The importance of scale for spatial-confounding bias and precision of spatial regression estimators

spconfShiny: An R Shiny application for calculating the spatial scale of smoothing splines for point data

Epidemiological analyses of environmental exposures often benefit from including spatial splines in models to account for confounding by spatial location. Understanding how the number of splines relates to physical spatial differences is not always intuitive and can be context-dependent. To address this, we developed a R Shiny application, spconfShiny, that provides a user-friendly platform to calculate an effective bandwidth metric that quantifies the relationship between spatial splines and the range of implied spatial smoothing. spconfShiny can be accessed at https://g2aging.shinyapps.io/spconfShiny/. We illustrate the procedure to compute the effective bandwidth and demonstrate its use for different numbers of spatial splines across England, India, Ireland, Northern Ireland, and the United States. Using spconfShiny, we show the effective bandwidth increases with the size of the region and decreases with the number of splines. Including 10 splines on a 10km grid corresponds to effective bandwidths of 92.2km in Ireland and 927.7km in the United States.

A comparison of PM2.5 exposure estimates from different estimation methods and their associations with cognitive testing and brain MRI outcomes

BACKGROUND

Reported associations between particulate matter with aerodynamic diameter ≤2.5 μm (PM2.5) and cognitive outcomes remain mixed. Differences in exposure estimation method may contribute to this heterogeneity.

OBJECTIVES

To assess agreement between PM2.5 exposure concentrations across 11 exposure estimation methods and to compare resulting associations between PM2.5 and cognitive or MRI outcomes.

METHODS

We used Visit 5 (2011-2013) cognitive testing and brain MRI data from the Atherosclerosis Risk in Communities (ARIC) Study. We derived address-linked average 2000-2007 PM2.5 exposure concentrations in areas immediately surrounding the four ARIC recruitment sites (Forsyth County, NC; Jackson, MS; suburbs of Minneapolis, MN; Washington County, MD) using 11 estimation methods. We assessed agreement between method-specific PM2.5 concentrations using descriptive statistics and plots, overall and by site. We used adjusted linear regression to estimate associations of method-specific PM2.5 exposure estimates with cognitive scores (n = 4678) and MRI outcomes (n = 1518) stratified by study site and combined site-specific estimates using meta-analyses to derive overall estimates. We explored the potential impact of unmeasured confounding by spatially patterned factors.

RESULTS

Exposure estimates from most methods had high agreement across sites, but low agreement within sites. Within-site exposure variation was limited for some methods. Consistently null findings for the PM2.5-cognitive outcome associations regardless of method precluded empirical conclusions about the potential impact of method on study findings in contexts where positive associations are observed. Not accounting for study site led to consistent, adverse associations, regardless of exposure estimation method, suggesting the potential for substantial bias due to residual confounding by spatially patterned factors.

DISCUSSION

PM2.5 estimation methods agreed across sites but not within sites. Choice of estimation method may impact findings when participants are concentrated in small geographic areas. Understanding unmeasured confounding by factors that are spatially patterned may be particularly important in studies of air pollution and cognitive or brain health.

Association of Gaseous Ambient Air Pollution and Dementia-Related Neuroimaging Markers in the ARIC Cohort, Comparing Exposure Estimation Methods and Confounding by Study Site

BACKGROUND

Evidence linking gaseous air pollution to late-life brain health is mixed.

OBJECTIVE

We explored associations between exposure to gaseous pollutants and brain magnetic resonance imaging (MRI) markers among Atherosclerosis Risk in Communities (ARIC) Study participants, with attention to the influence of exposure estimation method and confounding by site.

METHODS

We considered data from 1,665 eligible ARIC participants recruited from four US sites in the period 1987-1989 with valid brain MRI data from Visit 5 (2011-2013). We estimated 10-y (2001-2010) mean carbon monoxide (CO), nitrogen dioxide (NO 2 ), nitrogen oxides (NO x ), and 8- and 24-h ozone (O 3 ) concentrations at participant addresses, using multiple exposure estimation methods. We estimated site-specific associations between pollutant exposures and brain MRI outcomes (total and regional volumes; presence of microhemorrhages, infarcts, lacunes, and severe white matter hyperintensities), using adjusted linear and logistic regression models. We compared meta-analytically combined site-specific associations to analyses that did not account for site.

RESULTS

Within-site exposure distributions varied across exposure estimation methods. Meta-analytic associations were generally not statistically significant regardless of exposure, outcome, or exposure estimation method; point estimates often suggested associations between higher NO 2   and   NO x and smaller temporal lobe, deep gray, hippocampal, frontal lobe, and Alzheimer disease signature region of interest volumes and between higher CO and smaller temporal and frontal lobe volumes. Analyses that did not account for study site more often yielded significant associations and sometimes different direction of associations.

DISCUSSION

Patterns of local variation in estimated air pollution concentrations differ by estimation method. Although we did not find strong evidence supporting impact of gaseous pollutants on brain changes detectable by MRI, point estimates suggested associations between higher exposure to CO, NO x , and NO 2 and smaller regional brain volumes. Analyses of air pollution and dementia-related outcomes that do not adjust for location likely underestimate uncertainty and may be susceptible to confounding bias. https://doi.org/10.1289/EHP13906.

Spectral adjustment for spatial confounding

Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the exposure to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matérn coherence function to more robust semiparametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.

Global long-term trends and spatial cluster analysis of pancreatic cancer incidence and mortality over a 30-year period using the global burden of disease study 2019 data

INTRODUCTION

Pancreatic cancer (PC) is one of the most fatal malignancies, and its incidence and mortality rates are growing annually throughout the world. In this research, we aimed to investigate the time trends and identify the spatial clusters of incidence and mortality on a global scale over the last 30 years, using the Global Burden of Disease (GBD) study 2019 data.

METHODS

Age-standardized incidence and mortality data due to PC were extracted from the GBD study, which was carried out from 1990 to 2019. A Joinpoint regression analysis was utilized to examine trends in the incidence and mortality of PC over the past three decades. As such, spatial analyses were undertaken to detect the spatial distribution and clustering of the metrics globally.

RESULTS

It was observed that both the incidence and mortality rates were higher in males than in females worldwide. The global mortality and incidence rates significantly increased by 0.8% per year over the time of follow-up period (p<0.05). By spatial cluster analysis for mortality, European and North African countries, as well as Greenland were explored as hot spots; while South African and Southeast Asian countries were explored as cold spots. Regarding incidence, hot spots were found in European countries, Southern America, and Greenland; whilst cold spots were determined in Southern Africa and Madagascar.

CONCLUSIONS

Collectively, the temporal trends disclosed a gradual rise in PC incidence and mortality rates over the period 1990-2019, reflecting the global health concern. We further found geographical variations in the patterns and identified high- and low-risk areas for incidence and mortality. These findings facilitate the design and implementation of more resource-efficient and geographically targeted treatments. Given the results of the current study, a practical approach to minimizing the future PC burden involves planned population-wide interventions, as well as primary prevention through healthier lifestyles.

Bias Amplification and Variance Inflation in Distributed Lag Models Using Low-Spatial-Resolution Data

Distributed lag models (DLMs) are often used to estimate lagged associations and identify critical exposure windows. In a simulation study of prenatal nitrogen dioxide (NO2) exposure and birth weight, we demonstrate that bias amplification and variance inflation can manifest under certain combinations of DLM estimation approaches and time-trend adjustment methods when using low-spatial-resolution exposures with extended lags. Our simulations showed that when using high-spatial-resolution exposure data, any time-trend adjustment method produced low bias and nominal coverage for the distributed lag estimator. When using either low- or no-spatial-resolution exposures, bias due to time trends was amplified for all adjustment methods. Variance inflation was higher in low- or no-spatial-resolution DLMs when using a long-term spline to adjust for seasonality and long-term trends due to concurvity between a distributed lag function and secular function of time. NO2-birth weight analyses in a Massachusetts-based cohort showed that associations were negative for exposures experienced in gestational weeks 15-30 when using high-spatial-resolution DLMs; however, associations were null and positive for DLMs with low- and no-spatial-resolution exposures, respectively, which is likely due to bias amplification. DLM analyses should jointly consider the spatial resolution of exposure data and the parameterizations of the time trend adjustment and lag constraints.

The effect of physician density on colorectal cancer stage at diagnosis: causal inference methods for spatial data applied on regional-level data

BACKGROUND

The early detection of colorectal cancer (CRC) through regular screening decreases its incidence and mortality rates and improves survival rates. Norway has an extremely high percentage of CRC cases diagnosed at late stages, with large variations across municipalities and hospital catchment areas. This study examined whether the availability of physicians related to CRC primary diagnosis and preoperative investigations, or physician density, contributes to the observed geographical differences in late-stage incidence rates.

METHOD

Municipality-level data on CRC stage at diagnosis were obtained from the Cancer Registry of Norway for the period 2012-2020. Physician density was calculated as the number of physicians related to CRC investigations, general practitioners (GPs) and specialists per 10,000 people, using physician counts per municipality and hospital areas from Statistics Norway. The relationship was examined using a novel causal inference method for spatial data-neighbourhood adjustment method via spatial smoothing (NA approach)-which allowed for studying the region-level effect of physician supply on CRC outcome by using spatially referenced data and still providing causal relationships.

RESULTS

According to the NA approach, an increase in one general practitioner per 10,000 people will result in a 3.6% (CI -0.064 to -0.008) decrease in late-stage CRC rates. For specialists, there was no evidence of a significant correlation with late-stage CRC distribution, while for both groups, GPs and specialists combined, an increase of 1 physician per 10,000 people would be equal to an average decrease in late-stage incidence rates by 2.79% (CI -0.055 to -0.001).

CONCLUSION

The study confirmed previous findings that an increase in GP supply will significantly improve CRC outcomes. In contrast to previous research, this study identified the importance of accessibility to both groups of physicians-GPs and specialists. If GPs encounter insufficient workforces in hospitals and long delays in colonoscopy scheduling, they will less often recommend colonoscopy examinations to patients. This study also highlighted the efficiency of the novel methodology for spatially referenced data, which allowed us to study the effect of physician density on cancer outcomes within a causal inference framework.

Spatial+: A novel approach to spatial confounding

In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non-Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial model formulations.

Bias in product availability estimates from contraceptive outlet surveys: Evidence from the Consumer’s Market for Family Planning (CM4FP) study

Area-based sampling approaches designed to capture pharmacies, drug shops, and other non-facility service delivery outlets are critical for accurately measuring the contraceptive service environment in contexts of increasing de-medicalization of contraceptive commodities and services. Evidence from other disciplines has demonstrated area-based estimates may be biased if there is spatial heterogeneity in product distribution, but this bias has not yet been assessed in the context of contraceptive supply estimates. The Consumer’s Marker for Family Planning (CM4FP) study conducted censuses and product audits of contraceptive outlets across 12 study sites and 2–3 rounds of quarterly data collection in Kenya, Nigeria, and Uganda. We assessed bias in estimates of contraceptive product availability by comparing estimates from simulations of area-based sampling approaches with census counts among all audited facilities for each study site and round of data collection. We found evidence of bias in estimates of contraceptive availability generated from simulated area-based sampling. Within specific study sites and rounds, we observed biased sampling estimates for several but not all contraceptive method types, with bias more likely to occur in sites with heterogeneity in both spatial distribution of outlets and product availability within outlets. In simulations varying size of enumeration areas (EA) and number of outlets sampled per EA, we demonstrated that the likelihood of substantial bias decreases as EA size decreases and as the number of outlets sampled per EA increases. Straightforward approaches such as increasing sample size per EA or applying statistical weights may be used to reduce area-based sampling bias, indicating a pragmatic way forward to improve estimates where design-based sampling is infeasible. Such approaches should be considered in development of improved methods for area-based estimates of contraceptive supply-side environments.

Bayesian disease mapping: Past, present, and future

On the occasion of the Spatial Statistics' 10th Anniversary, I reflect on the past and present of Bayesian disease mapping and look into its future. I focus on some key developments of models, and on recent evolution of multivariate and adaptive Gaussian Markov random fields and their impact and importance in disease mapping. I reflect on Bayesian disease mapping as a subject of spatial statistics that has advanced to date, and continues to grow, in scope and complexity alongside increasing needs of analytic tools for contemporary health science research, such as spatial epidemiology, population and public health, and medicine. I illustrate (potential) utility and impact of some of the disease mapping models and methods for analysing and monitoring communicable disease such as the COVID-19 infection risks during an ongoing pandemic.

Community confounding in joint species distribution models

Joint species distribution models have become ubiquitous for studying species-environment relationships and dependence among species. Accounting for community structure often improves predictive power, but can also affect inference on species-environment relationships. Specifically, some parameterizations of joint species distribution models allow interspecies dependence and environmental effects to explain the same sources of variability in species distributions, a phenomenon we call community confounding. We present a method for measuring community confounding and show how to orthogonalize the environmental and random species effects in suite of joint species distribution models. In a simulation study, we show that community confounding can lead to computational difficulties and that orthogonalizing the environmental and random species effects can alleviate these difficulties. We also discuss the inferential implications of community confounding and orthogonalizing the environmental and random species effects in a case study of mammalian responses to the Colorado bark beetle epidemic in the subalpine forest by comparing the outputs from occupancy models that treat species independently or account for interspecies dependence. We illustrate how joint species distribution models that restrict the random species effects to be orthogonal to the fixed effects can have computational benefits and still recover the inference provided by an unrestricted joint species distribution model.

Estimating the effect of friction on crash risk: Reducing the effect of omitted variable bias that results from spatial correlation

Omitted variable bias is one of the main factors that lead to incorrect estimates of the effect of a variable on the expected number of crashes using regression modeling. We propose to use differencing of the (spatially adjacent) variables to reduce the effect of omitted variable bias. Differencing is a linear transformation that preserves the structure of the (generalized) linear model but can often result in significantly reducing the correlation between the variables. It is special case of (generalized) partial linear model regression which itself is a special case of a generalized additive model (GAM). In the spatial context used in this paper, differencing is similar to the well-known approach of including a spatial correlation structure (spatial error term) in the analysis of crash data. It is generally not clear how to interpret the results of models that include a spatial correlation structure and whether and how the added spatial correlation structure reduces the bias in the estimated regression parameters. However, for the case of differencing, it becomes clear how the effect of omitted variable bias is reduced by reducing the correlation between the variable of interest and the omitted variables. The order of differencing determines the dominant spatial scales of the variables considered in the model which affect how much the correlation is reduced. This reveals that omitted variable bias can be reduced when there are spatial scales at which the covariate of interest varies but the omitted variables either 1) are relatively homogeneous or 2) have variations that are not correlated to those of the variable of interest.

Spatial Regression Models for Field Trials: A Comparative Study and New Ideas

Naturally occurring variability within a study region harbors valuable information on relationships between biological variables. Yet, spatial patterns within these study areas, e.g., in field trials, violate the assumption of independence of observations, setting particular challenges in terms of hypothesis testing, parameter estimation, feature selection, and model evaluation. We evaluate a number of spatial regression methods in a simulation study, including more realistic spatial effects than employed so far. Based on our results, we recommend generalized least squares (GLS) estimation for experimental as well as for observational setups and demonstrate how it can be incorporated into popular regression models for high-dimensional data such as regularized least squares. This new method is available in the BioConductor R-package pengls. Inclusion of a spatial error structure improves parameter estimation and predictive model performance in low-dimensional settings and also improves feature selection in high-dimensional settings by reducing "red-shift": the preferential selection of features with spatial structure. In addition, we argue that the absence of spatial autocorrelation (SAC) in the model residuals should not be taken as a sign of a good fit, since it may result from overfitting the spatial trend. Finally, we confirm our findings in a case study on the prediction of winter wheat yield based on multispectral measurements.

RESTRICTED SPATIAL REGRESSION METHODS: IMPLICATIONS FOR INFERENCE

The issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature. Multiple authors have offered perspectives and potential solutions. In this paper, for the areal spatial data setting, we show that many of the methods designed to alleviate spatial confounding can be viewed as special cases of a general class of models. We refer to this class as Restricted Spatial Regression (RSR) models, extending terminology currently in use. We offer a mathematically based exploration of the impact that RSR methods have on inference for regression coefficients for the linear model. We then explore whether these results hold in the generalized linear model setting for count data using simulations. We show that the use of these methods have counterintuitive consequences which defy the general expectations in the literature. In particular, our results and the accompanying simulations suggest that RSR methods will typically perform worse than non-spatial methods. These results have important implications for dimension reduction strategies in spatial regression modeling. Specifically, we demonstrate that the problems with RSR models cannot be fixed with a selection of "better" spatial basis vectors or dimension reduction techniques.

Differential associations of the built environment on weight gain by sex and race/ethnicity but not age

OBJECTIVE

To explore the built environment (BE) and weight change relationship by age, sex, and racial/ethnic subgroups in adults.

METHODS

Weight trajectories were estimated using electronic health records for 115,260 insured Kaiser Permanente Washington members age 18-64 years. Member home addresses were geocoded using ArcGIS. Population, residential, and road intersection densities and counts of area supermarkets and fast food restaurants were measured with SmartMaps (800 and 5000-meter buffers) and categorized into tertiles. Linear mixed-effect models tested whether associations between BE features and weight gain at 1, 3, and 5 years differed by age, sex, and race/ethnicity, adjusting for demographics, baseline weight, and residential property values.

RESULTS

Denser urban form and greater availability of supermarkets and fast food restaurants were associated with differential weight change across sex and race/ethnicity. At 5 years, the mean difference in weight change comparing the 3rd versus 1st tertile of residential density was significantly different between males (-0.49 kg, 95% CI: -0.68, -0.30) and females (-0.17 kg, 95% CI: -0.33, -0.01) (P-value for interaction = 0.011). Across race/ethnicity, the mean difference in weight change at 5 years for residential density was significantly different among non-Hispanic (NH) Whites (-0.47 kg, 95% CI: -0.61, -0.32), NH Blacks (-0.86 kg, 95% CI: -1.37, -0.36), Hispanics (0.10 kg, 95% CI: -0.46, 0.65), and NH Asians (0.44 kg, 95% CI: 0.10, 0.78) (P-value for interaction <0.001). These findings were consistent for other BE measures.

CONCLUSION

The relationship between the built environment and weight change differs across demographic groups. Careful consideration of demographic differences in associations of BE and weight trajectories is warranted for investigating etiological mechanisms and guiding intervention development.

A Review of Spatial Causal Inference Methods for Environmental and Epidemiological Applications

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines but have only recently begun to take hold in spatial applications. Spatial causal inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided.

PAHs in an urban-industrial area: The role of lichen transplants in the detection of local and study area scale patterns

Spatial variation of the levels of polycyclic aromatic hydrocarbons (PAHs) was evaluated within an urban-industrial district where the main anthropogenic pressures are a 15 MW biomass power plant (BPP) and road traffic. The use of a high-density lichen transplant network and wind quantitative relationships made it possible to perform a hierarchical analysis of contamination. Combined uni-bi and multivariate statistical analyses of the resulting databases revealed a dual pattern. In its surroundings (local scale), the BPP affected the bioaccumulation of fluoranthene, pyrene and total PAHs, although a confounding effect of traffic (mostly petrol/gasoline engines) was evident. Spatial variation of the rate of diesel vehicles showed a significant association with that of acenaphthylene, acenaphthene, fluorene, anthracene and naphthalene. The series of high-speed wind values suggests that wind promotes diffusion rather than dispersion of the monitored PAHs. At the whole study area scale, the BPP was a source of acenaphthylene and acenaphthene, while diesel vehicles were a source of acenaphthylene. PAHs contamination strongly promotes oxidative stress (a threefold increase vs pre-exposure levels) in lichen transplants, suggesting a marked polluting effect of anthropogenic sources especially at the expense of the mycobiont. The proposed monitoring approach could improve the apportionment of the different contributions of point and linear anthropogenic sources of PAHs, mitigating the reciprocal biases affecting their spatial patterns.

Analysis of local habitat selection and large-scale attraction/avoidance based on animal tracking data: is there a single best method?

BACKGROUND

New wildlife telemetry and tracking technologies have become available in the last decade, leading to a large increase in the volume and resolution of animal tracking data. These technical developments have been accompanied by various statistical tools aimed at analysing the data obtained by these methods.

METHODS

We used simulated habitat and tracking data to compare some of the different statistical methods frequently used to infer local resource selection and large-scale attraction/avoidance from tracking data. Notably, we compared spatial logistic regression models (SLRMs), spatio-temporal point process models (ST-PPMs), step selection models (SSMs), and integrated step selection models (iSSMs) and their interplay with habitat and animal movement properties in terms of statistical hypothesis testing.

RESULTS

We demonstrated that only iSSMs and ST-PPMs showed nominal type I error rates in all studied cases, whereas SSMs may slightly and SLRMs may frequently and strongly exceed these levels. iSSMs appeared to have on average a more robust and higher statistical power than ST-PPMs.

CONCLUSIONS

Based on our results, we recommend the use of iSSMs to infer habitat selection or large-scale attraction/avoidance from animal tracking data. Further advantages over other approaches include short computation times, predictive capacity, and the possibility of deriving mechanistic movement models.

A Generalized Additive Model Correlating Blacklegged Ticks With White-Tailed Deer Density, Temperature, and Humidity in Maine, USA, 1990-2013

Geographical range expansions of blacklegged tick [Ixodes scapularis Say (Acari: Ixodidae)] populations over time in the United States have been attributed to a mosaic of factors including 20th century reforestation followed by suburbanization, burgeoning populations of the white-tailed deer [Odocoileus virginianus Zimmerman (Artiodactyla: Cervidae)], and, at the northern edge of I. scapularis' range, climate change. Maine, a high Lyme disease incidence state, has been experiencing warmer and shorter winter seasons, and relatively more so in its northern tier. Maine served as a case study to investigate the interacting impacts of deer and seasonal climatology on the spatial and temporal distribution of I. scapularis. A passive tick surveillance dataset indexed abundance of I. scapularis nymphs for the state, 1990-2013. With Maine's wildlife management districts as the spatial unit, we used a generalized additive model to assess linear and nonlinear relationships between I. scapularis nymph abundance and predictors. Nymph submission rate increased with increasing deer densities up to ~5 deer/km2 (13 deer/mi2), but beyond this threshold did not vary with deer density. This corroborated the idea of a saturating relationship between I. scapularis and deer density. Nymphs also were associated with warmer minimum winter temperatures, earlier degree-day accumulation, and higher relative humidity. However, nymph abundance only increased with warmer winters and degree-day accumulation where deer density exceeded ~2 deer/km2 (~6/mi2). Anticipated increases in I. scapularis in the northern tier could be partially mitigated through deer herd management.

Spatial regression and spillover effects in cluster randomized trials with count outcomes

This paper describes methodology for analyzing data from cluster randomized trials with count outcomes, taking indirect effects as well spatial effects into account. Indirect effects are modeled using a novel application of a measure of depth within the intervention arm. Both direct and indirect effects can be estimated accurately even when the proposed model is misspecified. We use spatial regression models with Gaussian random effects, where the individual outcomes have distributions overdispersed with respect to the Poisson, and the corresponding direct and indirect effects have a marginal interpretation. To avoid spatial confounding, we use orthogonal regression, in which random effects represent spatial dependence using a homoscedastic and dimensionally reduced modification of the intrinsic conditional autoregression model. We illustrate the methodology using spatial data from a pair-matched cluster randomized trial against the dengue mosquito vector Aedes aegypti, done in Trujillo, Venezuela.

Selecting a Scale for Spatial Confounding Adjustment

Unmeasured, spatially-structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the spline degrees of freedom do not provide an easily interpretable spatial scale. We describe a method for quantifying the extent of spatial confounding adjustment in terms of the Euclidean distance at which variation is removed. We develop this approach for confounding adjustment with splines and using Fourier and wavelet filtering. We demonstrate differences in the spatial scales these bases can represent and provide a comparison of methods for selecting the amount of confounding adjustment. We find the best performance for selecting the amount of adjustment using an information criterion evaluated on an outcome model without exposure. We apply this method to spatial adjustment in an analysis of fine particulate matter and blood pressure in a cohort of United States women.

Greenspace and Infant Mortality in Philadelphia, PA

Despite mounting evidence that urban greenspace protects against mortality in adults, few studies have explored the relationship between greenspace and death among infants. Here, we describe results from an analysis of associations between greenness and infant mortality in Philadelphia, PA. We used images of the normalized difference vegetation index (NDVI), derived from processed satellite data, to estimate greenness density in each census tract. We linked these data with census tract level counts of total infant mortality cases (n = 963) and births (n = 113,610) in years 2010-2014, and used Bayesian spatial areal unit, conditional autoregressive models to estimate associations between greenness and infant mortality. The models included a set of random effects to account for spatial autocorrelation between neighboring census tracts. Infant mortality counts were modeled using a Poisson distribution, and the logarithm of total births in each census tract was specified as the offset term. The following variables were included as potential confounders and effect modifiers: percentage non-Hispanic black, percentage living below the poverty line, an indicator of housing quality, and population density. In adjusted models, the rate of infant mortality was 27% higher in less green compared to more green tracts (95% CI 1.02-1.59). These results contribute further evidence that greenspace may be a health promoting environmental asset.

Adjusting for unmeasured spatial confounding with distance adjusted propensity score matching

Propensity score matching is a common tool for adjusting for observed confounding in observational studies, but is known to have limitations in the presence of unmeasured confounding. In many settings, researchers are confronted with spatially-indexed data where the relative locations of the observational units may serve as a useful proxy for unmeasured confounding that varies according to a spatial pattern. We develop a new method, termed distance adjusted propensity score matching (DAPSm) that incorporates information on units' spatial proximity into a propensity score matching procedure. We show that DAPSm can adjust for both observed and some forms of unobserved confounding and evaluate its performance relative to several other reasonable alternatives for incorporating spatial information into propensity score adjustment. The method is motivated by and applied to a comparative effectiveness investigation of power plant emission reduction technologies designed to reduce population exposure to ambient ozone pollution. Ultimately, DAPSm provides a framework for augmenting a "standard" propensity score analysis with information on spatial proximity and provides a transparent and principled way to assess the relative trade-offs of prioritizing observed confounding adjustment versus spatial proximity adjustment.

GIS for empirical research design: An illustration with georeferenced point data

This paper demonstrates how Geographic Information Systems (GIS) can be utilized to study the effects of spatial phenomena. Since experimental designs such as Randomized Controlled Trials are generally not feasible for spatial problems, researchers need to rely on quasi-experimental approaches using observational data. We provide a regression-based framework of the key procedures for GIS-based empirical research design using georeferenced point data for both spatial events of interest and subjects exposed to the events. We illustrate its utility and implementation through a case study on the impacts of the Cambodian genocide under the Pol Pot regime on post-conflict education.

Spatial Joint Species Distribution Modeling using Dirichlet Processes

Species distribution models usually attempt to explain presence-absence or abundance of a species at a site in terms of the environmental features (so-called abiotic features) present at the site. Historically, such models have considered species individually. However, it is well-established that species interact to influence presence-absence and abundance (envisioned as biotic factors). As a result, there has been substantial recent interest in joint species distribution models with various types of response, e.g., presence-absence, continuous and ordinal data. Such models incorporate dependence between species response as a surrogate for interaction. The challenge we address here is how to accommodate such modeling in the context of a large number of species (e.g., order 102) across sites numbering on the order of 102 or 103 when, in practice, only a few species are found at any observed site. Again, there is some recent literature to address this; we adopt a dimension reduction approach. The novel wrinkle we add here is spatial dependence. That is, we have a collection of sites over a relatively small spatial region so it is anticipated that species distribution at a given site would be similar to that at a nearby site. Specifically, we handle dimension reduction through Dirichlet processes, enabling clustering of species, joined with spatial dependence across sites through Gaussian processes. We use both simulated data and a plant communities dataset for the Cape Floristic Region (CFR) of South Africa to demonstrate our approach. The latter consists of presence-absence measurements for 639 tree species at 662 locations. Through both data examples we are able to demonstrate improved predictive performance using the foregoing specification.

Associations between maternal residential proximity to air emissions from industrial facilities and low birth weight in Texas, USA

BACKGROUND

Most previous studies examining associations between maternal exposures to air pollutants during pregnancy and low birth weight (LBW) in offspring focused on criteria air pollutants (PM_2.5, PM₁₀, O₃, NO₂, SO₂, CO, and Pb). The relationship between non-criteria air pollutants and LBW is understudied and requires greater coverage.

OBJECTIVES

This study investigated associations between maternal residential exposure to industrial air pollutants during pregnancy and LBW in offspring.

METHODS

This study used a case-control study design that included 94,106 term LBW cases and 376,424 controls. It covered 78 air pollutants common to both the Toxics Release Inventory (TRI) and ground air quality monitoring databases in Texas during 1996-2008. A modified version of the Emission Weighted Proximity Model (EWPM), calibrated with ground monitoring data, was used to estimate maternal residential exposure to industrial air pollutants during pregnancy. Binary logistic regression analyses were performed to calculate odds ratios (ORs) reflecting the associations of maternal exposure to industrial air pollutants and LBW in offspring, adjusted for child's sex, gestational weeks, maternal age, education, race/ethnicity, marital status, prenatal care, tobacco use during pregnancy, public health region of maternal residence, and year of birth. In addition, the Bonferroni correction for multiple comparisons was applied to the results of logistic regression analysis.

RESULTS

Relative to the non-exposed reference group, maternal residential exposure to benzene (adjusted odds ratio (aOR) 1.06, 95% confidence interval (CI) 1.04, 1.08), benzo(g,h,i)perylene (aOR 1.04, 95% CI 1.02, 1.07), cumene (aOR 1.05, 95% CI 1.03, 1.07), cyclohexane (aOR 1.04, 95% CI 1.02, 1.07), dichloromethane (aOR 1.04, 95% CI 1.03, 1.07), ethylbenzene (aOR 1.05, 95% CI 1.03, 1.06), ethylene (aOR 1.06, 95% CI 1.03, 1.09), mercury (aOR 1.04, 95% CI 1.02, 1.07), naphthalene (aOR 1.03, 95% CI 1.01, 1.05), n-hexane (aOR 1.06, 95% CI 1.04, 1.08), propylene (aOR 1.06, 95% CI 1.03, 1.10), styrene (aOR 1.06, 95% CI 1.04, 1.08), toluene (aOR 1.05, 95% CI 1.03, 1.07), and zinc (fume or dust) (aOR 1.10, 95% CI 1.06, 1.13) was found to have significantly higher odds of LBW in offspring. When the estimated exposures were categorized into four different groups (zero, low, medium, and high) in the analysis, eleven of the fourteen air pollutants, with the exception of benzo(g,h,i)perylene, ethylene, and propylene, remained as significant risk factors.

CONCLUSIONS

Results indicate that maternal residential proximity to industrial facilities emitting any of the fourteen pollutants identified by this study during pregnancy may be associated with LBW in offspring. With the exception of benzene, ethylbenzene, toluene, and zinc, the rest of the fourteen air pollutants are identified as LBW risk factors for the first time by this study. Further epidemiological, biological, and toxicological studies are suggested to verify the findings from this study.

Industrial air pollution and low birth weight: a case-control study in Texas, USA

Many studies have investigated associations between maternal residential exposures to air pollutants and low birth weight (LBW) in offspring. However, most studies focused on the criteria air pollutants (PM_2.5, PM₁₀, O₃, NO₂, SO₂, CO, and Pb), and only a few studies examined the potential impact of other air pollutants on LBW. This study investigated associations between maternal residential exposure to industrial air emissions of 449 toxics release inventory (TRI) chemicals and LBW in offspring using a case-control study design based on a large dataset consisting of 94,106 LBW cases and 376,424 controls in Texas from 1996 to 2008. Maternal residential exposure to chemicals was estimated using a modified version of the emission-weighted proximity model (EWPM). The model takes into account reported quantities of annual air emission from industrial facilities and the distances between the locations of industrial facilities and maternal residence locations. Binary logistic regression was used to compute odds ratios measuring the association between maternal exposure to different TRI chemicals and LBW in offspring. Odds ratios were adjusted for child's sex, birth year, gestational length, maternal age, education, race/ethnicity, and public health region of maternal residence. Among the ten chemicals selected for a complete analysis, maternal residential exposures to five TRI chemicals were positively associated with LBW in offspring. These five chemicals include acetamide (adjusted odds ratio [aOR] 2.29, 95% confidence interval [CI] 1.24, 4.20), p-phenylenediamine (aOR 1.63, 95% CI 1.18, 2.25), 2,2-dichloro-1,1,1-trifluoroethane (aOR 1.41, 95% CI 1.20, 1.66), tributyltin methacrylate (aOR 1.20, 95% CI 1.06, 1.36), and 1,1,1-trichloroethane (aOR 1.11, 95% CI 1.03, 1.20). These findings suggest that maternal residential proximity to industrial air emissions of some chemicals during pregnancy may be associated with LBW in offspring.

Associations between birth outcomes and maternal PM2.5 exposure in Shanghai: A comparison of three exposure assessment approaches

BACKGROUND

Few studies have estimated effects of maternal PM_2.5 exposure on birth outcomes in China due to the lack of historical air pollution data.

OBJECTIVES

We estimated the associations between maternal PM_2.5 exposure and birth outcomes using gap-filled satellite estimates in Shanghai, China.

METHODS

We obtained birth registration records of 132,783 singleton live births during 2011-2014 in Shanghai. PM_2.5 exposures were assessed from satellite-derived estimates or central-site measurements. Linear and logistic regressions were used to estimate associations with term birth weight and term low birth weight (LBW), respectively. Logistic and discrete-time survival models were used to estimate associations with preterm birth. Effect modification by maternal age and parental education levels was investigated.

RESULTS

A 10 μg/m³ increase in gap-filled satellite-based whole-pregnancy PM_2.5 exposure was associated with a -12.85 g (95% CI: -18.44, -7.27) change in term birth weight, increased risk of preterm birth (OR 1.27, 95% CI: 1.20, 1.36), and increased risk of term LBW (OR 1.22, 95% CI: 1.06, 1.41). Sensitivity analyses during 2013-2014, when ground PM_2.5 measurements were available, showed that the health associations using gap-filled satellite PM_2.5 concentrations were higher than those obtained using satellite PM_2.5 concentrations without accounting for missingness. The health associations using gap-filled satellite PM_2.5 had similar magnitudes to those using central-site measurements, but with narrower confidence intervals.

CONCLUSIONS

The magnitude of associations between maternal PM_2.5 exposure and adverse birth outcomes in Shanghai was higher than previous findings. One reason could be reduced exposure error of the gap-filled high-resolution satellite PM_2.5 estimates.

Geostatistical Methods for Disease Mapping and Visualisation Using Data from Spatio-temporally Referenced Prevalence Surveys

In this paper, we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio-temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualisation of spatio-temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1 334 surveys conducted in Senegal between 1905 and 2014.

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.

Toward a diagnostic toolkit for linear models with Gaussian-process distributed random effects

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely related Bayesian analysis. This article addresses two problems. First, we propose tools for understanding how data determine estimates in these models, using a spectral basis approximation to the GP under which the restricted likelihood is formally identical to the likelihood for a gamma-errors GLM with identity link. Second, to examine the data's support for a covariate and to understand how adding that covariate moves variation in the outcome y out of the GP and error parts of the fit, we apply a linear-model diagnostic, the added variable plot (AVP), both to the original observations and to projections of the data onto the spectral basis functions. The spectral- and observation-domain AVPs estimate the same coefficient for a covariate but emphasize low- and high-frequency data features respectively and thus highlight the covariate's effect on the GP and error parts of the fit, respectively. The spectral approximation applies to data observed on a regular grid; for data observed at irregular locations, we propose smoothing the data to a grid before applying our methods. The methods are illustrated using the forest-biomass data of Finley et al. (2008).

Spatially explicit survival modeling for small area cancer data

In this paper we propose a novel Bayesian statistical methodology for spatial survival data. Our methodology broadens the definition of the survival, density and hazard functions by explicitly modeling the spatial dependency using direct derivations of these functions and their marginals and conditionals. We also derive spatially dependent likelihood functions. Finally we examine the applications of these derivations with geographically augmented survival distributions in the context of the Louisiana Surveillance, Epidemiology, and End Results (SEER) registry prostate cancer data.

The basis function approach for modeling autocorrelation in ecological data

Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many seemingly disparate statistical methods used to account for autocorrelation can be expressed as regression models that include basis functions. Basis functions also enable ecologists to modify a wide range of existing ecological models in order to account for autocorrelation, which can improve inference and predictive accuracy. Furthermore, understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of collinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.

Association between aircraft, road and railway traffic noise and depression in a large case-control study based on secondary data

BACKGROUND

Few studies have examined the relationship between traffic noise and depression providing inconclusive results. This large case-control study is the first to assess and directly compare depression risks by aircraft, road traffic and railway noise.

METHODS

The study population included individuals aged ≥40 years that were insured by three large statutory health insurance funds and were living in the region of Frankfurt international airport. Address-specific exposure to aircraft, road and railway traffic noise in 2005 was estimated. Based on insurance claims and prescription data, 77,295 cases with a new clinical depression diagnosis between 2006 and 2010 were compared with 578,246 control subjects.

RESULTS

For road traffic noise, a linear exposure-risk relationship was found with an odds ratio (OR) of 1.17 (95% CI=1.10-1.25) for 24-h continuous sound levels ≥70dB. For aircraft noise, the risk estimates reached a maximum OR of 1.23 (95% CI=1.19-1.28) at 50-55dB and decreased at higher exposure categories. For railway noise, risk estimates peaked at 60-65dB (OR=1.15, 95% CI=1.08-1.22). The highest OR of 1.42 (95% CI=1.33-1.52) was found for a combined exposure to noise above 50dB from all three sources.

CONCLUSIONS

This study indicates that traffic noise exposure might lead to depression. As a potential explanation for the decreasing risks at high traffic noise levels, vulnerable people might actively cope with noise (e.g. insulate or move away).

Spatial regression with covariate measurement error: A semiparametric approach

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.