they lacked adjustment for spatio-temporal structures. This paper addresses this research gap by examining the association between air pollution and cause-specific mortality in South Korea between 2012 and 2015 using a two-stage Bayesian spatio-temporal model. We used 2012–2014 mortality and air pollution data for parameter estimation (i.e., model fitting) and 2015 data for model validation. Our results suggest that the relative risks of total, cardiovascular, and respiratory mortality were 1.028, 1.047, and 1.045, respectively, with every 10-µg/m³ increase in monthly PM_2.5 (fine particulate matter) exposure. These findings warrant protection of populations who experience elevated ambient air pollution exposure to mitigate mortality burden in South Korea.

A Bayesian two-stage spatially dependent variable selection model for space-time health data

In space-time epidemiological modeling, most studies have considered the overall variations in relative risk to better estimate the effects of risk factors on health outcomes. However, the associations between risk factors and health outcomes may vary across space and time. Especially, the temporal patterns of the covariate effects may depend on space. Thus, we propose a Bayesian two-stage spatially dependent variable selection approach for space-time health data to determine the spatially varying subsets of regression coefficients with common temporal dependence. The two-stage structure allows reduction of the spatial confounding bias in the estimates of the regression coefficients. A simulation study is conducted to examine the performance of the proposed two-stage model. We apply the proposed model to the number of inpatients with lung cancer in 159 counties of Georgia, USA.

Spatiotemporal multivariate mixture models for Bayesian model selection in disease mapping

It is often the case that researchers wish to simultaneously explore the behavior of and estimate overall risk for multiple, related diseases with varying rarity while accounting for potential spatial and/or temporal correlation. In this paper, we propose a flexible class of multivariate spatio-temporal mixture models to fill this role. Further, these models offer flexibility with the potential for model selection as well as the ability to accommodate lifestyle, socio-economic, and physical environmental variables with spatial, temporal, or both structures. Here, we explore the capability of this approach via a large scale simulation study and examine a motivating data example involving three cancers in South Carolina. The results which are focused on four model variants suggest that all models possess the ability to recover simulation ground truth and display improved model fit over two baseline Knorr-Held spatio-temporal interaction model variants in a real data application.

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.

A Comparison of Spatio-Temporal Disease Mapping Approaches Including an Application to Ischaemic Heart Disease in New South Wales, Australia

The field of spatio-temporal modelling has witnessed a recent surge as a result of developments in computational power and increased data collection. These developments allow analysts to model the evolution of health outcomes in both space and time simultaneously. This paper models the trends in ischaemic heart disease (IHD) in New South Wales, Australia over an eight-year period between 2006 and 2013. A number of spatio-temporal models are considered, and we propose a novel method for determining the goodness-of-fit for these models by outlining a spatio-temporal extension of the Moran's I statistic. We identify an overall decrease in the rates of IHD, but note that the extent of this health improvement varies across the state. In particular, we identified a number of remote areas in the north and west of the state where the risk stayed constant or even increased slightly.

An analysis of temporal and spatial patterns in Italian hospitalization rates for multiple diagnosis

In this paper, the Italian hospitalization database provided by the Ministry of Health is analyzed in terms of the temporal and spatial patterns of the hospitalization rates. The database covers the period 2010-2012 and the rates are evaluated for 110 Italian provinces and 18 diagnosis groups as defined by the ICD-9 classification. The analysis is based on a novel model-based clustering approach which enables clustering of spatially registered time series with respect to latent temporal patterns. The clustering result is analyzed to study the spatial distribution of the latent temporal patterns and their trend in order to identify possible critical areas in terms of increasing rates. Additionally, emerging spatial patterns may help common causes driving the hospitalization rates to be identified.

Quantifying the Spatial Inequality and Temporal Trends in Maternal Smoking Rates in Glasgow

Maternal smoking is well known to adversely affect birth outcomes, and there is considerable spatial variation in the rates of maternal smoking in the city of Glasgow, Scotland. This spatial variation is a partial driver of health inequalities between rich and poor communities, and it is of interest to determine the extent to which these inequalities have changed over time. Therefore in this paper we develop a Bayesian hierarchical model for estimating the spatio-temporal pattern in smoking incidence across Glasgow between 2000 and 2013, which can identify the changing geographical extent of clusters of areas exhibiting elevated maternal smoking incidences that partially drive health inequalities. Additionally, we provide freely available software via the R package CARBayesST to allow others to implement the model we have developed. The study period includes the introduction of a ban on smoking in public places in 2006, and the results show an average decline of around 11% in maternal smoking rates over the study period.

Bayesian spatially dependent variable selection for small area health modeling

Statistical methods for spatial health data to identify the significant covariates associated with the health outcomes are of critical importance. Most studies have developed variable selection approaches in which the covariates included appear within the spatial domain and their effects are fixed across space. However, the impact of covariates on health outcomes may change across space and ignoring this behavior in spatial epidemiology may cause the wrong interpretation of the relations. Thus, the development of a statistical framework for spatial variable selection is important to allow for the estimation of the space-varying patterns of covariate effects as well as the early detection of disease over space. In this paper, we develop flexible spatial variable selection approaches to find the spatially-varying subsets of covariates with significant effects. A Bayesian hierarchical latent model framework is applied to account for spatially-varying covariate effects. We present a simulation example to examine the performance of the proposed models with the competing models. We apply our models to a county-level low birth weight incidence dataset in Georgia.

How robust are the estimated effects of air pollution on health? Accounting for model uncertainty using Bayesian model averaging

•

We explored the sensitivity of the pollution-health effect to three factors.

•

Estimation of NO2, choice of deprivation and choice of spatial autocorrelation model.

•

Choice of these factors leads to a wide variation in pollution-health effects.

•

BMA is utilised to estimate an overall effect while accounting for model uncertainty.

•

Overall, a positive but borderline pollution-health effect was obtained.

The long-term impact of air pollution on human health can be estimated from small-area ecological studies in which the health outcome is regressed against air pollution concentrations and other covariates, such as socio-economic deprivation. Socio-economic deprivation is multi-factorial and difficult to measure, and includes aspects of income, education, and housing as well as others. However, these variables are potentially highly correlated, meaning one can either create an overall deprivation index, or use the individual characteristics, which can result in a variety of pollution-health effects. Other aspects of model choice may affect the pollution-health estimate, such as the estimation of pollution, and spatial autocorrelation model. Therefore, we propose a Bayesian model averaging approach to combine the results from multiple statistical models to produce a more robust representation of the overall pollution-health effect. We investigate the relationship between nitrogen dioxide concentrations and cardio-respiratory mortality in West Central Scotland between 2006 and 2012.

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

Exposure to high levels of air pollutant concentration is known to be associated with respiratory problems which can translate into higher morbidity and mortality rates. The link between air pollution and population health has mainly been assessed considering air quality and hospitalisation or mortality data. However, this approach limits the analysis to individuals characterised by severe conditions. In this paper we evaluate the link between air pollution and respiratory diseases using general practice drug prescriptions for chronic respiratory diseases, which allow to draw conclusions based on the general population. We propose a two-stage statistical approach: in the first stage we specify a space-time model to estimate the monthly NO2 concentration integrating several data sources characterised by different spatio-temporal resolution; in the second stage we link the concentration to the β2-agonists prescribed monthly by general practices in England and we model the prescription rates through a small area approach.

Controlling for unmeasured confounding and spatial misalignment in long-term air pollution and health studies

The health impact of long-term exposure to air pollution is now routinely estimated using spatial ecological studies, owing to the recent widespread availability of spatial referenced pollution and disease data. However, this areal unit study design presents a number of statistical challenges, which if ignored have the potential to bias the estimated pollution-health relationship. One such challenge is how to control for the spatial autocorrelation present in the data after accounting for the known covariates, which is caused by unmeasured confounding. A second challenge is how to adjust the functional form of the model to account for the spatial misalignment between the pollution and disease data, which causes within-area variation in the pollution data. These challenges have largely been ignored in existing long-term spatial air pollution and health studies, so here we propose a novel Bayesian hierarchical model that addresses both challenges and provide software to allow others to apply our model to their own data. The effectiveness of the proposed model is compared by simulation against a number of state-of-the-art alternatives proposed in the literature and is then used to estimate the impact of nitrogen dioxide and particulate matter concentrations on respiratory hospital admissions in a new epidemiological study in England in 2010 at the local authority level. © 2015 The Authors. Environmetrics published by John Wiley & Sons Ltd.

A spatio-temporal model for estimating the long-term effects of air pollution on respiratory hospital admissions in Greater London

It has long been known that air pollution is harmful to human health, as many epidemiological studies have been conducted into its effects. Collectively, these studies have investigated both the acute and chronic effects of pollution, with the latter typically based on individual level cohort designs that can be expensive to implement. As a result of the increasing availability of small-area statistics, ecological spatio-temporal study designs are also being used, with which a key statistical problem is allowing for residual spatio-temporal autocorrelation that remains after the covariate effects have been removed. We present a new model for estimating the effects of air pollution on human health, which allows for residual spatio-temporal autocorrelation, and a study into the long-term effects of air pollution on human health in Greater London, England. The individual and joint effects of different pollutants are explored, via the use of single pollutant models and multiple pollutant indices.

Controlling for localised spatio-temporal autocorrelation in long-term air pollution and health studies

Estimating the long-term health impact of air pollution using an ecological spatio-temporal study design is a challenging task, due to the presence of residual spatio-temporal autocorrelation in the health counts after adjusting for the covariate effects. This autocorrelation is commonly modelled by a set of random effects represented by a Gaussian Markov random field (GMRF) prior distribution, as part of a hierarchical Bayesian model. However, GMRF models typically assume the random effects are globally smooth in space and time, and thus are likely to be collinear to any spatially and temporally smooth covariates such as air pollution. Such collinearity leads to poor estimation performance of the estimated fixed effects, and motivated by this epidemiological problem, this paper proposes new GMRF methodology to allow for localised spatio-temporal smoothing. This means random effects that are either geographically or temporally adjacent are allowed to be autocorrelated or conditionally independent, which allows more flexible autocorrelation structures to be represented. This increased flexibility results in improved fixed effects estimation compared with global smoothing models, which is evidenced by our simulation study. The methodology is then applied to the motivating study investigating the long-term effects of air pollution on respiratory ill health in Greater Glasgow, Scotland between 2007 and 2011.