Modeling Multivariate Spatial Dependencies Using Graphical Models.

Graphical models have witnessed significant growth and usage in spatial data science for modeling data referenced over a massive number of spatial-temporal coordinates. Much of this literature has focused on a single or relatively few spatially dependent outcomes. Recent attention has focused upon addressing modeling and inference for substantially large number of outcomes. While spatial factor models and multivariate basis expansions occupy a prominent place in this domain, this article elucidates a recent approach, graphical Gaussian Processes, that exploits the notion of conditional independence among a very large number of spatial processes to build scalable graphical models for fully model-based Bayesian analysis of multivariate spatial data.

Joint species distribution models with imperfect detection for high-dimensional spatial data.

Determining the spatial distributions of species and communities is a key task in ecology and conservation efforts. Joint species distribution models are a fundamental tool in community ecology that use multi-species detection-nondetection data to estimate species distributions and biodiversity metrics. The analysis of such data is complicated by residual correlations between species, imperfect detection, and spatial autocorrelation. While many methods exist to accommodate each of these complexities, there are few examples in the literature that address and explore all three complexities simultaneously. Here we developed a spatial factor multi-species occupancy model to explicitly account for species correlations, imperfect detection, and spatial autocorrelation. The proposed model uses a spatial factor dimension reduction approach and Nearest Neighbor Gaussian Processes to ensure computational efficiency for data sets with both a large number of species (e.g., >100) and spatial locations (e.g., 100,000). We compared the proposed model performance to five alternative models, each addressing a subset of the three complexities. We implemented the proposed and alternative models in the spOccupancy software, designed to facilitate application via an accessible, well documented, and open-source R package. Using simulations, we found that ignoring the three complexities when present leads to inferior model predictive performance, and the impacts of failing to account for one or more complexities will depend on the objectives of a given study. Using a case study on 98 bird species across the continental US, the spatial factor multi-species occupancy model had the highest predictive performance among the alternative models. Our proposed framework, together with its implementation in spOccupancy, serves as a user-friendly tool to understand spatial variation in species distributions and biodiversity while addressing common complexities in multi-species detection-nondetection data.

Association between spill-related exposure to fine particulate matter and peripheral motor and sensory nerve function among oil spill response and cleanup workers following the Deepwater Horizon oil spill.

BACKGROUND: Burning/flaring of oil/gas during the Deepwater Horizon oil spill response and cleanup (OSRC) generated high concentrations of fine particulate matter (PM2.5). Personnel working on the water during these activities may have inhaled combustion products. Neurologic effects of PM2.5 have been reported previously but few studies have examined lasting effects following disaster exposures. The association of brief, high exposures and adverse effects on sensory and motor nerve function in the years following exposure have not been examined for OSRC workers. OBJECTIVES: We assessed the relationship between exposure to burning/flaring-related PM2.5 and measures of sensory and motor nerve function among OSRC workers. METHODS: PM2.5 concentrations were estimated from Gaussian plume dispersion models and linked to self-reported work histories. Quantitative measures of sensory and motor nerve function were obtained 4-6 years after the disaster during a clinical exam restricted to those living close to two clinics in Mobile, AL or New Orleans, LA (n = 3401). We obtained covariate data from a baseline enrollment survey and a home visit, both in 2011-2013. The analytic sample included 1186 participants. RESULTS: We did not find strong evidence of associations between exposure to PM2.5 and sensory or motor nerve function, although there was a suggestion of impairment based on single leg stance among individuals with high exposure to PM2.5. Results were generally consistent whether we examined average or cumulative maximum exposures or removed individuals with the highest crude oil exposures to account for co-pollutant confounding. There was no evidence of exposure-response trends. IMPACT STATEMENT: Remediating environmental disasters is essential for long-term human and environmental health. During the Deepwater Horizon oil spill disaster, burning and flaring of oil and gas were used to remove these pollutants from the environment, but led to potentially high fine particulate matter exposures for spill response workers working on the water. We investigate the potential adverse effects of these exposures on peripheral nerve function; understanding the potential health harm of remediation tactics is necessary to inform future clean up approaches and protect human health.

Inference for Gaussian Processes with Matérn Covariogram on Compact Riemannian Manifolds.

Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of machine learning. They have been widely studied over Euclidean spaces, where they are specified using covariance functions or covariograms for modelling complex dependencies. There is a growing literature on Gaussian processes over Riemannian manifolds in order to develop richer and more flexible inferential frameworks for non-Euclidean data. While numerical approximations through graph representations have been well studied for the Matérn covariogram and heat kernel, the behaviour of asymptotic inference on the parameters of the covariogram has received relatively scant attention. We focus on asymptotic behaviour for Gaussian processes constructed over compact Riemannian manifolds. Building upon a recently introduced Matérn covariogram on a compact Riemannian manifold, we employ formal notions and conditions for the equivalence of two Matérn Gaussian random measures on compact manifolds to derive the parameter that is identifiable, also known as the microergodic parameter, and formally establish the consistency of the maximum likelihood estimate and the asymptotic optimality of the best linear unbiased predictor. The circle is studied as a specific example of compact Riemannian manifolds with numerical experiments to illustrate and corroborate the theory.

Multivariate spatiotemporal functional principal component analysis for modeling hospitalization and mortality rates in the dialysis population.

Dialysis patients experience frequent hospitalizations and a higher mortality rate compared to other Medicare populations, in whom hospitalizations are a major contributor to morbidity, mortality, and healthcare costs. Patients also typically remain on dialysis for the duration of their lives or until kidney transplantation. Hence, there is growing interest in studying the spatiotemporal trends in the correlated outcomes of hospitalization and mortality among dialysis patients as a function of time starting from transition to dialysis across the United States Utilizing national data from the United States Renal Data System (USRDS), we propose a novel multivariate spatiotemporal functional principal component analysis model to study the joint spatiotemporal patterns of hospitalization and mortality rates among dialysis patients. The proposal is based on a multivariate Karhunen-Loéve expansion that describes leading directions of variation across time and induces spatial correlations among region-specific scores. An efficient estimation procedure is proposed using only univariate principal components decompositions and a Markov Chain Monte Carlo framework for targeting the spatial correlations. The finite sample performance of the proposed method is studied through simulations. Novel applications to the USRDS data highlight hot spots across the United States with higher hospitalization and/or mortality rates and time periods of elevated risk.

Exposure to volatile hydrocarbons and neurologic function among oil spill workers up to 6 years after the Deepwater Horizon disaster.

BACKGROUND: During the 2010 Deepwater Horizon (DWH) disaster, oil spill response and cleanup (OSRC) workers were exposed to toxic volatile components of crude oil. Few studies have examined exposure to individual volatile hydrocarbon chemicals below occupational exposure limits in relation to neurologic function among OSRC workers. OBJECTIVES: To investigate the association of several spill-related chemicals (benzene, toluene, ethylbenzene, xylene, n-hexane, i.e., BTEX-H) and total petroleum hydrocarbons (THC) with neurologic function among DWH spill workers enrolled in the Gulf Long-term Follow-up Study. METHODS: Cumulative exposure to THC and BTEX-H across the oil spill cleanup period were estimated using a job-exposure matrix that linked air measurement data to detailed self-reported DWH OSRC work histories. We ascertained quantitative neurologic function data via a comprehensive test battery at a clinical examination that occurred 4-6 years after the DWH disaster. We used multivariable linear regression and modified Poisson regression to evaluate relationships of exposures (quartiles (Q)) with 4 neurologic function measures. We examined modification of the associations by age at enrollment (<50 vs. ≥50 years). RESULTS: We did not find evidence of adverse neurologic effects from crude oil exposures among the overall study population. However, among workers ≥50 years of age, several individual chemical exposures were associated with poorer vibrotactile acuity of the great toe, with statistically significant effects observed in Q3 or Q4 of exposures (range of log mean difference in Q4 across exposures: 0.13-0.26 µm). We also observed suggestive adverse associations among those ≥ age 50 years for tests of postural stability and single-leg stance, although most effect estimates did not reach thresholds of statistical significance (p < 0.05). CONCLUSIONS: Higher exposures to volatile components of crude oil were associated with modest deficits in neurologic function among OSRC workers who were age 50 years or older at study enrollment.

Volatile Hydrocarbon Exposures and Incident Coronary Heart Disease Events: Up to Ten Years of Follow-up among Deepwater Horizon Oil Spill Workers.

BACKGROUND: During the 2010 Deepwater Horizon (DWH) disaster, response and cleanup workers were potentially exposed to toxic volatile components of crude oil. However, to our knowledge, no study has examined exposure to individual oil spill-related chemicals in relation to cardiovascular outcomes among oil spill workers. OBJECTIVES: Our aim was to investigate the association of several spill-related chemicals [benzene, toluene, ethylbenzene, xylene, n-hexane (BTEX-H)] and total hydrocarbons (THC) with incident coronary heart disease (CHD) events among workers enrolled in a prospective cohort. METHODS: Cumulative exposures to THC and BTEX-H across the cleanup period were estimated via a job-exposure matrix that linked air measurement data with self-reported DWH spill work histories. We ascertained CHD events following each worker's last day of cleanup work as the first self-reported physician-diagnosed myocardial infarction (MI) or a fatal CHD event. We estimated hazard ratios (HR) and 95% confidence intervals for the associations of exposure quintiles (Q) with risk of CHD. We applied inverse probability weights to account for bias due to confounding and loss to follow-up. We used quantile g-computation to assess the joint effect of the BTEX-H mixture. RESULTS: Among 22,655 workers with no previous MI diagnoses, 509 experienced an incident CHD event through December 2019. Workers in higher quintiles of each exposure agent had increased CHD risks in comparison with the referent group (Q1) of that agent, with the strongest associations observed in Q5 (range of HR=1.14-1.44). However, most associations were nonsignificant, and there was no evidence of exposure-response trends. We observed stronger associations among ever smokers, workers with ≤high school education, and workers with body mass index <30 kg/m2. No apparent positive association was observed for the BTEX-H mixture. CONCLUSIONS: Higher exposures to volatile components of crude oil were associated with modest increases in risk of CHD among oil spill workers, although we did not observe exposure-response trends. https://doi.org/10.1289/EHP11859.

Fine particulate matter and incident coronary heart disease events up to 10 years of follow-up among Deepwater Horizon oil spill workers.

BACKGROUND: During the 2010 Deepwater Horizon (DWH) disaster, in-situ burning and flaring were conducted to remove oil from the water. Workers near combustion sites were potentially exposed to burning-related fine particulate matter (PM2.5). Exposure to PM2.5 has been linked to increased risk of coronary heart disease (CHD), but no study has examined the relationship among oil spill workers. OBJECTIVES: To investigate the association between estimated PM2.5 from burning/flaring of oil/gas and CHD risk among the DWH oil spill workers. METHODS: We included workers who participated in response and cleanup activities on the water during the DWH disaster (N = 9091). PM2.5 exposures were estimated using a job-exposure matrix that linked modelled PM2.5 concentrations to detailed DWH spill work histories provided by participants. We ascertained CHD events as the first self-reported physician-diagnosed CHD or a fatal CHD event that occurred after each worker's last day of burning exposure. We estimated hazard ratios (HR) and 95% confidence intervals (95%CI) for the associations between categories of average or cumulative daily maximum PM2.5 exposure (versus a referent category of water workers not near controlled burning) and subsequent CHD. We assessed exposure-response trends by examining continuous exposure parameters in models. RESULTS: We observed increased CHD hazard among workers with higher levels of average daily maximum exposure (low vs. referent: HR = 1.26, 95% CI: 0.93, 1.70; high vs. referent: HR = 2.11, 95% CI: 1.08, 4.12; per 10 µg/m3 increase: HR = 1.10, 95% CI: 1.02, 1.19). We also observed suggestively elevated HRs among workers with higher cumulative daily maximum exposure (low vs. referent: HR = 1.19, 95% CI: 0.68, 2.08; medium vs. referent: HR = 1.38, 95% CI: 0.88, 2.16; high vs. referent: HR = 1.44, 95% CI: 0.96, 2.14; per 100 µg/m3-d increase: HR = 1.03, 95% CI: 1.00, 1.05). CONCLUSIONS: Among oil spill workers, exposure to PM2.5 from flaring/burning of oil/gas was associated with increased risk of CHD.

Spatial Difference Boundary Detection for Multiple Outcomes Using Bayesian Disease Mapping.

Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, and zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To capture health disparities over regions, we seek "difference boundaries" that separate neighboring regions with significantly different spatial effects. Matters are more challenging with multiple outcomes over each unit, where we capture dependence among diseases as well as across the areal units. Here, we address multivariate difference boundary detection for correlated diseases. We formulate the problem in terms of Bayesian pairwise multiple comparisons and seek the posterior probabilities of neighboring spatial effects being different. To achieve this, we endow the spatial random effects with a discrete probability law using a class of multivariate areally referenced Dirichlet process models that accommodate spatial and interdisease dependence. We evaluate our method through simulation studies and detect difference boundaries for multiple cancers using data from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute.

BAYESIAN HIERARCHICAL MODELING AND ANALYSIS FOR ACTIGRAPH DATA FROM WEARABLE DEVICES.

The majority of Americans fail to achieve recommended levels of physical activity, which leads to numerous preventable health problems such as diabetes, hypertension, and heart diseases. This has generated substantial interest in monitoring human activity to gear interventions toward environmental features that may relate to higher physical activity. Wearable devices, such as wrist-worn sensors that monitor gross motor activity (actigraph units) continuously record the activity levels of a subject, producing massive amounts of high-resolution measurements. Analyzing actigraph data needs to account for spatial and temporal information on trajectories or paths traversed by subjects wearing such devices. Inferential objectives include estimating a subject's physical activity levels along a given trajectory; identifying trajectories that are more likely to produce higher levels of physical activity for a given subject; and predicting expected levels of physical activity in any proposed new trajectory for a given set of health attributes. Here, we devise a Bayesian hierarchical modeling framework for spatial-temporal actigraphy data to deliver fully model-based inference on trajectories while accounting for subject-level health attributes and spatial-temporal dependencies. We undertake a comprehensive analysis of an original dataset from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study to ascertain spatial zones and trajectories exhibiting significantly higher levels of physical activity while accounting for various sources of heterogeneity.

A Bayesian multilevel time-varying framework for joint modeling of hospitalization and survival in patients on dialysis.

Over 782 000 individuals in the United States have end-stage kidney disease with about 72% of patients on dialysis, a life-sustaining treatment. Dialysis patients experience high mortality and frequent hospitalizations, at about twice per year. These poor outcomes are exacerbated at key time periods, such as the fragile period after transition to dialysis. In order to study the time-varying effects of modifiable patient and dialysis facility risk factors on hospitalization and mortality, we propose a novel Bayesian multilevel time-varying joint model. Efficient estimation and inference is achieved within the Bayesian framework using Markov chain Monte Carlo, where multilevel (patient- and dialysis facility-level) varying coefficient functions are targeted via Bayesian P-splines. Applications to the United States Renal Data System, a national database which contains data on nearly all patients on dialysis in the United States, highlight significant time-varying effects of patient- and facility-level risk factors on hospitalization risk and mortality. Finite sample performance of the proposed methodology is studied through simulations.

Co-kriging with a low-cost sensor network to estimate spatial variation of brake and tire-wear metals and oxidative stress potential in Southern California.

Due to regulations and technological advancements reducing tailpipe emissions, an increasing proportion of emissions arise from brake and tire wear particulate matter (PM). PM from these non-tailpipe sources contains heavy metals capable of generating oxidative stress in the lung. Although important, these particles remain understudied because the high cost of actively collecting filter samples. Improvements in electrical engineering, internet connectivity, and an increased public concern over air pollution have led to a proliferation of dense low-cost air sensor networks such as the PurpleAir monitors, which primarily measure unspeciated fine particulate matter (PM2.5). In this study, we model the concentrations of Ba, Zn, black carbon, reactive oxygen species concentration in the epithelial lining fluid, dithiothreitol (DTT) loss, and OH formation. We use a co-kriging approach, incorporating data from the PurpleAir network as a secondary predictor variable and a land-use regression (LUR) as an external drift. For most pollutant species, co-kriging models produced more accurate predictions than an LUR model, which did not incorporate data from the PurpleAir monitors. This finding suggests that low-cost sensors can enhance predictions of pollutants that are costly to measure extensively in the field.

Associations between airborne crude oil chemicals and symptom-based asthma.

RATIONALE: The 2010 Deepwater Horizon (DWH) oil spill response and cleanup (OSRC) workers were exposed to airborne total hydrocarbons (THC), benzene, toluene, ethylbenzene, o-, m-, and p-xylenes and n-hexane (BTEX-H) from crude oil and PM2.5 from burning/flaring oil and natural gas. Little is known about asthma risk among oil spill cleanup workers. OBJECTIVES: We assessed the relationship between asthma and several oil spill-related exposures including job classes, THC, individual BTEX-H chemicals, the BTEX-H mixture, and PM2.5 using data from the Gulf Long-Term Follow-up (GuLF) Study, a prospective cohort of 24,937 cleanup workers and 7,671 nonworkers following the DWH disaster. METHODS: Our analysis largely focused on the 19,018 workers without asthma before the spill who had complete exposure, outcome, and covariate information. We defined incident asthma 1-3 years following exposure using both self-reported wheeze and self-reported physician diagnosis of asthma. THC and BTEX-H were assigned to participants based on measurement data and work histories, while PM2.5 used modeled estimates. We used modified Poisson regression to estimate risk ratios (RR) and 95% confidence intervals (CIs) for associations between spill-related exposures and asthma and a quantile-based g-computation approach to explore the joint effect of the BTEX-H mixture on asthma risk. RESULTS: OSRC workers had greater asthma risk than nonworkers (RR: 1.60, 95% CI: 1.38, 1.85). Higher estimated THC exposure levels were associated with increased risk in an exposure-dependent manner (linear trend test p < 0.0001). Asthma risk also increased with increasing exposure to individual BTEX-H chemicals and the chemical mixture: A simultaneous quartile increase in the BTEX-H mixture was associated with an increased asthma risk of 1.45 (95% CI: 1.35,1.55). With fewer cases, associations were less apparent for physician-diagnosed asthma alone. CONCLUSIONS: THC and BTEX-H were associated with increased asthma risk defined using wheeze symptoms as well as a physician diagnosis.

Highly Scalable Bayesian Geostatistical Modeling via Meshed Gaussian Processes on Partitioned Domains.

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the Meshed Gaussian Process (MGP). A major contribution is the development of a MGPs on tessellated domains, accompanied by a Gibbs sampler for the efficient recovery of spatial random effects. In particular, the cubic MGP (Q-MGP) can harness high-performance computing resources by executing all large-scale operations in parallel within the Gibbs sampler, improving mixing and computing time compared to sequential updating schemes. Unlike some existing models for large spatial data, a Q-MGP facilitates massive caching of expensive matrix operations, making it particularly apt in dealing with spatiotemporal remote-sensing data. We compare Q-MGPs with large synthetic and real world data against state-of-the-art methods. We also illustrate using Normalized Difference Vegetation Index (NDVI) data from the Serengeti park region to recover latent multivariate spatiotemporal random effects at millions of locations. The source code is available at github.com/mkln/meshgp.

Multilevel Varying Coefficient Spatiotemporal Model.

Over 785,000 individuals in the U.S. have end-stage renal disease (ESRD) with about 70% of patients on dialysis, a life-sustaining treatment. Dialysis patients experience frequent hospitalizations. In order to identify risk factors of hospitalizations, we utilize data from the large national database, United States Renal Data System (USRDS). To account for the hierarchical structure of the data, with longitudinal hospitalization rates nested in dialysis facilities and dialysis facilities nested in geographic regions across the U.S., we propose a multilevel varying coefficient spatiotemporal model (M-VCSM) where region- and facility-specific random deviations are modeled through a multilevel Karhunen-Loéve (KL) expansion. The proposed M-VCSM includes time-varying effects of multilevel risk factors at the region- (e.g., urbanicity and area deprivation index) and facility-levels (e.g., patient demographic makeup) and incorporates spatial correlations across regions via a conditional autoregressive (CAR) structure. Efficient estimation and inference is achieved through the fusion of functional principal component analysis (FPCA) and Markov Chain Monte Carlo (MCMC). Applications to the USRDS data highlight significant region- and facility-level risk factors of hospitalizations and characterize time periods and spatial locations with elevated hospitalization risk. Finite sample performance of the proposed methodology is studied through simulations.

High-flow Nasal Oxygen Therapy in COVID-19 Critically Ill Patients with Acute Hypoxemic Respiratory Failure: A Prospective Observational Cohort Study.

Background: Coronavirus disease-2019 (COVID-19) is prone to acute hypoxemic respiratory failure (AHRF). Because tracheal intubation is associated with a higher risk of death in these patients, AHRF employs high-flow nasal oxygen therapy (HFNOT). The goal of this study was to assess the effect of HFNOT on oxygenation status as well as different predictors of HFNOT failure. Methods: A prospective observational cohort study was conducted in COVID-positive critically ill adult patients (age >18 years) with AHRF, who were unable to maintain SpO2 >90% on a non-rebreathing face mask at an oxygen flow ≥15 L/minute. Respiratory variables (PaO2/FiO2, SpO2, and RR) before HFNOT (baseline) and then at 1 hour, 6 hours, 7th day, and 14th day after HFNOT application were recorded. Borg CR10 scale and visual analogue scale were used to evaluate the subjective sensation of dyspnea and comfort level, respectively. As needed, Student's t, Mann-Whitney U, or Wilcoxon signed-rank tests were performed. To find parameters linked to HFNOT failure, multivariate logistic regression and receiver operating characteristic (ROC) analysis were employed. Results: A total of 114 patients were enrolled in the study, with an HFNOT failure rate of 29%. The median PaO2/FiO2 ratio at baseline (before the initiation of HFNOT) was 99.5 (80-110) which significantly increased at various time points (1 hour, 6 hours, 7th day, and 14th day) after HFNOT initiation in the successful group. Patients reported significant improvement in sensation of breathlessness [9 (8-10), 3 (2-4); p <0.001] as well as in comfort level [2 (1-2), 8 (4-9); p <0.001]. Multivariate logistic regression analysis, sequential organ failure assessment (SOFA) score >7, acute physiology and chronic health evaluation (APACHE) II score >20, admission P/F ratio <100, D-dimer >2 mg/L, IL-6 >40 pg/mL, random blood sugar (RBS) >250 mg/dL, and 6 hours ROX Index <3.5 were independent prognostic factors of HFNOT failure. Conclusion: The use of HFNOT significantly increased the oxygenation levels in COVID-19 patients with AHRF at various time periods after HFNOT beginning. Age, SOFA score, APACHE II score, ROX score, admission P/F ratio, IL-6, D-dimer, and RBS were independent prognostic factors of HFNOT failure in this cohort. How to cite this article: Khan MS, Prakash J, Banerjee S, Bhattacharya PK, Kumar R, Nirala DK. High-flow Nasal Oxygen Therapy in COVID-19 Critically Ill Patients with Acute Hypoxemic Respiratory Failure: A Prospective Observational Cohort Study. Indian J Crit Care Med 2022;26(5):596-603.

Hierarchical multivariate directed acyclic graph autoregressive models for spatial diseases mapping.

Disease mapping is an important statistical tool used by epidemiologists to assess geographic variation in disease rates and identify lurking environmental risk factors from spatial patterns. Such maps rely upon spatial models for regionally aggregated data, where neighboring regions tend to exhibit similar outcomes than those farther apart. We contribute to the literature on multivariate disease mapping, which deals with measurements on multiple (two or more) diseases in each region. We aim to disentangle associations among the multiple diseases from spatial autocorrelation in each disease. We develop multivariate directed acyclic graphical autoregression models to accommodate spatial and inter-disease dependence. The hierarchical construction imparts flexibility and richness, interpretability of spatial autocorrelation and inter-disease relationships, and computational ease, but depends upon the order in which the cancers are modeled. To obviate this, we demonstrate how Bayesian model selection and averaging across orders are easily achieved using bridge sampling. We compare our method with a competitor using simulation studies and present an application to multiple cancer mapping using data from the Surveillance, Epidemiology, and End Results program.