Spatial Random Effects Research Articles

Spatial and demographic heterogeneity in excess mortality in the United States, 2020-2023: a multi-model approach.

In this study, we assessed the overall impact of the Covid-19 pandemic in the United States between 2020 and 2023 through estimates of excess all-cause mortality. Monthly mortality rates over a 19-year period, stratified by age, sex and state of residence were used to forecast expected mortality for the pandemic years. A combination of models - two timeseries, a spatial random effects and a generalized additive -- was used to better capture uncertainty. Results indicate that US national excess mortality decreased in 2023 to 157 thousand (95% prediction interval: 35K-282K) from 502K (436K-567K), 574K(484K-666K) and 377K (264K-484K) during the years 2020-2022, respectively. Unlike in previous years, deaths with Covid-19 as the underlying-cause-of-death possibly accounted for all excess deaths during 2023. While for the older age groups (75+ years) the year 2020, before vaccines were available, had the highest excess mortality rate, the two younger age groups had the highest excess mortality in 2021. In each age group, women were estimated to have consistently lower excess mortality than men. West Virginia had the highest age-standardized excess mortality among all states in 2021 and 2022. Our findings demonstrate the value of a multi-model approach in capturing heterogeneity in excess mortality.

Geographical variation in prostate cancer testing explained by socio-economic position in Stockholm

Abstract Background Prostate cancer screening using prostate-specific antigen (PSA) testing is controversial but remains prevalent in many countries. Despite its prevalence there is little information in Sweden or globally on the spatial heterogeneity in PSA testing. This study aims to describe the spatio-temporal variation in PSA testing in the Stockholm region specifically at the municipality and small area level. Additionally, it aims to quantify the extent to which socio-economic position (SEP) indicators such as education, income, and country of birth explain the observed variation in PSA testing. Methods A retrospective population-based register study was conducted, encompassing men aged 40 years and older residing in the Stockholm region from 2007 to 2016. Utilizing spatial smoothing techniques, we calculated the age-standardised proportion of men undergoing PSA testing prior to any prostate cancer diagnosis within each area for every calendar year. Furthermore, we used Bayesian logistic regression models with spatial random effects to estimate the individual-level association between PSA testing and socio-economic position. The proportion of variance in PSA testing explained by various measures of SEP was also estimated at both the municipality and small area levels. Results Significant geographical disparities in PSA testing were observed across small areas within Stockholm. The proportion of variance explained in PSA testing at the small area level was highest for income (32.6%), followed by education (9.7%) and country of birth (7.4%). Incorporating all SEP measures led to a higher proportion of explained variance at the small area level (41.6%) compared to the municipality level (24.8%). Conclusions PSA testing was significantly associated with various socio-economic indicators and some of the spatial variation could be explained by SEP. It would be useful to ascertain whether similar patterns are observed in other regions or countries. Key messages • The findings suggested widespread and consistent opportunistic prostate cancer screening practices within the Stockholm region, raising concerns regarding potential overdiagnosis and overtreatment. • The socio-economic differences in prostate cancer screening could partially explain the differences in cancer incidence and mortality.

Impact of Areal Factors on Students’ Travel Mode Choices: A Bayesian Spatial Analysis

A preliminary analysis of the 2018/2019 Austin Travel Survey indicated that most off-campus students in Travis County, TX, tend to use cars rather than more sustainable transportation modes, significantly contributing to traffic congestion and environmental impact. This study aims to analyze the impacts of areal factors, including environmental and transportation factors, on students’ choices of travel mode in order to promote more sustainable transport behaviors. Additionally, we investigate the presence of spatial correlation and unobserved heterogeneity in travel data and their effects on students’ travel mode choices. We have proposed two Bayesian models—a basic model and a spatial model—with structured and unstructured random-effect terms to perform the analysis. The results indicate that the inclusion of spatial random effects considerably improves model performance, suggesting that students’ choices of mode are likely influenced by areal factors often ‘unobserved’ in many individual travel mode choice surveys. Furthermore, we found that the average slope, sidewalk density, and bus-stop density significantly affect students’ travel mode choices. These findings provide insights into promoting sustainable transport systems by addressing environmental and infrastructural factors in an effort to reduce car dependency among students, thereby supporting sustainable urban development.

Analysis of recurrent event data with spatial random effects using a Bayesian approach.

Recurrent event data, which represent the occurrence of repeated incidences, are common in observational studies. Furthermore, collecting possible spatial correlations in health and environmental data is likely to provide more information for risk prediction. This article proposes a comprehensive proportional intensity model considering spatial random effects for recurrent event data using a Bayesian approach. The spatial information for areal data (where the spatial location is known up to a geographic unit such as a county) and georeferenced data (where the location is exactly observed) is examined. A traditional constant baseline intensity function, as well as a flexible piecewise constant baseline intensity function, are both under consideration. To estimate the parameters, a Markov chain Monte Carlo method with the Metropolis-Hastings algorithm and the adaptive Metropolis algorithm are applied. To assess the performance of model fitting, the deviance information criterion and log pseudo marginal likelihood are proposed. Overall, simulation studies demonstrate that the proposed model is significantly better than models that do not consider spatial effects if spatial correlations exist. Finally, our approach is implemented using a dataset related to the recurrence of cardiovascular diseases, which incorporates spatial information.

Bayesian spatial-temporal analysis and determinants of cardiovascular diseases in Tanzania mainland

BackgroundCardiovascular Diseases (CVDs) are health-threatening conditions that account for high mortality in the world. Approximately 23.6 million deaths due to CVD is expected in the year 2030 worldwide. The CVD burden is more severe in developing countries, including Tanzania.ObjectivesThis study analyzed the spatial-temporal trends and determinants of cardiovascular diseases in Tanzania from 2010 to 2019.MethodsIndividual data were extracted from Jakaya Kikwete Cardiac Institute (JKCI), Mbeya Zonal Referral Hospital (MZRH), Kilimanjaro Christian Medical Centre (KCMC) and Bugando hospitals and the geographical data from TMA. The model containing spatial and temporal components was analyzed using the Bayesian hierarchical method implemented using Integrated Nested Laplace Approximation (INLA).ResultsThe results found that the incidence of CVD increased from 2010 to 2014 and decreased from 2015 to 2019. The southern highlands, lake, central and coastal zones were more likely to have CVD problems than others. It was also revealed that people aged 60–64 years OR = 1.49, females OR = 1.51, smokers OR = 1.76, alcohol drinkers OR = 1.48, and overweight OR = 1.89 were more likely to have CVD problems. Additionally, a 1oC increase in the average annual air maximum temperature was related to a 14% risk of developing CVD problems. The study revealed that the model, which included spatial and temporal random effects, was the best-predicting model.ConclusionThe study shows a decreased CVD incidence rate from 2015 to 2019. The CVD incidences occurred more in Tanzania’s coastal and lake areas between 2010 and 2019. The demographic, lifestyle and geographical risk factors were significantly associated with the CVD.

Structure Induced by a Multiple Membership Transformation on the Conditional Autoregressive Model

The objective of disease mapping is to model data aggregated at the areal level. In some contexts, however, (e.g. residential histories, general practitioner catchment areas) when data is arising from a variety of sources, not necessarily at the same spatial scale, it is possible to specify spatial random effects, or covariate effects, at the areal level, by using a multiple membership principle (MM) (Petrof et al., 2020; Gramatica et al., 2021). A weighted average of conditional autoregressive (CAR) spatial random effects embeds spatial information for a spatially-misaligned outcome and estimate relative risk for both frameworks (areas and memberships). In this paper we investigate the theoretical underpinnings of these application of the multiple membership principle to the CAR prior, in particular with regard to parameterisation, properness and identifiability. We carry out simulations involving different numbers of memberships as compared to number of areas and assess impact of this on estimating parameters of interest. Both analytical and simulation study results show under which conditions parameters of interest are identifiable, so that we can offer actionable recommendations to researchers. Finally, we present the results of an application of the multiple membership model to diabetes prevalence data in South London, together with strategic implications for public health considerations.

Long-Term Effect of Temperature Increase on Liver Cancer in Australia: A Bayesian Spatial Analysis.

While some evidence has potentially linked climate change to carcinogenic factors, the long-term effect of climate change on liver cancer risk largely remains unclear. Our objective is to evaluate the long-term relationship between temperature increase and liver cancer incidence in Australia. We mapped the spatial distribution of liver cancer incidence from 2001 to 2019 in Australia. A Bayesian spatial conditional autoregressive (CAR) model was used to estimate the relationships between the increase in temperature at different lags and liver cancer incidence in Australia, after controlling for chronic hepatitis B prevalence, chronic hepatitis C prevalence, and the Index of Relative Socio-economic Disadvantage. Spatial random effects obtained from the Bayesian CAR model were also mapped. The research showed that the distribution of liver cancer in Australia is spatially clustered, most areas in Northern Territory and Northern Queensland have higher incidence and relative risk. The increase in temperature at the lag of 30 years was found to correlate with the increase in liver cancer incidence in Australia, with a posterior mean of 30.57 [95% Bayesian credible interval (CrI): 0.17, 58.88] for the univariate model and 29.50 (95% CrI: 1.27, 58.95) after controlling for confounders, respectively. The results were not highly credible for other lags. Our Bayesian spatial analysis suggested a potential relationship between temperature increase and liver cancer. To our knowledge, this research marks the first attempt to assess the long-term effect of global warming on liver cancer. If the relationship is confirmed by other studies, these findings may inform the development of prevention and mitigation strategies based on climate change projections. https://doi.org/10.1289/EHP14574.

Bayesian spatio-temporal modelling of environmental, climatic, and socio-economic influences on malaria in Central Vietnam

BackgroundDespite the successful efforts in controlling malaria in Vietnam, the disease remains a significant health concern, particularly in Central Vietnam. This study aimed to assess correlations between environmental, climatic, and socio-economic factors in the district with malaria cases.MethodsThe study was conducted in 15 provinces in Central Vietnam from January 2018 to December 2022. Monthly malaria cases were obtained from the Institute of Malariology, Parasitology, and Entomology Quy Nhon, Vietnam. Environmental, climatic, and socio-economic data were retrieved using a Google Earth Engine script. A multivariable Zero-inflated Poisson regression was undertaken using a Bayesian framework with spatial and spatiotemporal random effects with a conditional autoregressive prior structure. The posterior random effects were estimated using Bayesian Markov Chain Monte Carlo simulation with Gibbs sampling.ResultsThere was a total of 5,985 Plasmodium falciparum and 2,623 Plasmodium vivax cases during the study period. Plasmodium falciparum risk increased by five times (95% credible interval [CrI] 4.37, 6.74) for each 1-unit increase of normalized difference vegetation index (NDVI) without lag and by 8% (95% CrI 7%, 9%) for every 1ºC increase in maximum temperature (TMAX) at a 6-month lag. While a decrease in risk of 1% (95% CrI 0%, 1%) for a 1 mm increase in precipitation with a 6-month lag was observed. A 1-unit increase in NDVI at a 1-month lag was associated with a four-fold increase (95% CrI 2.95, 4.90) in risk of P. vivax. In addition, the risk increased by 6% (95% CrI 5%, 7%) and 3% (95% CrI 1%, 5%) for each 1ºC increase in land surface temperature during daytime with a 6-month lag and TMAX at a 4-month lag, respectively. Spatial analysis showed a higher mean malaria risk of both species in the Central Highlands and southeast parts of Central Vietnam and a lower risk in the northern and north-western areas.ConclusionIdentification of environmental, climatic, and socio-economic risk factors and spatial malaria clusters are crucial for designing adaptive strategies to maximize the impact of limited public health resources toward eliminating malaria in Vietnam.

Spatio-temporal forecasting for the US Drought Monitor

Abstract The US Drought Monitor is the leading drought monitoring tool in the United States. Updated weekly and freely distributed, it records the drought conditions as geo-referenced polygons showing one of six ordered levels. These levels are determined by a mixture of quantitative environmental measurements and local expert opinion across the entire United States. At present, forecasts of the Drought Monitor only convey the expected direction of drought development (i.e. worsen, persist, subside) and do not communicate any uncertainty. This limits the utility of forecasts. In this paper, we describe a Bayesian spatio-temporal ordinal hierarchical model for use in modelling and projecting drought conditions. The model is flexible, scalable, and interpretable. By viewing drought data as areal rather than point-referenced, we reduce the cost of sampling from the posterior by avoiding dense matrix inversion. Draws from the posterior predictive distribution produce future forecasts of actual drought levels—rather than only the direction of drought development—and all sources of uncertainty are propagated into the posterior. Spatial random effects and an autoregressive model structure capture spatial and temporal dependence, and help ensure smoothness in forecasts over space and time. The result is a framework for modelling and forecasting drought levels and capturing forecast uncertainty.

Bayesian hierarchical modeling for bivariate multiscale spatial data with application to blood test monitoring

Public health spatial data are often recorded at different spatial scales (or geographic regions/divisions) and over different correlated variables. Motivated by data from the Dartmouth Atlas Project, we consider jointly analyzing average annual percentages of diabetic Medicare enrollees who have taken the hemoglobin A1c and blood lipid tests, observed at the hospital service area (HSA) and county levels, respectively. Capitalizing on bivariate relationships between these two scales is not immediate as counties are not nested within HSAs. It is well known that one can improve predictions by leveraging correlations across both variables and scales. There are very few methods available that simultaneously model multivariate and multiscale correlations. We propose three new hierarchical Bayesian models for bivariate multiscale spatial data, extending spatial random effects, multivariate conditional autoregressive (MCAR), and ordered hierarchical models through a multiscale spatial approach. We simulated data from each of the three models and compared the corresponding predictions, and found the computationally intensive multiscale MCAR model is more robust to model misspecification. In an analysis of 2015 Texas Dartmouth Atlas Project data, we produced finer resolution predictions (partitioning of HSAs and counties) than univariate analyses, determined that the novel multiscale MCAR and OH models were preferable via out-of-sample metrics, and determined the HSA with the highest within-HSA variability of hemoglobin A1c blood testing. Additionally, we compare the univariate multiscale models to the bivariate multiscale models and see clear improvements in prediction over univariate analyses.

Step selection functions with non‐linear and random effects

Abstract Step selection functions (SSFs) are used to jointly describe animal movement patterns and habitat preferences. Recent work has extended this framework to model inter‐individual differences, account for unexplained structure in animals' space use and capture temporally varying patterns of movement and habitat selection. In this paper, we formulate SSFs with penalised smooths (similar to generalised additive models) to unify new and existing extensions, and conveniently implement the models in the popular, open‐source mgcv R package. We explore non‐linear patterns of movement and habitat selection, and use the equivalence between penalised smoothing splines and random effects to implement individual‐level and spatial random effects. This framework can also be used to fit varying‐coefficient models to account for temporally or spatially heterogeneous patterns of selection (e.g. resulting from behavioural variation), or any other non‐linear interactions between drivers of the animal's movement decisions. We provide the necessary technical details to understand several key special cases of smooths and their implementation in mgcv, showcase the ecological relevance using two illustrative examples and provide R code to facilitate the adoption of these methods. This paper offers a broad overview of how smooth effects can be applied to increase the flexibility and biological realism of SSFs.

Research on the Validity of Bootstrap LM-Error Test in Spatial Random Effect Models

Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.

Fast Bayesian Functional Regression for Non-Gaussian Spatial Data

Functional generalized linear models (FGLM) have been widely used to study the relations between non-Gaussian response and functional covariates. However, most existing works for FGLM assume independence among observations and therefore they are of limited applicability for correlated data. A particularly important example is spatial functional data, where we observe functions over spatial domains, such as the age population curve or temperature curve at each areal unit. In this paper, we extend FGLM by incorporating spatial random effects. Especially, we study the relationship between the non-Gaussian response variable and functional covariates that are spatially observed. However, such model has computational and inferential challenges. The high-dimensional spatial random effects cause the slow mixing of Markov chain Monte Carlo (MCMC) algorithms. Furthermore, spatial confounding can lead to bias in parameter estimates and inflate their variances. To address these issues, we propose an efficient Bayesian method using a sparse reparameterization of high-dimensional random effects. We also study the average coverage probabilities of the credible intervals of functional parameters. We apply our methods to simulated and real data examples, including malaria incidence data and US COVID-19 data. The proposed method is fast while providing accurate functional estimates.

Domestic (re)infestation risk with the main vector Triatoma infestans increases with surrounding green vegetation and social vulnerability in the Argentine Chaco.

Chagas disease, caused by Trypanosoma cruzi, is still a public health problem in Latin America and in the Southern Cone countries, where Triatoma infestans is the main vector. We evaluated the relationships among the density of green vegetation around rural houses, sociodemographic characteristics, and domestic (re)infestation with T. infestans while accounting for their spatial dependence in the municipality of Pampa del Indio between 2007 and 2016. The study comprised sociodemographic and ecological variables from 734 rural houses with no missing data. Green vegetation density surrounding houses was estimated by the normalized difference vegetation index (NDVI). We used a hierarchical Bayesian logistic regression composed of fixed effects and spatial random effects to estimate domestic infestation risk and quantile regressions to evaluate the association between surrounding NDVI and selected sociodemographic variables. Qom ethnicity and the number of poultry were negatively associated with surrounding NDVI, whereas overcrowding was positively associated with surrounding NDVI. Hierarchical Bayesian models identified that domestic infestation was positively associated with surrounding NDVI, suitable walls for triatomines, and overcrowding over both intervention periods. Preintervention domestic infestation also was positively associated with Qom ethnicity. Models with spatial random effects performed better than models without spatial effects. The former identified geographic areas with a domestic infestation risk not accounted for by fixed-effect variables. Domestic infestation with T. infestans was associated with the density of green vegetation surrounding rural houses and social vulnerability over a decade of sustained vector control interventions. High density of green vegetation surrounding rural houses was associated with households with more vulnerable social conditions. Evaluation of domestic infestation risk should simultaneously consider social, landscape and spatial effects to control for their mutual dependency. Hierarchical Bayesian models provided a proficient methodology to identify areas for targeted triatomine and disease surveillance and control.

Differential gene expression analysis of spatial transcriptomic experiments using spatial mixed models

Spatial transcriptomics (ST) assays represent a revolution in how the architecture of tissues is studied by allowing for the exploration of cells in their spatial context. A common element in the analysis is delineating tissue domains or “niches” followed by detecting differentially expressed genes to infer the biological identity of the tissue domains or cell types. However, many studies approach differential expression analysis by using statistical approaches often applied in the analysis of non-spatial scRNA data (e.g., two-sample t-tests, Wilcoxon’s rank sum test), hence neglecting the spatial dependency observed in ST data. In this study, we show that applying linear mixed models with spatial correlation structures using spatial random effects effectively accounts for the spatial autocorrelation and reduces inflation of type-I error rate observed in non-spatial based differential expression testing. We also show that spatial linear models with an exponential correlation structure provide a better fit to the ST data as compared to non-spatial models, particularly for spatially resolved technologies that quantify expression at finer scales (i.e., single-cell resolution).

A zero‐inflated Poisson spatial model with misreporting for wildfire occurrences in southern Italian municipalities

AbstractWe propose a Poisson model for zero‐inflated spatial counts contaminated by measurement error: we accommodate the excess of zeroes in the counts, consider the possible under/over reporting of the response and account for the neighboring structure of spatial areal units. Bayesian inferences are provided by MCMC implementation through the R package NIMBLE. To evaluate the model performance, a simulation study is carried out under configurations that allow for structured and unstructured spatial random effects. The proposed model is applied to investigate the distribution of the counts of wildfire occurrences in the municipal areas of two neighboring Italian regions for the summer season 2021. Fire counts are obtained by processing MODIS satellite data, while several socio‐economic and environmental‐driven potential risk factors are also considered in the model formulation. Data from multiple sources with different spatial support are processed in order to comply with the municipal units. Results suggest the appropriateness of the approach and provide some insights on the features of wildfire occurrences.

Updated range map of an endangered salamander and congeneric competitor reveals different niche preferences.

Estimating distributions for cryptic and highly range-restricted species induces unique challenges for species distribution modeling. In particular, bioclimatic covariates that are typically used to model species ranges at regional and continental scales may not show strong variation at scales of 100s and 10s of meters. This limits both the likelihood and usefulness of correlated occurrence to data typically used in distribution models. Here, we present analyses of species distributions, at 100 × 100 m resolution, for a highly range restricted salamander species (Shenandoah salamander, Plethodon shenandoah) and a closely related congener (red-backed salamander, Plethodon cinereus). We combined data across multiple survey types, account for seasonal variation in availability of our target species, and control for repeated surveys at locations- all typical challenges in range-scale monitoring datasets. We fit distribution models using generalized additive models that account for spatial covariates as well as unexplained spatial variation and spatial uncertainty. Our model accommodates different survey protocols using offsets and incorporates temporal variation in detection and availability resulting from survey-specific variation in temperature and precipitation. Our spatial random effect was crucial in identifying small-scale differences in the occurrence of each species and provides cell-specific estimates of uncertainty in the density of salamanders across the range. Counts of both species were seen to increase in the 3 days following a precipitation event. However, P. cinereus were observed even in extremely wet conditions, while surface activity of P. shenandoah was associated with a more narrow range. Our results demonstrate how a flexible analytical approach improves estimates of both distribution and uncertainty, and identify key abiotic relationships, even at small spatial scales and when scales of empirical data are mismatched. While our approach is especially valuable for species with small ranges, controlling for spatial autocorrelation, estimating spatial uncertainty, and incorporating survey-specific information in estimates can improve the reliability of distribution models in general.

Mesoscale activity drives the habitat suitability of yellowfin tuna in the Gulf of Mexico

Yellowfin tuna, Thunnus albacares, represents an important component of commercial and recreational fisheries in the Gulf of Mexico (GoM). We investigated the influence of environmental conditions on the spatiotemporal distribution of yellowfin tuna using fisheries’ catch data spanning 2012–2019 within Mexican waters. We implemented hierarchical Bayesian regression models with spatial and temporal random effects and fixed effects of several environmental covariates to predict habitat suitability (HS) for the species. The best model included spatial and interannual anomalies of the absolute dynamic topography of the ocean surface (ADTSA and ADTIA, respectively), bottom depth, and a seasonal cyclical random effect. High catches occurred mainly towards anticyclonic features at bottom depths > 1000 m. The spatial extent of HS was higher in years with positive ADTIA, which implies more anticyclonic activity. The highest values of HS (> 0.7) generally occurred at positive ADTSA in oceanic waters of the central and northern GoM. However, high HS values (> 0.6) were observed in the southern GoM, in waters with cyclonic activity during summer. Our results highlight the importance of mesoscale features for the spatiotemporal distribution of yellowfin tunas and could help to develop dynamic fisheries management strategies in Mexico and the U.S. for this valuable resource.

Geographic, Patient, and VA Medical Center Variation in the Receipt and Mode of Primary Care in a National Sample of Veterans with Diabetes during 2020.

While telemedicine infrastructure was in place within the Veterans Health Administration (VHA) healthcare system before the onset of the COVID-19 pandemic, geographically varying ordinances/closures disrupted vital care for chronic disease patients such as those with type 2 diabetes. We created a national cohort of 1,647,158 non-Hispanic White, non-Hispanic Black, and Hispanic veterans with diabetes including patients with at least one primary care visit and HbA1c lab result between 3.5% and 20% in the fiscal year (FY) 2018 or 2019. For each VAMC, the proportion of telehealth visits in FY 2019 was calculated. Two logistic Bayesian spatial models were employed for in-person primary care or telehealth primary care in the fourth quarter of the FY 2020, with spatial random effects incorporated at the VA medical center (MC) catchment area level. Finally, we computed and mapped the posterior probability of receipt of primary care for an "average" patient within each catchment area. Non-Hispanic Black veterans and Hispanic veterans were less likely to receive in-person primary care but more likely to receive tele-primary care than non-Hispanic white veterans during the study period. Veterans living in the most socially vulnerable areas were more likely to receive telehealth primary care in the fourth quarter of FY 2020 compared to the least socially vulnerable group but were less likely to receive in-person care. In summary, racial minorities and those in the most socially vulnerable areas were less likely to receive in-person primary care but more likely to receive telehealth primary care, potentially indicating a disparity in the impact of the pandemic across these groups.

Bayesian Shared Component Spatial Modeling for Assessing the Shared and Age Group-Specific Mental Health Disorder Risk of Young and Old Age Groups: A Case Study of Toronto Neighborhoods, Canada

Mental health disorder risks of young and old age groups hold considerable importance for understanding present and future risk burdens. However, assessing mental health risks is significantly constrained by the influence of shared and age group-specific spatial processes and risk factors. Therefore, this study employed Bayesian shared component spatial modeling (BSCSM) to analyze mental health disorder data obtained from young (20–44 years) and old (65+ years) age groups in Toronto. BSCSM was employed to model the shared and age group-specific disorder risk and to identify hotspot areas. The unmeasured covariates, overdispersion, and latent spatial processes were adjusted using spatial and non-spatial random effect terms. The findings from BSCSM were finally compared with non-shared component modeling approaches. The results suggest that over 60% of variations in mental health disorder risk for both age groups could be explained by the shared component. The high-risk neighborhoods were mainly localized in southern and north-central Toronto for the young and old age groups. Deviance information criterion values suggested that models from BSCSM outperformed non-BSCSM models. BSCSM risk maps were also better at identifying high-risk areas. This work demonstrated that both shared and age group-specific risks are essential for assessing mental health disorder risk and devising targeted interventions.