Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan

Bayesian compositional models for ordinal response

Ordinal response is commonly found in medicine, biology, and other fields. In many situations, the predictors for this ordinal response are compositional, which means that the sum of predictors for each sample is fixed. Examples of compositional data include the relative abundance of species in microbiome data and the relative frequency of nutrition concentrations. Moreover, the predictors that are strongly correlated tend to have similar influence on the response outcome. Conventional cumulative logistic regression models for ordinal responses ignore the fixed-sum constraint on predictors and their associated interrelationships, and thus are not appropriate for analyzing compositional predictors.To solve this problem, we proposed Bayesian Compositional Models for Ordinal Response to analyze the relationship between compositional data and an ordinal response with a structured regularized horseshoe prior for the compositional coefficients and a soft sum-to-zero restriction on coefficients through the prior distribution. The method was implemented with R package rstan using efficient Hamiltonian Monte Carlo algorithm. We performed simulations to compare the proposed approach and existing methods for ordinal responses. Results revealed that our proposed method outperformed the existing methods in terms of parameter estimation and prediction. We also applied the proposed method to a microbiome study HMP2Data, to find microorganisms linked to ordinal inflammatory bowel disease levels. To make this work reproducible, the code and data used in this paper are available at https://github.com/Li-Zhang28/BCO.

Impact of Indoor Radon Exposure on Lung Cancer Incidence in Slovenia

Indoor radon is an important risk factor for lung cancer, as 3-14% of lung cancer cases can be attributed to radon. The aim of our study was to estimate the impact of indoor radon exposure on lung cancer incidence over the last 40 years in Slovenia. We analyzed the distribution of lung cancer incidence across 212 municipalities and 6032 settlements in Slovenia. The standardized incidence ratios were smoothed with the Besag-York-Mollie model and fitted with the integrated nested Laplace approximation. A categorical explanatory variable, the risk of indoor radon exposure with low, moderate and high risk values, was added to the models. We also calculated the population attributable fraction. Between 2.8% and 6.5% of the lung cancer cases in Slovenia were attributable to indoor radon exposure, with values varying by time period. The relative risk of developing lung cancer was significantly higher among the residents of areas with a moderate and high risk of radon exposure. Indoor radon exposure is an important risk factor for lung cancer in Slovenia in areas with high natural radon radiation (especially in the southern and south-eastern parts of the country).

Modelling spatiotemporal variation in under-five malaria risk in Ghana in 2016-2021

BACKGROUND

Ghana is among the top 10 highest malaria burden countries, with about 20,000 children dying annually, 25% of which were under five years. This study aimed to produce interactive web-based disease spatial maps and identify the high-burden malaria districts in Ghana.

METHODS

The study used 2016-2021 data extracted from the routine health service nationally representative and comprehensive District Health Information Management System II (DHIMS2) implemented by the Ghana Health Service. Bayesian geospatial modelling and interactive web-based spatial disease mapping methods were employed to quantify spatial variations and clustering in malaria risk across 260 districts. For each district, the study simultaneously mapped the observed malaria counts, district name, standardized incidence rate, and predicted relative risk and their associated standard errors using interactive web-based visualization methods.

RESULTS

A total of 32,659,240 malaria cases were reported among children < 5 years from 2016 to 2021. For every 10% increase in the number of children, malaria risk increased by 0.039 (log-mean 0.95, 95% credible interval = - 13.82-15.73) and for every 10% increase in the number of males, malaria risk decreased by 0.075, albeit not statistically significant (log-mean - 1.82, 95% credible interval = - 16.59-12.95). The study found substantial spatial and temporal differences in malaria risk across the 260 districts. The predicted national relative risk was 1.25 (95% credible interval = 1.23, 1.27). The malaria risk is relatively the same over the entire year. However, a slightly higher relative risk was recorded in 2019 while in 2021, residing in Keta, Abuakwa South, Jomoro, Ahafo Ano South East, Tain, Nanumba North, and Tatale Sanguli districts was associated with the highest malaria risk ranging from a relative risk of 3.00 to 4.83. The district-level spatial patterns of malaria risks changed over time.

CONCLUSION

This study identified high malaria risk districts in Ghana where urgent and targeted control efforts are required. Noticeable changes were also observed in malaria risk for certain districts over some periods in the study. The findings provide an effective, actionable tool to arm policymakers and programme managers in their efforts to reduce malaria risk and its associated morbidity and mortality in line with the Sustainable Development Goals (SDG) 3.2 for limited public health resource settings, where universal intervention across all districts is practically impossible.

Extended excess hazard models for spatially dependent survival data

Relative survival represents the preferred framework for the analysis of population cancer survival data. The aim is to model the survival probability associated with cancer in the absence of information about the cause of death. Recent data linkage developments have allowed for incorporating the place of residence into the population cancer databases; however, modeling this spatial information has received little attention in the relative survival setting. We propose a flexible parametric class of spatial excess hazard models (along with inference tools), named "Relative Survival Spatial General Hazard," that allows for the inclusion of fixed and spatial effects in both time-level and hazard-level components. We illustrate the performance of the proposed model using an extensive simulation study, and provide guidelines about the interplay of sample size, censoring, and model misspecification. We present a case study using real data from colon cancer patients in England. This case study illustrates how a spatial model can be used to identify geographical areas with low cancer survival, as well as how to summarize such a model through marginal survival quantities and spatial effects.

Bayesian compositional generalized linear models for analyzing microbiome data

The crucial impact of the microbiome on human health and disease has gained significant scientific attention. Researchers seek to connect microbiome features with health conditions, aiming to predict diseases and develop personalized medicine strategies. However, the practicality of conventional models is restricted due to important aspects of microbiome data. Specifically, the data observed is compositional, as the counts within each sample are bound by a fixed-sum constraint. Moreover, microbiome data often exhibits high dimensionality, wherein the number of variables surpasses the available samples. In addition, microbiome features exhibiting phenotypical similarity usually have similar influence on the response variable. To address the challenges posed by these aspects of the data structure, we proposed Bayesian compositional generalized linear models for analyzing microbiome data (BCGLM) with a structured regularized horseshoe prior for the compositional coefficients and a soft sum-to-zero restriction on coefficients through the prior distribution. We fitted the proposed models using Markov Chain Monte Carlo (MCMC) algorithms with R package rstan. The performance of the proposed method was assessed by extensive simulation studies. The simulation results show that our approach outperforms existing methods with higher accuracy of coefficient estimates and lower prediction error. We also applied the proposed method to microbiome study to find microorganisms linked to inflammatory bowel disease (IBD). To make this work reproducible, the code and data used in this article are available at https://github.com/Li-Zhang28/BCGLM.

Quantifying spatial under-reporting disparities in resident crowdsourcing

Modern city governance relies heavily on crowdsourcing to identify problems such as downed trees and power lines. A major concern is that residents do not report problems at the same rates, with heterogeneous reporting delays directly translating to downstream disparities in how quickly incidents can be addressed. Here we develop a method to identify reporting delays without using external ground-truth data. Our insight is that the rates at which duplicate reports are made about the same incident can be leveraged to disambiguate whether an incident has occurred by investigating its reporting rate once it has occurred. We apply our method to over 100,000 resident reports made in New York City and to over 900,000 reports made in Chicago, finding that there are substantial spatial and socioeconomic disparities in how quickly incidents are reported. We further validate our methods using external data and demonstrate how estimating reporting delays leads to practical insights and interventions for a more equitable, efficient government service.

Bayesian spatial modelling of localised SARS-CoV-2 transmission through mobility networks across England

In the early phases of growth, resurgent epidemic waves of SARS-CoV-2 incidence have been characterised by localised outbreaks. Therefore, understanding the geographic dispersion of emerging variants at the start of an outbreak is key for situational public health awareness. Using telecoms data, we derived mobility networks describing the movement patterns between local authorities in England, which we have used to inform the spatial structure of a Bayesian BYM2 model. Surge testing interventions can result in spatio-temporal sampling bias, and we account for this by extending the BYM2 model to include a random effect for each timepoint in a given area. Simulated-scenario modelling and real-world analyses of each variant that became dominant in England were conducted using our BYM2 model at local authority level in England. Simulated datasets were created using a stochastic metapopulation model, with the transmission rates between different areas parameterised using telecoms mobility data. Different scenarios were constructed to reproduce real-world spatial dispersion patterns that could prove challenging to inference, and we used these scenarios to understand the performance characteristics of the BYM2 model. The model performed better than unadjusted test positivity in all the simulation-scenarios, and in particular when sample sizes were small, or data was missing for geographical areas. Through the analyses of emerging variant transmission across England, we found a reduction in the early growth phase geographic clustering of later dominant variants as England became more interconnected from early 2022 and public health interventions were reduced. We have also shown the recent increased geographic spread and dominance of variants with similar mutations in the receptor binding domain, which may be indicative of convergent evolution of SARS-CoV-2 variants.

Ambient temperatures associated with reduced cognitive function in older adults in China

The cognitive function status of older adults determines the social function and living quality of older adults, which is related to the healthy development and stability of the society. However, the impact of high or low ambient temperature on cognitive function in older adults remains unclear. Based on data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS), we comprehensively assessed the impact of ambient temperature on the cognitive function of older adults in this study. The findings exhibited that for each 1 °C ascent in monthly temperature of high temperature, the examination score of global cognitive function of older adults decreased by 0.48 (95% CI 0.21-0.74), which was greater than that of 0.14 (95% CI 0.06-0.25) for each 1 °C reduction in low temperature. Overall, the detrimental effect of high temperature on cognitive function in older adults was more significant than that of low temperature, including on the five sub-cognitive functions involved. Our research provides vital technical guidance and reference for the health protection and prevention of cognitive function of older adults in specific external environmental conditions under the current climatic variation and temperature rise.

Spatio-temporal changes in pre-exposure prophylaxis uptake among MSM in mainland France between 2016 and 2021: a Bayesian small area approach with MSM population estimation

INTRODUCTION

In France, oral pre-exposure prophylaxis (PrEP) for HIV prevention has been publicly available since 2016, mainly targeting at men who have sex with men (MSM). Reliable and robust estimations of the actual PrEP uptake among MSM on a localized level can provide additional insights to identify and better reach marginalized MSM within current HIV prevention service provision. This study used national pharmaco-epidemiology surveillance data and regional MSM population estimations to model the spatio-temporal distribution of PrEP uptake among MSM in France 2016-2021 to identify marginalized MSM at risk for HIV and increase their PrEP uptake.

METHODS

We first applied Bayesian spatial analyses with survey-surveillance-based HIV incidence data as a spatial proxy to estimate the size of (1) regional HIV-negative MSM populations and (2) MSM who could be eligible for PrEP use according to French PrEP guidelines. We then applied Bayesian spatio-temporal ecological regression modelling to estimate the regional prevalence and relative probability of the overall- and new-PrEP uptake from 2016 to 2021 across France.

RESULTS

HIV-negative and PrEP-eligible MSM populations vary regionally across France. Île-de-France was estimated to have the highest MSM density compared to other French regions. According to the final spatio-temporal model, the relative probability of overall PrEP uptake was heterogeneous across France but remained stable over time. Urban areas have higher-than-average probabilities of PrEP uptake. The prevalence of PrEP use increased steadily (ranging from 8.8% [95% credible interval 8.5%;9.0%] in Nouvelle-Aquitaine to 38.2% [36.5%;39.9%] in Centre-Val-de-Loire in 2021).

CONCLUSIONS

Our results show that using Bayesian spatial analysis as a novel methodology to estimate the localized HIV-negative MSM population is feasible and applicable. Spatio-temporal models showed that despite the increasing prevalence of PrEP use in all regions, geographical disparities and inequalities of PrEP uptake continued to exist over time. We identified regions that would benefit from greater tailoring and delivery efforts. Based on our findings, public health policies and HIV prevention strategies could be adjusted to better combat HIV infections and to accelerate ending the HIV epidemic.

A Systematic Review of Joint Spatial and Spatiotemporal Models in Health Research

With the advancement of spatial analysis approaches, methodological research addressing the technical and statistical issues related to joint spatial and spatiotemporal models has increased. Despite the benefits of spatial modelling of several interrelated outcomes simultaneously, there has been no published systematic review on this topic, specifically when such models would be useful. This systematic review therefore aimed at reviewing health research published using joint spatial and spatiotemporal models. A systematic search of published studies that applied joint spatial and spatiotemporal models was performed using six electronic databases without geographic restriction. A search with the developed search terms yielded 4077 studies, from which 43 studies were included for the systematic review, including 15 studies focused on infectious diseases and 11 on cancer. Most of the studies (81.40%) were performed based on the Bayesian framework. Different joint spatial and spatiotemporal models were applied based on the nature of the data, population size, the incidence of outcomes, and assumptions. This review found that when the outcome is rare or the population is small, joint spatial and spatiotemporal models provide better performance by borrowing strength from related health outcomes which have a higher prevalence. A framework for the design, analysis, and reporting of such studies is also needed.

Relationship between changes in the public health nurses' workforce and the empirical Bayes estimates of standardized mortality ratio: a longitudinal ecological study of municipalities in Japan

BACKGROUND

The role of public health nurses (PHNs) in the community is expected to become increasingly important, along with the promotion of a comprehensive community care system. However, a comprehensive study of all municipalities is yet to be undertaken, and the relationship between the workforce of PHNs and health indicators is yet to be clarified. This study examined the effect of workforce change among PHNs, one of the structural indicators of PHNs' activities regarding changes in the empirical Bayes estimate of standardized mortality ratios (EBSMRs).

METHODS

An ecological study was conducted using municipality-level aggregate data. The data used were publicly available Japanese government statistics. The first-difference model of panel data analysis was used to examine the relationship between changes in EBSMR and changes in the number of PHNs per 100,000 population from 2010 to 2015, adjusting for the effects of population and other healthcare resources, including the number of physicians, medical clinics, general hospitals, and welfare facilities. The variation by the 47 prefectures was added to the linear model as a random effect. We also performed a sensitivity analysis using the full Bayesian inference using the Besag-York-Mollie model.

RESULTS

For males, EBSMRs for all causes and malignant neoplasms significantly decreased with an increase in the number of PHNs per population (coefficients: -1.00 and -0.89, p values: 0.008 and 0.043, respectively). For females, although all EBSMRs except malignant neoplasms showed decreased tendencies due to the increase in the number of PHNs per population, none of them were significant. The full Bayesian inference confirmed these associations.

CONCLUSIONS

An increase in the number of PHNs per population was significantly associated with a greater reduction in deaths from all causes and malignant neoplasms in males. The results of the full Bayesian inference also suggest that the workforce of PHNs may be related to changes in standardized mortality ratios for deaths from all causes in females.

Exposure to industrial hog and poultry operations and urinary tract infections in North Carolina, USA

An increasing share of urinary tract infections (UTIs) are caused by extraintestinal pathogenic Escherichia coli (ExPEC) lineages that have also been identified in poultry and hogs with high genetic similarity to human clinical isolates. We investigated industrial food animal production as a source of uropathogen transmission by examining relationships of hog and poultry density with emergency department (ED) visits for UTIs in North Carolina (NC). ED visits for UTI in 2016-2019 were identified by ICD-10 code from NC's ZIP code-level syndromic surveillance system and livestock counts were obtained from permit data and aerial imagery. We calculated separate hog and poultry spatial densities (animals/km²) by Census block with a 5 km buffer on the block perimeter and weighted by block population to estimate mean ZIP code densities. Associations between livestock density and UTI incidence were estimated using a reparameterized Besag-York-Mollié (BYM2) model with ZIP code population offsets to account for spatial autocorrelation. We excluded metropolitan and offshore ZIP codes and assessed effect measure modification by calendar year, ZIP code rurality, and patient sex, age, race/ethnicity, and health insurance status. In single-animal models, hog exposure was associated with increased UTI incidence (rate ratio [RR]: 1.21, 95 % CI: 1.07-1.37 in the highest hog-density tertile), but poultry exposure was associated with reduced UTI rates (RR: 0.86, 95 % CI: 0.81-0.91). However, the reference group for single-animal poultry models included ZIP codes with only hogs, which had some of the highest UTI rates; when compared with ZIP codes without any hogs or poultry, there was no association between poultry exposure and UTI incidence. Hog exposure was associated with increased UTI incidence in areas that also had medium to high poultry density, but not in areas with low poultry density, suggesting that intense hog production may contribute to increased UTI incidence in neighboring communities.

Spatio-temporal monitoring of health facility-level malaria trends in Zambia and adaptive scaling for operational intervention

Background

The spatial and temporal variability inherent in malaria transmission within countries implies that targeted interventions for malaria control in high-burden settings and subnational elimination are a practical necessity. Identifying the spatio-temporal incidence, risk, and trends at different administrative geographies within malaria-endemic countries and monitoring them in near real-time as change occurs is crucial for developing and introducing cost-effective, subnational control and elimination intervention strategies.

Methods

This study developed intelligent data analytics incorporating Bayesian trend and spatio-temporal Integrated Laplace Approximation models to analyse high-burden over 32 million reported malaria cases from 1743 health facilities in Zambia between 2009 and 2015.

Results

The results show that at least 5.4 million people live in catchment areas with increasing trends of malaria, covering over 47% of all health facilities, while 5.7 million people live in areas with a declining trend (95% CI), covering 27% of health facilities. A two-scale spatio-temporal trend comparison identified significant differences between health facilities and higher-level districts, and the pattern observed in the southeastern region of Zambia provides the first evidence of the impact of recently implemented localised interventions.

Conclusions

The results support our recommendation for an adaptive scaling approach when implementing national malaria monitoring, control and elimination strategies and a particular need for stratified subnational approaches targeting high-burden regions with increasing disease trends. Strong clusters along borders with highly endemic countries in the north and south of Zambia underscore the need for coordinated cross-border malaria initiatives and strategies.

Malaria is an infectious disease that is widespread in many African countries. Malaria transmission within a country can vary between regions, so tailored interventions for malaria control and elimination targeted to different regions are necessary. To achieve this, it is important to measure and monitor the frequency of malaria infections, its risk, and trends at different geographic administrative scales. This study analysed over 32 million reported malaria cases from 1743 health facilities in Zambia between 2009 and 2015. The results showed an increasing national trend in malaria risk and malaria infection frequency and identified differences between health facility and district trends. These findings support a flexible approach when implementing and expanding national malaria monitoring, control and elimination strategies, especially in areas bordering countries where malaria is widespread, cross-border movement is common, and cross-border initiatives could be beneficial.

Lubinda et al. analyse over 32 million health-facility reported malaria cases in Zambia (2009–15) to examine spatially-structured temporal trends. They observe overall increasing trends in risk and rates and highlight the potential benefits of using an adaptive scaling approach in national malaria strategies, and a need for cross-border initiatives.

Small area disease mapping of cancer incidence in British Columbia using Bayesian spatial models and the smallareamapp R Package

INTRODUCTION

There is an increasing interest in small area analyses in cancer surveillance; however, technical capacity is limited and accessible analytical approaches remain to be determined. This study demonstrates an accessible approach for small area cancer risk estimation using Bayesian hierarchical models and data visualization through the smallareamapp R package.

MATERIALS AND METHODS

Incident lung (N = 26,448), female breast (N = 28,466), cervical (N = 1,478), and colorectal (N = 25,457) cancers diagnosed among British Columbia (BC) residents between 2011 and 2018 were obtained from the BC Cancer Registry. Indirect age-standardization was used to derive age-adjusted expected counts and standardized incidence ratios (SIRs) relative to provincial rates. Moran's I was used to assess the strength and direction of spatial autocorrelation. A modified Besag, York and Mollie model (BYM2) was used for model incidence counts to calculate posterior median relative risks (RR) by Community Health Service Areas (CHSA; N = 218), adjusting for spatial dependencies. Integrated Nested Laplace Approximation (INLA) was used for Bayesian model implementation. Areas with exceedance probabilities (above a threshold RR = 1.1) greater or equal to 80% were considered to have an elevated risk. The posterior median and 95% credible intervals (CrI) for the spatially structured effect were reported. Predictive posterior checks were conducted through predictive integral transformation values and observed versus fitted values.

RESULTS

The proportion of variance in the RR explained by a spatial effect ranged from 4.4% (male colorectal) to 19.2% (female breast). Lung cancer showed the greatest number of CHSAs with elevated risk (Nwomen = 50/218, Nmen = 44/218), representing 2357 total excess cases. The largest lung cancer RRs were 1.67 (95% CrI = 1.06-2.50; exceedance probability = 96%; cases = 13) among women and 2.49 (95% CrI = 2.14-2.88; exceedance probability = 100%; cases = 174) among men. Areas with small population sizes and extreme SIRs were generally smoothed towards the null (RR = 1.0).

DISCUSSION

We present a ready-to-use approach for small area cancer risk estimation and disease mapping using BYM2 and exceedance probabilities. We developed the smallareamapp R package, which provides a user-friendly interface through an R-Shiny application, for epidemiologists and surveillance experts to examine geographic variation in risk. These methods and tools can be used to estimate risk, generate hypotheses, and examine ecologic associations while adjusting for spatial dependency.

Modeling infectious disease dynamics: Integrating contact tracing-based stochastic compartment and spatio-temporal risk models

Major infectious diseases such as COVID-19 have a significant impact on population lives and put enormous pressure on healthcare systems globally. Strong interventions, such as lockdowns and social distancing measures, imposed to prevent these diseases from spreading, may also negatively impact society, leading to jobs losses, mental health problems, and increased inequalities, making crucial the prioritization of riskier areas when applying these protocols. The modeling of mobility data derived from contact-tracing data can be used to forecast infectious trajectories and help design strategies for prevention and control. In this work, we propose a new spatial-stochastic model that allows us to characterize the temporally varying spatial risk better than existing methods. We demonstrate the use of the proposed model by simulating an epidemic in the city of Valencia, Spain, and comparing it with a contact tracing-based stochastic compartment reference model. The results show that, by accounting for the spatial risk values in the model, the peak of infected individuals, as well as the overall number of infected cases, are reduced. Therefore, adding a spatial risk component into compartment models may give finer control over the epidemic dynamics, which might help the people in charge to make better decisions.

Laplace approximation for conditional autoregressive models for spatial data of diseases

Conditional autoregressive (CAR) distributions are used to account for spatial autocorrelation in small areal or lattice data to assess the spatial risks of diseases. The intrinsic CAR (ICAR) distribution has been primarily used as the priori distribution of spatially autocorrelated random variables in the framework of Bayesian statistics. The posterior distributions of spatial variates and unknown parameters of Bayesian ICAR models are estimated with the Markov chain Monte Carlo (MCMC) methods or integrated nested Laplace approximation (INLA), which may suffer from failures in numeric convergence. This study used the Laplace approximation, a fast computational method available in software Template Model Builder (TMB), for the maximum likelihood estimation (MLEs) of the ICAR model parameters. This study used the TMB to integrate out the latent spatial variates for the fast computations of marginal likelihood functions. This study compared the runtime and performance among the TMB, MCMC, and INLA implementations with three case studies of human diseases in the United Kingdom and the United States. The MLEs of the ICAR model with TMB were similar to those by the MCMC and INLA methods. The TMB implementation was faster than the MCMC (up to 100–200 times) and INLA (nine times) models.

• This study built conditional autoregressive models in template model builder

• TMB implementation was 100-200 times faster than the MCMC method

• TMB implementation was also faster than Bayesian approximation with R INLA

Spatio-temporal variations in neonatal mortality rates in Ghana: An application of hierarchical Bayesian methods

Ghana might not meet the SDGs target 3.2 of reducing neonatal mortality to 12 deaths per 1000 live births by 2030. Identifying core determinants of neonatal deaths provide policy guidelines and a framework aimed at mitigating the effect of neonatal deaths. Most studies have identified household and individual-level factors that contribute to neonatal mortality. However, there are relatively few studies that have rigorously assessed geospatial covariates and spatiotemporal variations of neonatal deaths in Ghana. This study focuses on modeling and mapping of spatiotemporal variations in the risk of neonatal mortality in Ghana using Bayesian Hierarchical Spatiotemporal models. This study used data from the Ghana Demographic and Health Surveys (GDHS) conducted in 1993, 1998, 2003, 2008, and 2014. We employed Bayesian Hierarchical Spatiotemporal regression models to identify geospatial correlates and spatiotemporal variations in the risk of neonatal mortality. The estimated weighted crude neonatal mortality rate for the period under consideration was 33.2 neonatal deaths per 1000 live births. The results obtained from Moran's I statistics and CAR model showed the existence of spatial clustering of neonatal mortality. The map of smooth relative risk identified Ashanti region as the most consistent hot-spot region for the entire period under consideration. Small body size babies contributed significantly to an increased risk of neonatal mortality at the regional level [Posterior Mean: 0.003 (95% CrI: 0.00,0.01)]. Hot spot GDHS clusters exhibiting high risk of neonatal mortality were identified by LISA cluster map. Rural residents, small body size babies, parity, and aridity contributed significantly to a higher risk of neonatal mortality at the GDHS cluster level. The findings provide actionable and insightful information to prioritize and distribute the scarce health resources equitably to tackle the menace of neonatal mortality. The regions and GDHS clusters with excess risk of neonatal mortality should receive optimum attention and interventions to reduce the neonatal mortality rate.

Variation in smoking attributable all-cause mortality across municipalities in Belgium, 2018: application of a Bayesian approach for small area estimations

BACKGROUND

Smoking is one of the leading causes of preventable mortality and morbidity worldwide, with the European Region having the highest prevalence of tobacco smoking among adults compared to other WHO regions. The Belgian Health Interview Survey (BHIS) provides a reliable source of national and regional estimates of smoking prevalence; however, currently there are no estimates at a smaller geographical resolution such as the municipality scale in Belgium. This hinders the estimation of the spatial distribution of smoking attributable mortality at small geographical scale (i.e., number of deaths that can be attributed to tobacco). The objective of this study was to obtain estimates of smoking prevalence in each Belgian municipality using BHIS and calculate smoking attributable mortality at municipality level.

METHODS

Data of participants aged 15 + on smoking behavior, age, gender, educational level and municipality of residence were obtained from the BHIS 2018. A Bayesian hierarchical Besag-York-Mollie (BYM) model was used to model the logit transformation of the design-based Horvitz-Thompson direct prevalence estimates. Municipality-level variables obtained from Statbel, the Belgian statistical office, were used as auxiliary variables in the model. Model parameters were estimated using Integrated Nested Laplace Approximation (INLA). Deviance Information Criterion (DIC) and Conditional Predictive Ordinate (CPO) were computed to assess model fit. Population attributable fractions (PAF) were computed using the estimated prevalence of smoking in each of the 589 Belgian municipalities and relative risks obtained from published meta-analyses. Smoking attributable mortality was calculated by multiplying PAF with age-gender standardized and stratified number of deaths in each municipality.

RESULTS

BHIS 2018 data included 7,829 respondents from 154 municipalities. Smoothed estimates for current smoking ranged between 11% [Credible Interval 3;23] and 27% [21;34] per municipality, and for former smoking between 4% [0;14] and 34% [21;47]. Estimates of smoking attributable mortality constituted between 10% [7;15] and 47% [34;59] of total number of deaths per municipality.

CONCLUSIONS

Within-country variation in smoking and smoking attributable mortality was observed. Computed estimates should inform local public health prevention campaigns as well as contribute to explaining the regional differences in mortality.

Methods Used in the Spatial and Spatiotemporal Analysis of COVID-19 Epidemiology: A Systematic Review

The spread of the COVID-19 pandemic was spatially heterogeneous around the world; the transmission of the disease is driven by complex spatial and temporal variations in socioenvironmental factors. Spatial tools are useful in supporting COVID-19 control programs. A substantive review of the merits of the methodological approaches used to understand the spatial epidemiology of the disease is hardly undertaken. In this study, we reviewed the methodological approaches used to identify the spatial and spatiotemporal variations of COVID-19 and the socioeconomic, demographic and climatic drivers of such variations. We conducted a systematic literature search of spatial studies of COVID-19 published in English from Embase, Scopus, Medline, and Web of Science databases from 1 January 2019 to 7 September 2021. Methodological quality assessments were also performed using the Joanna Briggs Institute (JBI) risk of bias tool. A total of 154 studies met the inclusion criteria that used frequentist (85%) and Bayesian (15%) modelling approaches to identify spatial clusters and the associated risk factors. Bayesian models in the studies incorporated various spatial, temporal and spatiotemporal effects into the modelling schemes. This review highlighted the need for more local-level advanced Bayesian spatiotemporal modelling through the multi-level framework for COVID-19 prevention and control strategies.

A Spatially Correlated Model with Generalized Autoregressive Conditionally Heteroskedastic Structure for Counts of Crimes

Crime is a negative phenomenon that affects the daily life of the population and its development. When modeling crime data, assumptions on either the spatial or the temporal relationship between observations are necessary if any statistical analysis is to be performed. In this paper, we structure space–time dependency for count data by considering a stochastic difference equation for the intensity of the space–time process rather than placing structure on a latent space–time process, as Cox processes would do. We introduce a class of spatially correlated self-exciting spatio-temporal models for count data that capture both dependence due to self-excitation, as well as dependence in an underlying spatial process. We follow the principles in Clark and Dixon (2021) but considering a generalized additive structure on spatio-temporal varying covariates. A Bayesian framework is proposed for inference of model parameters. We analyze three distinct crime datasets in the city of Riobamba (Ecuador). Our model fits the data well and provides better predictions than other alternatives.

PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context, they are used to encode correlation structures over space and can generalize well in interpolation tasks. Despite their flexibility, off-the-shelf GPs present serious computational challenges which limit their scalability and practical usefulness in applied settings. Here, we propose a novel, deep generative modelling approach to tackle this challenge, termed PriorVAE: for a particular spatial setting, we approximate a class of GP priors through prior sampling and subsequent fitting of a variational autoencoder (VAE). Given a trained VAE, the resultant decoder allows spatial inference to become incredibly efficient due to the low dimensional, independently distributed latent Gaussian space representation of the VAE. Once trained, inference using the VAE decoder replaces the GP within a Bayesian sampling framework. This approach provides tractable and easy-to-implement means of approximately encoding spatial priors and facilitates efficient statistical inference. We demonstrate the utility of our VAE two-stage approach on Bayesian, small-area estimation tasks.

Estimation of COVID-19 mortality in the United States using Spatio-temporal Conway Maxwell Poisson model

Spatio-temporal Poisson models are commonly used for disease mapping. However, after incorporating the spatial and temporal variation, the data do not necessarily have equal mean and variance, suggesting either over- or under-dispersion. In this paper, we propose the Spatio-temporal Conway Maxwell Poisson model. The advantage of Conway Maxwell Poisson distribution is its ability to handle both under- and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider data from the pandemic caused by the SARS-CoV-2 virus in 2019 (COVID-19) that has threatened people all over the world. Understanding the spatio-temporal pattern of the disease is of great importance. We apply a spatio-temporal Conway Maxwell Poisson model to data on the COVID-19 deaths and find that this model achieves better performance than commonly used spatio-temporal Poisson model.

Capturing spatial dependence of COVID-19 case counts with cellphone mobility data

Spatial dependence is usually introduced into spatial models using some measure of physical proximity. When analysing COVID-19 case counts, this makes sense as regions that are close together are more likely to have more people moving between them, spreading the disease. However, using the actual number of trips between each region may explain COVID-19 case counts better than physical proximity. In this paper, we investigate the efficacy of using telecommunications-derived mobility data to induce spatial dependence in spatial models applied to two Spanish communities' COVID-19 case counts. We do this by extending Besag York Mollié (BYM) models to include both a physical adjacency effect, alongside a mobility effect. The mobility effect is given a Gaussian Markov random field prior, with the number of trips between regions as edge weights. We leverage modern parametrizations of BYM models to conclude that the number of people moving between regions better explains variation in COVID-19 case counts than physical proximity data. We suggest that this data should be used in conjunction with physical proximity data when developing spatial models for COVID-19 case counts.

Bayesian imputation of COVID-19 positive test counts for nowcasting under reporting lag

Obtaining up to date information on the number of UK COVID-19 regional infections is hampered by the reporting lag in positive test results for people with COVID-19 symptoms. In the UK, for 'Pillar 2' swab tests for those showing symptoms, it can take up to five days for results to be collated. We make use of the stability of the under reporting process over time to motivate a statistical temporal model that infers the final total count given the partial count information as it arrives. We adopt a Bayesian approach that provides for subjective priors on parameters and a hierarchical structure for an underlying latent intensity process for the infection counts. This results in a smoothed time-series representation nowcasting the expected number of daily counts of positive tests with uncertainty bands that can be used to aid decision making. Inference is performed using sequential Monte Carlo.

Impact of the Timing of Stay-at-Home Orders and Mobility Reductions on First-Wave COVID-19 Deaths in US Counties

As severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission continues to evolve, understanding the contribution of location-specific variations in nonpharmaceutical interventions and behaviors to disease transmission during the initial epidemic wave will be key for future control strategies. We offer a rigorous statistical analysis of the relative effectiveness of the timing of both official stay-at-home orders and population mobility reductions during the initial stage of the US coronavirus disease 2019 (COVID-19) epidemic. We used a Bayesian hierarchical regression to fit county-level mortality data from the first case on January 21, 2020, through April 20, 2020, and quantify associations between the timing of stay-at-home orders and population mobility with epidemic control. We found that among 882 counties with an early local epidemic, a 10-day delay in the enactment of stay-at-home orders would have been associated with 14,700 additional deaths by April 20 (95% credible interval: 9,100, 21,500), whereas shifting orders 10 days earlier would have been associated with nearly 15,700 fewer lives lost (95% credible interval: 11,350, 18,950). Analogous estimates are available for reductions in mobility-which typically occurred before stay-at-home orders-and are also stratified by county urbanicity, showing significant heterogeneity. Results underscore the importance of timely policy and behavioral action for early-stage epidemic control.

A Bayesian Hierarchical Spatial Model to Correct for Misreporting in Count Data: Application to State-Level COVID-19 Data in the United States

The COVID-19 pandemic that began at the end of 2019 has caused hundreds of millions of infections and millions of deaths worldwide. COVID-19 posed a threat to human health and profoundly impacted the global economy and people’s lifestyles. The United States is one of the countries severely affected by the disease. Evidence shows that the spread of COVID-19 was significantly underestimated in the early stages, which prevented governments from adopting effective interventions promptly to curb the spread of the disease. This paper adopts a Bayesian hierarchical model to study the under-reporting of COVID-19 at the state level in the United States as of the end of April 2020. The model examines the effects of different covariates on the under-reporting and accurate incidence rates and considers spatial dependency. In addition to under-reporting (false negatives), we also explore the impact of over-reporting (false positives). Adjusting for misclassification requires adding additional parameters that are not directly identified by the observed data. Informative priors are required. We discuss prior elicitation and include R functions that convert expert information into the appropriate prior distribution.

The spike-and-slab elastic net as a classification tool in Alzheimer's disease

Alzheimer's disease (AD) is the leading cause of dementia and has received considerable research attention, including using neuroimaging biomarkers to classify patients and/or predict disease progression. Generalized linear models, e.g., logistic regression, can be used as classifiers, but since the spatial measurements are correlated and often outnumber subjects, penalized and/or Bayesian models will be identifiable, while classical models often will not. Many useful models, e.g., the elastic net and spike-and-slab lasso, perform automatic variable selection, which removes extraneous predictors and reduces model variance, but neither model exploits spatial information in selecting variables. Spatial information can be incorporated into variable selection by placing intrinsic autoregressive priors on the logit probabilities of inclusion within a spike-and-slab elastic net framework. We demonstrate the ability of this framework to improve classification performance by using cortical thickness and tau-PET images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to classify subjects as cognitively normal or having dementia, and by using a simulation study to examine model performance using finer resolution images.

The unbalanced risk of pulmonary tuberculosis in China at subnational scale: A spatio-temporal analysis (Preprint)

Background

China has one of the highest tuberculosis (TB) burdens in the world. However, the unbalanced spatial and temporal trends of TB risk at a fine level remain unclear.

Objective

We aimed to investigate the unbalanced risks of pulmonary tuberculosis (PTB) at different levels and how they evolved from both temporal and spatial aspects using PTB notification data from 2851 counties over a decade in China.

Methods

County-level notified PTB case data were collected from 2009 to 2018 in mainland China. A Bayesian hierarchical model was constructed to analyze the unbalanced spatiotemporal patterns of PTB notification rates during this period at subnational scales. The Gini coefficient was calculated to assess the inequality of the relative risk (RR) of PTB across counties.

Results

From 2009 to 2018, the number of notified PTB cases in mainland China decreased from 946,086 to 747,700. The average number of PTB cases in counties was 301 (SD 26) and the overall average notification rate was 60 (SD 6) per 100,000 people. There were obvious regional differences in the RRs for PTB (Gini coefficient 0.32, 95% CI 0.31-0.33). Xinjiang had the highest PTB notification rate, with a multiyear average of 155/100,000 (RR 2.3, 95% CI 1.6-2.8; P<.001), followed by Guizhou (117/100,000; RR 1.8, 95% CI 1.3-1.9; P<.001) and Tibet (108/100,000; RR 1.7, 95% CI 1.3-2.1; P<.001). The RR for PTB showed a steady downward trend. Gansu (local trend [LT] 0.95, 95% CI 0.93-0.96; P<.001) and Shanxi (LT 0.94, 95% CI 0.92-0.96; P<.001) experienced the fastest declines. However, the RRs for PTB in the western region (such as counties in Xinjiang, Guizhou, and Tibet) were significantly higher than those in the eastern and central regions (P<.001), and the decline rate of the RR for PTB was lower than the overall level (P<.001).

Conclusions

PTB risk showed significant regional inequality among counties in China, and western China presented a high plateau of disease burden. Improvements in economic and medical service levels are required to boost PTB case detection and eventually reduce PTB risk in the whole country.

Relative risk of gastrointestinal cancers in Isfahan County, Iran, 2005–2010

Background:

Spatial disease mapping is a widespread tool in ecological analysis to obtain accurate estimates for incidence, relative risks (RRs), prevalence, or mortality rates regarding to increase the incidence of gastrointestinal (GI) cancer in Isfahan in recent years. This study aimed to inspect the RR of GI cancer in Isfahan counties using empirical and full Bayesian model.

Materials and Methods:

Data of this ecological study were GI cancer cases which registered in health-care system of Isfahan University of Sciences during 2005–2010. We applied shared component model to model the spatial variation incidence rates of the GI cancers. We compared three models such as Gamma–Poisson, lognormal, and Besag, York, and Mollie (BYM) Bayesian. WinBUGS and GIS 10.1 software were used.

Results:

According to the fitted model, BYM model had best fit to the data. However, in general, ranks of RRs in most counties are identical; counties with higher RR in one map have higher RR in other maps. Geographical maps for three cancers in women were smoother than men. Isfahan has high RR in women, whereas this point is slightly different in men. Daran, FreidoonShahr, and Isfahan are cities which have high RR in esophagus, stomach, and colon cancer, respectively.

Conclusions:

Lognormal and BYM maps had very similar results. Despite some differences in estimation values, in nearly all maps arias Isfahan had high RR in GI cancer. It is recommended to promote the use of screening programs and increase awareness of people in high RR areas to reduce the incidence of GI cancer.

A spatial-mechanistic model to estimate subnational tuberculosis burden with routinely collected data: An application in Brazilian municipalities

Reliable subnational estimates of TB incidence would allow national policy makers to focus disease control resources in areas of highest need. We developed an approach for generating small area estimates of TB incidence, and the fraction of individuals missed by routine case detection, based on available notification and mortality data. We demonstrate the feasibility of this approach by creating municipality-level burden estimates for Brazil. We developed a mathematical model describing the relationship between TB incidence and TB case notifications and deaths, allowing for known biases in each of these data sources. We embedded this model in a regression framework with spatial dependencies between local areas, and fitted the model to municipality-level case notifications and death records for Brazil during 2016-2018. We estimated outcomes for 5568 municipalities. Incidence rate ranged from 8.6 to 57.2 per 100,000 persons/year for 90% of municipalities, compared to 44.8 (95% UI: 43.3, 46.8) per 100,000 persons/year nationally. Incidence was concentrated geographically, with 1% of municipalities accounting for 50% of incident TB. The estimated fraction of incident TB cases receiving diagnosis and treatment ranged from 0.73 to 0.95 across municipalities (compared to 0.86 (0.82, 0.89) nationally), and the rate of untreated TB ranged from 0.8 to 72 cases per 100,000 persons/year (compared to 6.3 (4.8, 8.3) per 100,000 persons/year nationally). Granular disease burden estimates can be generated using routine data. These results reveal substantial subnational differences in disease burden and other metrics useful for designing high-impact TB control strategies.

Geographic Disparities in Readmissions for Peripheral Artery Disease in South Carolina

Readmissions constitute a major health care burden among peripheral artery disease (PAD) patients. This study aimed to 1) estimate the zip code tabulation area (ZCTA)-level prevalence of readmission among PAD patients and characterize the effect of covariates on readmissions; and (2) identify hotspots of PAD based on estimated prevalence of readmission. Thirty-day readmissions among PAD patients were identified from the South Carolina Revenue and Fiscal Affairs Office All Payers Database (2010-2018). Bayesian spatial hierarchical modeling was conducted to identify areas of high risk, while controlling for confounders. We mapped the estimated readmission rates and identified hotspots using local Getis Ord (G*) statistics. Of the 232,731 individuals admitted to a hospital or outpatient surgery facility with PAD diagnosis, 30,366 (13.1%) experienced an unplanned readmission to a hospital within 30 days. Fitted readmission rates ranged from 35.3 per 1000 patients to 370.7 per 1000 patients and the risk of having a readmission was significantly associated with the percentage of patients who are 65 and older (0.992, 95%CI: 0.985-0.999), have Medicare insurance (1.013, 1.005-1.020), and have hypertension (1.014, 1.005-1.023). Geographic analysis found significant variation in readmission rates across the state and identified priority areas for targeted interventions to reduce readmissions.

Spatio-temporal models of bovine tuberculosis in the Irish cattle population, 2012-2019

INTRODUCTION

Bovine tuberculosis (bTB) is an important zoonotic disease which has serious and sometimes fatal effects on both human and non-human animals. In many countries it is endemic in the cattle population and has a considerable economic impact through losses in productivity and impacts on trade. The incidence rate in Ireland varies by herd and location and it is hoped that statistical disease-mapping models accounting for both spatio-temporal correlation and covariates might contribute towards explaining this variation.

METHODS

Ireland was divided into equally sized hexagons for computational efficiency (n = 997). Different spatio-temporal random-effects models (e.g. negative binomial Besag-York-Mollié) were explored, using comprehensive data from the national bTB eradication programme to examine the association between covariates and the number of bTB cattle. Leveraging a Bayesian framework, model parameter estimates were obtained using the integrated nested Laplace approximation (INLA) approach. Exceedance probabilities were calculated to identify spatial clusters of cases.

RESULTS

Models accounting for spatial correlation significantly improved model fit in comparison to non-spatial versions where independence between regions was assumed. In our final model at hexagon level, the number of cattle (IR = 1.142, CrI: 1.108 - 1.177 per 1000), the capture of badgers (IR = 5.951, CrI: 4.482 - 7.912), percentage of forest cover (IR = 1.031, CrI: 1.020 - 1.042) and number of farm fragments (IR = 1.012, CrI: 1.009 - 1.015 per 10 fragments) were all associated with an increased incidence of bTB. Habitat suitability for badgers, percentage of dairy herds and the number of cattle movements into the herd were not. As an epidemiological tool and to suggest future work, an interactive online dashboard was developed to monitor disease progression and disseminate results to the general public.

CONCLUSION

Accounting for spatial correlation is an important consideration in disease mapping applications and is often ignored in statistical models examining bTB risk factors. Over time, the same regions in Ireland generally show highest incidences of bTB and allocation of more resources to these areas may be needed to combat the disease. This study highlights national bTB incidence rates. Shifting from national level analysis to smaller geographical regions may help identify localised high-risk areas.

Long-term air pollution and other risk factors associated with COVID-19 at the census tract level in Colorado

Previous nationwide studies have reported links between long-term concentrations of fine particulate matter (PM2.5) and COVID-19 infection and mortality rates. In order to translate these results to the state level, we use Bayesian hierarchical models to explore potential links between long-term PM2.5 concentrations and census tract-level rates of COVID-19 outcomes (infections, hospitalizations, and deaths) in Colorado. We explicitly consider how the uncertainty in PM2.5 estimates affects our results by comparing four different PM2.5 surfaces from academic and governmental organizations. After controlling for 20 census tract-level covariates, we find that our results depend heavily on the choice of PM2.5 surface. Using PM2.5 estimates from the United States EPA, we find that a 1 μg/m³ increase in long-term PM2.5 concentrations is associated with a statistically significant 26% increase in the relative risk of hospitalizations and a 34% increase in mortality. Results for all other surfaces and outcomes were not statistically significant. At the same time, we find a clear association between communities of color and COVID-19 outcomes at the Colorado census tract level that is minimally affected by the choice of PM2.5 surface. A per-interquartile range (IQR) increase in the percent of non-African American people of color was associated with a 31%, 43%, and 56% increase in the relative risk of infection, hospitalization, and mortality respectively, while a per-IQR increase in the proportion of non-Hispanic African Americans was associated with a 4% and 7% increase in the relative risk of infections and hospitalizations. The current disagreement among the different PM2.5 estimates is a key factor limiting our ability to link environmental exposures and health outcomes at the census tract level. These results have strong implications for the implementation of an equitable public health response during the crisis and suggest targeted areas for additional air monitoring in Colorado.

Improving multilevel regression and poststratification with structured priors

A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multilevel regression and poststratification (MRP), a model-based approach, is gaining traction against the traditional weighted approach for survey estimates. MRP estimates are susceptible to bias if there is an underlying structure that the methodology does not capture. This work aims to provide a new framework for specifying structured prior distributions that lead to bias reduction in MRP estimates. We use simulation studies to explore the benefit of these prior distributions and demonstrate their efficacy on non-representative US survey data. We show that structured prior distributions offer absolute bias reduction and variance reduction for posterior MRP estimates in a large variety of data regimes.

Migratory strategy drives species-level variation in bird sensitivity to vegetation green-up

Animals and plants are shifting the timing of key life events in response to climate change, yet despite recent documentation of escalating phenological change, scientists lack a full understanding of how and why phenological responses vary across space and among species. Here, we used over 7 million community-contributed bird observations to derive species-specific, spatially explicit estimates of annual spring migration phenology for 56 bird species across eastern North America. We show that changes in the spring arrival of migratory birds are coarsely synchronized with fluctuations in vegetation green-up and that the sensitivity of birds to plant phenology varied extensively. Bird arrival responded more synchronously with vegetation green-up at higher latitudes, where phenological shifts over time are also greater. Critically, species' migratory traits explained variation in sensitivity to green-up, with species that migrate more slowly, arrive earlier and overwinter further north showing greater responsiveness to earlier springs. Identifying how and why species vary in their ability to shift phenological events is fundamental to predicting species' vulnerability to climate change. Such variation in sensitivity across taxa, with long-distance neotropical migrants exhibiting reduced synchrony, may help to explain substantial declines in these species over the last several decades.

Modeling Community Health with Areal Data: Bayesian Inference with Survey Standard Errors and Spatial Structure

Epidemiologists and health geographers routinely use small-area survey estimates as covariates to model areal and even individual health outcomes. American Community Survey (ACS) estimates are accompanied by standard errors (SEs), but it is not yet standard practice to use them for evaluating or modeling data reliability. ACS SEs vary systematically across regions, neighborhoods, socioeconomic characteristics, and variables. Failure to consider probable observational error may have substantial impact on the large bodies of literature relying on small-area estimates, including inferential biases and over-confidence in results. The issue is particularly salient for predictive models employed to prioritize communities for service provision or funding allocation. Leveraging the tenets of plausible reasoning and Bayes' theorem, we propose a conceptual framework and workflow for spatial data analysis with areal survey data, including visual diagnostics and model specifications. To illustrate, we follow Krieger et al.'s (2018) call to routinely use the Index of Concentration at the Extremes (ICE) to monitor spatial inequalities in health and mortality. We construct and examine SEs for the ICE, use visual diagnostics to evaluate our observational error model for the ICE, and then estimate an ICE-mortality gradient by incorporating the latter model into our model of sex-specific, midlife (ages 55-64), all-cause United States county mortality rates. We urge researchers to consider data quality as a criterion for variable selection prior to modeling, and to incorporate data reliability information into their models whenever possible.

Examining the Geospatial Distribution of Health and Support Services for Transgender, Gender Nonbinary, and Other Gender Diverse People in New York City

A geospatial analysis of services that support transgender and gender diverse ("trans") people in New York City (NYC) was conducted to investigate associations with neighborhood-level sociodemographic characteristics. In June 2019, there were 5.3 services for every 100,000 of the general NYC population; controlling for other covariates, they were more commonly located in neighborhoods with larger populations of non-Hispanic Black (rate ratio [RR]=1.02, 95% confidence interval [CI]: 1.00-1.04), Hispanic/Latino (RR=1.03, 95% CI: 1.00-1.06), and gay/lesbian people (RR=1.53, 95% CI: 1.03-2.34). These findings suggest that the distribution of trans-focused services in NYC is proximal to communities that are most in need, but research should examine proximity to trans people specifically and distribution in nonurban areas.

Spatio-temporal modelling of the first Chikungunya epidemic in an intra-urban setting: The role of socioeconomic status, environment and temperature

Three key elements are the drivers of Aedes-borne disease: mosquito infestation, virus circulating, and susceptible human population. However, information on these aspects is not easily available in low- and middle-income countries. We analysed data on factors that influence one or more of those elements to study the first chikungunya epidemic in Rio de Janeiro city in 2016. Using spatio-temporal models, under the Bayesian framework, we estimated the association of those factors with chikungunya reported cases by neighbourhood and week. To estimate the minimum temperature effect in a non-linear fashion, we used a transfer function considering an instantaneous effect and propagation of a proportion of such effect to future times. The sociodevelopment index and the proportion of green areas (areas with agriculture, swamps and shoals, tree and shrub cover, and woody-grass cover) were included in the model with time-varying coefficients, allowing us to explore how their associations with the number of cases change throughout the epidemic. There were 13627 chikungunya cases in the study period. The sociodevelopment index presented the strongest association, inversely related to the risk of cases. Such association was more pronounced in the first weeks, indicating that socioeconomically vulnerable neighbourhoods were affected first and hardest by the epidemic. The proportion of green areas effect was null for most weeks. The temperature was directly associated with the risk of chikungunya for most neighbourhoods, with different decaying patterns. The temperature effect persisted longer where the epidemic was concentrated. In such locations, interventions should be designed to be continuous and to work in the long term. We observed that the role of the covariates changes over time. Therefore, time-varying coefficients should be widely incorporated when modelling Aedes-borne diseases. Our model contributed to the understanding of the spatio-temporal dynamics of an urban Aedes-borne disease introduction in a tropical metropolitan city.

Coronavirus testing disparities associated with community level deprivation, racial inequalities, and food insecurity in West Virginia

PURPOSE

Social determinants of health and racial inequalities impact healthcare access and subsequent coronavirus testing. Limited studies have described the impact of these inequities on rural minorities living in Appalachia. This study investigates factors affecting testing in rural communities.

METHODS

PCR testing data were obtained for March through September 2020. Spatial regression analyses were fit at the census tract level. Model outcomes included testing and positivity rate. Covariates included rurality, percent Black population, food insecurity, and area deprivation index (a comprehensive indicator of socioeconomic status).

RESULTS

Small clusters in coronavirus testing were detected sporadically, while test positivity clustered in mideastern and southwestern WV. In regression analyses, percent food insecurity (IRR = 3.69×10⁹, [796, 1.92×10¹⁶]), rurality (IRR=1.28, [1.12, 1.48]), and percent population Black (IRR = 0.88, [0.84, 0.94]) had substantial effects on coronavirus testing. However, only percent food insecurity (IRR = 5.98 × 10⁴, [3.59, 1.07×10⁹]) and percent Black population (IRR = 0.94, [0.90, 0.97]) displayed substantial effects on the test positivity rate.

CONCLUSIONS

Findings highlight disparities in coronavirus testing among communities with rural minorities. Limited testing in these communities may misrepresent coronavirus incidence.

Fernandez–Steel Skew Normal Conditional Autoregressive (FSSN CAR) Model in Stan for Spatial Data

In spatial data analysis, the prior conditional autoregressive (CAR) model is used to express the spatial dependence on random effects from adjacent regions. This paper provides a new proposed approach regarding the development of the existing normal CAR model into a more flexible, Fernandez–Steel skew normal (FSSN) CAR model. This approach is able to capture spatial random effects that have both symmetrical and asymmetrical patterns. The FSSN CAR model is built on the basis of the normal CAR with an additional skew parameter. The FSSN distribution is able to provide good estimates for symmetry with heavy- or light-tailed and skewed-right and skewed-left data. The effects of this approach are demonstrated by establishing the FSSN distribution and FSSN CAR model in spatial data using Stan language. On the basis of the plot of the estimation results and histogram of the model error, the FSSN CAR model was shown to behave better than both models without a spatial effect and with the normal CAR model. Moreover, the smallest widely applicable information criterion (WAIC) and leave-one-out (LOO) statistical values also validate the model, as FSSN CAR is shown to be the best model used.

Evaluating equality in prescribing Novel Oral Anticoagulants (NOACs) in England: The protocol of a Bayesian small area analysis

Background

Atrial fibrillation (AF) is the most common cardiac arrhythmia, affecting about 1.6% of the population in England. Novel oral anticoagulants (NOACs) are approved AF treatments that reduce stroke risk. In this study, we estimate the equality in individual NOAC prescriptions with high spatial resolution in Clinical Commissioning Groups (CCGs) across England from 2014 to 2019.

Methods

A Bayesian spatio-temporal model will be used to estimate and predict the individual NOAC prescription trend on ‘prescription data’ as an indicator of health services utilisation, using a small area analysis methodology. The main dataset in this study is the “Practice Level Prescribing in England,” which contains four individual NOACs prescribed by all registered GP practices in England. We will use the defined daily dose (DDD) equivalent methodology, as recommended by the World Health Organization (WHO), to compare across space and time. Four licensed NOACs datasets will be summed per 1,000 patients at the CCG-level over time. We will also adjust for CCG-level covariates, such as demographic data, Multiple Deprivation Index, and rural-urban classification. We aim to employ the extended BYM2 model (space-time model) using the RStan package.

Discussion

This study suggests a new statistical modelling approach to link prescription and socioeconomic data to model pharmacoepidemiologic data. Quantifying space and time differences will allow for the evaluation of inequalities in the prescription of NOACs. The methodology will help develop geographically targeted public health interventions, campaigns, audits, or guidelines to improve areas of low prescription. This approach can be used for other medications, especially those used for chronic diseases that must be monitored over time.

Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates

In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods.

Spatial-Temporal Modelling of Disease Risk Accounting for PM2.5 Exposure in the Province of Pavia: An Area of the Po Valley

Spatio-temporal Bayesian disease mapping is the branch of spatial epidemiology interested in providing valuable risk estimates in certain geographical regions using administrative areas as statistical units. The aim of the present paper is to describe spatio-temporal distribution of cardiovascular mortality in the Province of Pavia in 2010 through 2015 and assess its association with environmental pollution exposure. To produce reliable risk estimates, eight different models (hierarchical log-linear model) have been assessed: temporal parametric trend components were included together with some random effects that allowed the accounting of spatial structure of the region. The Bayesian approach allowed the borrowing information effect, including simpler model results in the more complex setting. To compare these models, Watanabe–Akaike Information Criteria (WAIC) and Leave One Out Information Criteria (LOOIC) were applied. In the modelling phase, the relationship between the disease risk and pollutants exposure (PM2.5) accounting for the urbanisation level of each geographical unit showed a strong significant effect of the pollutant exposure (OR = 1.075 and posterior probability, or PP, >0.999, equivalent to p < 0.001). A high-risk cluster of Cardiovascular mortality in the Lomellina subareas in the studied window was identified.

A tutorial on spatio-temporal disease risk modelling in R using Markov chain Monte Carlo simulation and the CARBayesST package

Population-level disease risk varies in space and time, and is typically estimated using aggregated disease count data relating to a set of non-overlapping areal units for multiple consecutive time periods. A large research base of statistical models and corresponding software has been developed for such data, with most analyses being undertaken in a Bayesian setting using either Markov chain Monte Carlo (MCMC) simulation or integrated nested Laplace approximations (INLA). This paper presents a tutorial for undertaking spatio-temporal disease modelling using MCMC simulation, utilising the CARBayesST package in the R software environment. The tutorial describes the complete modelling journey, starting with data input, wrangling and visualisation, before focusing on model fitting, model assessment and results presentation. It is illustrated by a new case study of pneumonia mortality at the local authority level in England, and answers important public health questions including the effect of covariate risk factors, spatio-temporal trends, and health inequalities.

State-space modeling of the dynamics of temporal plant cover using visually determined class data

A lot of vegetation-related data have been collected as an ordered plant cover class that can be determined visually. However, they are difficult to analyze numerically as they are in an ordinal scale and have uncertainty in their classification. Here, I constructed a state-space model to estimate unobserved plant cover proportions (ranging from zero to one) from such cover class data. The model assumed that the data were measured longitudinally, so that the autocorrelations in the time-series could be utilized to estimate the unobserved cover proportion. The model also assumed that the quadrats where the data were collected were arranged sequentially, so that the spatial autocorrelations also could be utilized to estimate the proportion. Assuming a beta distribution as the probability distribution of the cover proportion, the model was implemented with a regularized incomplete beta function, which is the cumulative density function of the beta distribution. A simulated dataset and real datasets, with one-dimensional spatial structure and longitudinal survey, were fit to the model, and the parameters were estimated using the Markov chain Monte Carlo method. Then, the validity was examined using posterior predictive checks. As a result of the fitting, the Markov chain successfully converged to the stationary distribution, and the posterior predictive checks did not show large discrepancies. For the simulated dataset, the estimated values were close to the values used for the data generation. The estimated values for the real datasets also seemed to be reasonable. These results suggest that the proposed state-space model was able to successfully estimate the unobserved cover proportion. The present model is applicable to similar types of plant cover class data, and has the possibility to be expanded, for example, to incorporate a two-dimensional spatial structure and/or zero-inflation.