Detecting interaction between random region and fixed age effects in disease mapping

Non-stationary Bayesian spatial model for disease mapping based on sub-regions

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes.

Joint quantile disease mapping with application to malaria and G6PD deficiency

Statistical analysis based on quantile methods is more comprehensive, flexible and less sensitive to outliers when compared to mean methods. Joint disease mapping is useful for inferring correlation between different diseases. Most studies investigate this link through multiple correlated mean regressions. We propose a joint quantile regression framework for multiple diseases where different quantile levels can be considered. We are motivated by the theorized link between the presence of malaria and the gene deficiency G6PD, where medical scientists have anecdotally discovered a possible link between high levels of G6PD and lower than expected levels of malaria initially pointing towards the occurrence of G6PD inhibiting the occurrence of malaria. Thus, the need for flexible joint quantile regression in a disease mapping framework arises. Our model can be used for linear and nonlinear effects of covariates by stochastic splines since we define it as a latent Gaussian model. We perform Bayesian inference using the R integrated nested Laplace approximation, suitable even for large datasets. Finally, we illustrate the model's applicability by considering data from 21 countries, although better data are needed to prove a significant relationship. The proposed methodology offers a framework for future studies of interrelated disease phenomena.

Small area variations in non-affective first-episode psychosis: the role of socioeconomic and environmental factors

BACKGROUND

There is strong evidence supporting the association between environmental factors and increased risk of non-affective psychotic disorders. However, the use of sound statistical methods to account for spatial variations associated with environmental risk factors, such as urbanicity, migration, or deprivation, is scarce in the literature.

METHODS

We studied the geographical distribution of non-affective first-episode psychosis (NA-FEP) in a northern region of Spain (Navarra) during a 54-month period considering area-level socioeconomic indicators as putative explanatory variables. We used several Bayesian hierarchical Poisson models to smooth the standardized incidence ratios (SIR). We included neighborhood-level variables in the spatial models as covariates.

RESULTS

We identified 430 NA-FEP cases over a 54-month period for a population at risk of 365,213 inhabitants per year. NA-FEP incidence risks showed spatial patterning and a significant ecological association with the migrant population, unemployment, and consumption of anxiolytics and antidepressants. The high-risk areas corresponded mostly to peripheral urban regions; very few basic health sectors of rural areas emerged as high-risk areas in the spatial models with covariates.

DISCUSSION

Increased rates of unemployment, the migrant population, and consumption of anxiolytics and antidepressants showed significant associations linked to the spatial-geographic incidence of NA-FEP. These results may allow targeting geographical areas to provide preventive interventions that potentially address modifiable environmental risk factors for NA-FEP. Further investigation is needed to understand the mechanisms underlying the associations between environmental risk factors and the incidence of NA-FEP.

Geographic patterns and hotspots of pediatric tuberculosis: the role of socioeconomic determinants

OBJECTIVE

Children are an important demographic group for understanding overall tuberculosis epidemiology, and monitoring of childhood tuberculosis is essential for appropriate prevention. The present study sought to characterize the spatial distribution of childhood tuberculosis notification rates in continental Portugal; identify high-risk areas; and evaluate the association between childhood tuberculosis notification rates and socioeconomic deprivation.

METHODS

Using hierarchical Bayesian spatial models, we analyzed the geographic distribution of pediatric tuberculosis notification rates across 278 municipalities between 2016 and 2020 and determined high-risk and low-risk areas. We used the Portuguese version of the European Deprivation Index to estimate the association between childhood tuberculosis and area-level socioeconomic deprivation.

RESULTS

Notification rates ranged from 1.8 to 13.15 per 100,000 children under 5 years of age. We identified seven high-risk areas, the relative risk of which was significantly above the study area average. All seven high-risk areas were located in the metropolitan area of Porto or Lisbon. There was a significant relationship between socioeconomic deprivation and pediatric tuberculosis notification rates (relative risk = 1.16; Bayesian credible interval, 1.05-1.29).

CONCLUSIONS

Identified high-risk and socioeconomically deprived areas should constitute target areas for tuberculosis control, and these data should be integrated with other risk factors to define more precise criteria for BCG vaccination.

Big problems in spatio-temporal disease mapping: Methods and software

BACKGROUND AND OBJECTIVE

Fitting spatio-temporal models for areal data is crucial in many fields such as cancer epidemiology. However, when data sets are very large, many issues arise. The main objective of this paper is to propose a general procedure to analyze high-dimensional spatio-temporal areal data, with special emphasis on mortality/incidence relative risk estimation.

METHODS

We present a pragmatic and simple idea that permits hierarchical spatio-temporal models to be fitted when the number of small areas is very large. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatial domain. We also use parallel and distributed strategies to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming or even unfeasible.

RESULTS

Using simulated and real data, we show that our method outperforms classical global models. We implement the methods and algorithms that we develop in the open-source R package bigDM where specific vignettes have been included to facilitate the use of the methodology for non-expert users.

CONCLUSIONS

Our scalable methodology proposal provides reliable risk estimates when fitting Bayesian hierarchical spatio-temporal models for high-dimensional data.

Intra-urban variation in tuberculosis and community socioeconomic deprivation in Lisbon metropolitan area: a Bayesian approach

Background

Multidrug resistant tuberculosis (MDR-TB) is a recognized threat to global efforts to TB control and remains a priority of the National Tuberculosis Programs. Additionally, social determinants and socioeconomic deprivation have since long been associated with worse health and perceived as important risk factors for TB. This study aimed to analyze the spatial distribution of non-MDR-TB and MDR-TB across parishes of the Lisbon metropolitan area of Portugal and to estimate the association between non-MDR-TB and MDR-TB and socioeconomic deprivation.

Methods

In this study, we used hierarchical Bayesian spatial models to analyze the spatial distribution of notification of non-MDR-TB and MDR-TB cases for the period from 2000 to 2016 across 127 parishes of the seven municipalities of the Lisbon metropolitan area (Almada, Amadora, Lisboa, Loures, Odivelas, Oeiras, Sintra), using the Portuguese TB Surveillance System (SVIG-TB). In order to characterise the populations, we used the European Deprivation Index for Portugal (EDI-PT) as an indicator of poverty and estimated the association between non-MDR-TB and MDR-TB and socioeconomic deprivation.

Results

The notification rates per 10,000 population of non-MDR TB ranged from 18.95 to 217.49 notifications and that of MDR TB ranged from 0.83 to 3.70. We identified 54 high-risk areas for non-MDR-TB and 13 high-risk areas for MDR-TB. Parishes in the third [relative risk (RR) = 1.281, 95% credible interval (CrI): 1.021–1.606], fourth (RR = 1.786, 95% CrI: 1.420–2.241) and fifth (RR = 1.935, 95% CrI: 1.536–2.438) quintile of socioeconomic deprivation presented higher non-MDR-TB notifications rates. Parishes in the fourth (RR = 2.246, 95% CrI: 1.374–3.684) and fifth (RR = 1.828, 95% CrI: 1.049–3.155) quintile of socioeconomic deprivation also presented higher MDR-TB notifications rates.

Conclusions

We demonstrated significant heterogeneity in the spatial distribution of both non-MDR-TB and MDR-TB at the parish level and we found that socioeconomically disadvantaged parishes are disproportionally affected by both non-MDR-TB and MDR-TB. Our findings suggest that the emergence of MDR-TB and transmission are specific from each location and often different from the non-MDR-TB settings. We identified priority areas for intervention for a more efficient plan of control and prevention of non-MDR-TB and MDR-TB.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-022-00949-1.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Identifying extreme COVID-19 mortality risks in English small areas: a disease cluster approach

The COVID-19 pandemic is having a huge impact worldwide and has highlighted the extent of health inequalities between countries but also in small areas within a country. Identifying areas with high mortality is important both of public health mitigation in COVID-19 outbreaks, and of longer term efforts to tackle social inequalities in health. In this paper we consider different statistical models and an extension of a recent method to analyze COVID-19 related mortality in English small areas during the first wave of the epidemic in the first half of 2020. We seek to identify hotspots, and where they are most geographically concentrated, taking account of observed area factors as well as spatial correlation and clustering in regression residuals, while also allowing for spatial discontinuities. Results show an excess of COVID-19 mortality cases in small areas surrounding London and in other small areas in North-East and and North-West of England. Models alleviating spatial confounding show ethnic isolation, air quality and area morbidity covariates having a significant and broadly similar impact on COVID-19 mortality, whereas nursing home location seems to be slightly less important.

Spatial Statistical Models: An Overview under the Bayesian Approach

Spatial documentation is exponentially increasing given the availability of Big Data in the Internet of Things, enabled by device miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence structure and hidden patterns in space through prior knowledge and data likelihood. However, this class of modeling is not yet well explored when compared to adopting classification and regression in machine-learning models, in which the assumption of the spatiotemporal independence of the data is often made, that is an inexistent or very weak dependence. Thus, this systematic review aims to address the main models presented in the literature over the past 20 years, identifying the gaps and research opportunities. Elements such as random fields, spatial domains, prior specification, the covariance function, and numerical approximations are discussed. This work explores the two subclasses of spatial smoothing: global and local.

Estimating LOCP cancer mortality rates in small domains in Spain using its relationship with lung cancer

The distribution of lip, oral cavity, and pharynx (LOCP) cancer mortality rates in small domains (defined as the combination of province, age group, and gender) remains unknown in Spain. As many of the LOCP risk factors are preventable, specific prevention programmes could be implemented but this requires a clear specification of the target population. This paper provides an in-depth description of LOCP mortality rates by province, age group and gender, giving a complete overview of the disease. This study also presents a methodological challenge. As the number of LOCP cancer cases in small domains (province, age groups and gender) is scarce, univariate spatial models do not provide reliable results or are even impossible to fit. In view of the close link between LOCP and lung cancer, we consider analyzing them jointly by using shared component models. These models allow information-borrowing among diseases, ultimately providing the analysis of cancer sites with few cases at a very disaggregated level. Results show that males have higher mortality rates than females and these rates increase with age. Regions located in the north of Spain show the highest LOCP cancer mortality rates.

Spatio-Temporal Spread Pattern of COVID-19 in Italy

This paper investigates the spatio-temporal spread pattern of COVID-19 in Italy, during the first wave of infections, from February to October 2020. Disease mappings of the virus infections by using the Besag–York–Mollié model and some spatio-temporal extensions are provided. This modeling framework, which includes a temporal component, allows the studying of the time evolution of the spread pattern among the 107 Italian provinces. The focus is on the effect of citizens’ mobility patterns, represented here by the three distinct phases of the Italian virus first wave, identified by the Italian government, also characterized by the lockdown period. Results show the effectiveness of the lockdown action and an inhomogeneous spatial trend that characterizes the virus spread during the first wave. Furthermore, the results suggest that the temporal evolution of each province’s cases is independent of the temporal evolution of the other ones, meaning that the contagions and temporal trend may be caused by some province-specific aspects rather than by the subjects’ spatial movements.

Integrating Spatiotemporal Epidemiology, Eco-Phylogenetics, and Distributional Ecology to Assess West Nile Disease Risk in Horses

Mosquito-borne West Nile virus (WNV) is the causative agent of West Nile disease in humans, horses, and some bird species. Since the initial introduction of WNV to the United States (US), approximately 30,000 horses have been impacted by West Nile neurologic disease and hundreds of additional horses are infected each year. Research describing the drivers of West Nile disease in horses is greatly needed to better anticipate the spatial and temporal extent of disease risk, improve disease surveillance, and alleviate future economic impacts to the equine industry and private horse owners. To help meet this need, we integrated techniques from spatiotemporal epidemiology, eco-phylogenetics, and distributional ecology to assess West Nile disease risk in horses throughout the contiguous US. Our integrated approach considered horse abundance and virus exposure, vector and host distributions, and a variety of extrinsic climatic, socio-economic, and environmental risk factors. Birds are WNV reservoir hosts, and therefore we quantified avian host community dynamics across the continental US to show intra-annual variability in host phylogenetic structure and demonstrate host phylodiversity as a mechanism for virus amplification in time and virus dilution in space. We identified drought as a potential amplifier of virus transmission and demonstrated the importance of accounting for spatial non-stationarity when quantifying interaction between disease risk and meteorological influences such as temperature and precipitation. Our results delineated the timing and location of several areas at high risk of West Nile disease and can be used to prioritize vaccination programs and optimize virus surveillance and monitoring.

Dealing with risk discontinuities to estimate cancer mortality risks when the number of small areas is large

Many statistical models have been developed during the last years to smooth risks in disease mapping. However, most of these modeling approaches do not take possible local discontinuities into consideration or if they do, they are computationally prohibitive or simply do not work when the number of small areas is large. In this paper, we propose a two-step method to deal with discontinuities and to smooth noisy risks in small areas. In a first stage, a novel density-based clustering algorithm is used. In contrast to previous proposals, this algorithm is able to automatically detect the number of spatial clusters, thus providing a single cluster structure. In the second stage, a Bayesian hierarchical spatial model that takes the cluster configuration into account is fitted, which accounts for the discontinuities in disease risk. To evaluate the performance of this new procedure in comparison to previous proposals, a simulation study has been conducted. Results show competitive risk estimates at a much better computational cost. The new methodology is used to analyze stomach cancer mortality data in Spanish municipalities.

Alleviating confounding in spatio-temporal areal models with an application on crimes against women in India

Assessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of such associations due to confounding effects if they are not carefully handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong conclusions about the underlying associations between the response and the covariates. In spatio-temporal areal models, the temporal dimension may emerge as a new source of confounding, and the problem may be even worse. In this work, we propose two approaches to deal with confounding of fixed effects by spatial and temporal random effects, while obtaining good model predictions. In particular, restricted regression and an apparently—though in fact not—equivalent procedure using constraints are proposed within both fully Bayes and empirical Bayes approaches. The methods are compared in terms of fixed-effect estimates and model selection criteria. The techniques are used to assess the association between dowry deaths and certain socio-demographic covariates in the districts of Uttar Pradesh, India.

Vector Surveillance, Host Species Richness, and Demographic Factors as West Nile Disease Risk Indicators

West Nile virus (WNV) is the most common arthropod-borne virus (arbovirus) in the United States (US) and is the leading cause of viral encephalitis in the country. The virus has affected tens of thousands of US persons total since its 1999 North America introduction, with thousands of new infections reported annually. Approximately 1% of humans infected with WNV acquire neuroinvasive West Nile Disease (WND) with severe encephalitis and risk of death. Research describing WNV ecology is needed to improve public health surveillance, monitoring, and risk assessment. We applied Bayesian joint-spatiotemporal modeling to assess the association of vector surveillance data, host species richness, and a variety of other environmental and socioeconomic disease risk factors with neuroinvasive WND throughout the conterminous US. Our research revealed that an aging human population was the strongest disease indicator, but climatic and vector-host biotic interactions were also significant in determining risk of neuroinvasive WND. Our analysis also identified a geographic region of disproportionately high neuroinvasive WND disease risk that parallels the Continental Divide, and extends southward from the US-Canada border in the states of Montana, North Dakota, and Wisconsin to the US-Mexico border in western Texas. Our results aid in unraveling complex WNV ecology and can be applied to prioritize disease surveillance locations and risk assessment.

Mapping Geographical Patterns and High Rate Areas for Sexually Transmitted Infections in Portugal: A Retrospective Study Based on the National Epidemiological Surveillance System

OBJECTIVE

Monitoring disease variation using finer scales to identify high-rate communities is a critical aspect for precision public health and for efficient resource allocation. This study aimed to map the spatial patterns of chlamydia, gonorrhea, and syphilis; identify high-rate areas across Portuguese municipalities; and determine the association of these sexually transmitted infections (STIs) with socioeconomic deprivation, urbanicity level, and population density.

METHODS

The STI notifications at municipality level for the period 2015 to 2017 were obtained from Portugal's Epidemiologic Surveillance System (Sistema Nacional de Vigilância Epidemiológica). Spatial Bayesian models were used to calculate smoothed standardized notification rates, identify high- and low-rate areas and estimate associations (relative risk [RR], 95% credible intervals [95%CrI]).

RESULTS

There were 4819 cases of chlamydia, gonorrhea, and syphilis reported, accounting for 15.3%, 33.2%, and 51.5% of the notifications, respectively. The STI notification rates were substantially higher in Porto and Lisbon Metropolitan Areas and concentrically disperse around those. Notification rates of the 3 STIs were strongly correlated (r > 0.8). Rates of gonorrhea (Q1-lowest density vs. Q5-highest RR, 2.10; 95% CrI, 1.08-4.25) and syphilis (RR, 3.16; 95% CrI, 2.00-5.13) were associated with population density. Notifications of chlamydia (Q1-least urban vs. Q5-most RR, 9.64; 95% CrI, 1.73-93.59) and syphilis (RR, 1.92; 95% CrI, 1.30-2.88) increased with urbanicity level. We also found that notification rates of gonorrhea were associated with socioeconomic deprivation (Q1-least vs. Q5-most deprived RR, 1.75; 95% CrI, 1.07-2.88).

CONCLUSIONS

Wide spatial inequalities in STI notification rates were observed, which were predominantly concentrated in the 2 metropolitan areas of the country. Our findings can help guide more targeted interventions to reduce STIs incidence.

Propensity score matching for multilevel spatial data: accounting for geographic confounding in health disparity studies

BACKGROUND

Diabetes is a public health burden that disproportionately affects military veterans and racial minorities. Studies of racial disparities are inherently observational, and thus may require the use of methods such as Propensity Score Analysis (PSA). While traditional PSA accounts for patient-level factors, this may not be sufficient when patients are clustered at the geographic level and thus important confounders, whether observed or unobserved, vary by geographic location.

METHODS

We employ a spatial propensity score matching method to account for "geographic confounding", which occurs when the confounding factors, whether observed or unobserved, vary by geographic region. We augment the propensity score and outcome models with spatial random effects, which are assigned scaled Besag-York-Mollié priors to address spatial clustering and improve inferences by borrowing information across neighboring geographic regions. We apply this approach to a study exploring racial disparities in diabetes specialty care between non-Hispanic black and non-Hispanic white veterans. We construct multiple global estimates of the risk difference in diabetes care: a crude unadjusted estimate, an estimate based solely on patient-level matching, and an estimate that incorporates both patient and spatial information.

RESULTS

In simulation we show that in the presence of an unmeasured geographic confounder, ignoring spatial heterogeneity results in increased relative bias and mean squared error, whereas incorporating spatial random effects improves inferences. In our study of racial disparities in diabetes specialty care, the crude unadjusted estimate suggests that specialty care is more prevalent among non-Hispanic blacks, while patient-level matching indicates that it is less prevalent. Hierarchical spatial matching supports the latter conclusion, with a further increase in the magnitude of the disparity.

CONCLUSIONS

These results highlight the importance of accounting for spatial heterogeneity in propensity score analysis, and suggest the need for clinical care and management strategies that are culturally sensitive and racially inclusive.

Using Bayesian spatial models to map and to identify geographical hotspots of multidrug-resistant tuberculosis in Portugal between 2000 and 2016

Multidrug-resistant tuberculosis (MDR-TB) is a major threat to the eradication of tuberculosis. TB control strategies need to be adapted to the necessities of different countries and adjusted in high-risk areas. In this study, we analysed the spatial distribution of the MDR- and non-MDR-TB cases across municipalities in Continental Portugal between 2000 and 2016. We used Bayesian spatial models to estimate age-standardized notification rates and standardized notification ratios in each area, and to delimitate high- and low-risk areas, those whose standardized notification ratio is significantly above or below the country’s average, respectively. The spatial distribution of MDR- and non-MDR-TB was not homogeneous across the country. Age-standardized notification rates of MDR-TB ranged from 0.08 to 1.20 and of non-MDR-TB ranged from 7.73 to 83.03 notifications per 100,000 population across the municipalities. We identified 36 high-risk areas for non-MDR-TB and 8 high-risk areas for MDR-TB, which were simultaneously high-risk areas for non-MDR-TB. We found a moderate correlation (ρ = 0.653; 95% CI 0.457–0.728) between MDR- and non-MDR-TB standardized notification ratios. We found heterogeneity in the spatial distribution of MDR-TB across municipalities and we identified priority areas for intervention against TB. We recommend including geographical criteria in the application of molecular drug resistance to provide early MDR-TB diagnosis, in high-risk areas.

A Bayesian spatiotemporal statistical analysis of out-of-hospital cardiac arrests

We propose a Bayesian spatiotemporal statistical model for predicting out-of-hospital cardiac arrests (OHCAs). Risk maps for Ticino, adjusted for demographic covariates, are built for explaining and forecasting the spatial distribution of OHCAs and their temporal dynamics. The occurrence intensity of the OHCA event in each area of interest, and the cardiac risk-based clustering of municipalities are efficiently estimated, through a statistical model that decomposes OHCA intensity into overall intensity, demographic fixed effects, spatially structured and unstructured random effects, time polynomial dependence, and spatiotemporal random effect. In the studied geography, time evolution and dependence on demographic features are robust over different categories of OHCAs, but with variability in their spatial and spatiotemporal structure. Two main OHCA incidence-based clusters of municipalities are identified.

Bayesian Spatial Joint Model for Disease Mapping of Zero-Inflated Data with R-INLA: A Simulation Study and an Application to Male Breast Cancer in Iran

Hierarchical Bayesian log-linear models for Poisson-distributed response data, especially Besag, York and Mollié (BYM) model, are widely used for disease mapping. In some cases, due to the high proportion of zero, Bayesian zero-inflated Poisson models are applied for disease mapping. This study proposes a Bayesian spatial joint model of Bernoulli distribution and Poisson distribution to map disease count data with excessive zeros. Here, the spatial random effect is simultaneously considered into both logistic and log-linear models in a Bayesian hierarchical framework. In addition, we focus on the BYM2 model, a re-parameterization of the common BYM model, with penalized complexity priors for the latent level modeling in the joint model and zero-inflated Poisson models with different type of zeros. To avoid model fitting and convergence issues, Bayesian inferences are implemented using the integrated nested Laplace approximation (INLA) method. The models are compared according to the deviance information criterion and the logarithmic scoring. A simulation study with different proportions of zero exhibits INLA ability in running the models and also shows slight differences between the popular BYM and BYM2 models in terms of model choice criteria. In an application, we apply the fitting models on male breast cancer data in Iran at county level in 2014.

Online relative risks/rates estimation in spatial and spatio-temporal disease mapping

BACKGROUND AND OBJECTIVE

Spatial and spatio-temporal analyses of count data are crucial in epidemiology and other fields to unveil spatial and spatio-temporal patterns of incidence and/or mortality risks. However, fitting spatial and spatio-temporal models is not easy for non-expert users. The objective of this paper is to present an interactive and user-friendly web application (named SSTCDapp) for the analysis of spatial and spatio-temporal mortality or incidence data. Although SSTCDapp is simple to use, the underlying statistical theory is well founded and all key issues such as model identifiability, model selection, and several spatial priors and hyperpriors for sensitivity analyses are properly addressed.

METHODS

The web application is designed to fit an extensive range of fairly complex spatio-temporal models to smooth the very often extremely variable standardized incidence/mortality risks or crude rates. The application is built with the R package shiny and relies on the well founded integrated nested Laplace approximation technique for model fitting and inference.

RESULTS

The use of the web application is shown through the analysis of Spanish spatio-temporal breast cancer data. Different possibilities for the analysis regarding the type of model, model selection criteria, and a range of graphical as well as numerical outputs are provided.

CONCLUSIONS

Unlike other software used in disease mapping, SSTCDapp facilitates the fit of complex statistical models to non-experts users without the need of installing any software in their own computers, since all the analyses and computations are made in a powerful remote server. In addition, a desktop version is also available to run the application locally in those cases in which data confidentiality is a serious issue.

Livestock host composition rather than land use or climate explains spatial patterns in bluetongue disease in South India

Culicoides-borne arboviruses of livestock impair animal health, livestock production and livelihoods worldwide. As these arboviruses are multi-host, multi-vector systems, predictions to improve targeting of disease control measures require frameworks that quantify the relative impacts of multiple abiotic and biotic factors on disease patterns. We develop such a framework to predict long term (1992-2009) average patterns in bluetongue (BT), caused by bluetongue virus (BTV), in sheep in southern India, where annual BT outbreaks constrain the livelihoods and production of small-holder farmers. In Bayesian spatial general linear mixed models, host factors outperformed landscape and climate factors as predictors of disease patterns, with more BT outbreaks occurring on average in districts with higher densities of susceptible sheep breeds and buffalo. Since buffalo are resistant to clinical signs of BT, this finding suggests they are a source of infection for sympatric susceptible sheep populations. Sero-monitoring is required to understand the role of buffalo in maintaining BTV transmission and whether they must be included in vaccination programs to protect sheep adequately. Landscape factors, namely the coverage of post-flooding, irrigated and rain-fed croplands, had weak positive effects on outbreaks. The intimate links between livestock host, vector composition and agricultural practices in India require further investigation at the landscape scale.

The Portuguese version of the European Deprivation Index: Development and association with all-cause mortality

Socioeconomic inequalities are major health determinants. To monitor and understand them at local level, ecological indexes of socioeconomic deprivation constitute essential tools. In this study, we describe the development of the updated version of the European Deprivation Index for Portuguese small-areas (EDI-PT), describe its spatial distribution and evaluate its association with a general health indicator–all-cause mortality in the period 2009–2012. Using data from the 2011 European Union–Statistics on Income and Living Conditions Survey (EU-SILC), we obtained an indicator of individual deprivation. After identifying variables that were common to both the EU-SILC and the census, we used the indicator of individual deprivation to test if these variables were associated with individual-level deprivation, and to compute weights. Accordingly, eight variables were included. The EDI-PT was produced for the smallest area unit possible (n = 18084 census block groups, mean/area = 584 inhabitants) and resulted from the weighted sum of the eight selected variables. It was then categorized into quintiles (Q1-least deprived to Q5-most deprived). To estimate the association with mortality we fitted Bayesian spatial models. The EDI-PT was unevenly distributed across Portugal–most deprived areas concentrated in the South and in the inner North and Centre of the country, and the least deprived in the coastal North and Centre. The EDI-PT was positively and significantly associated with overall mortality, and this relation followed a rather clear dose-response relation of increasing mortality as deprivation increases (Relative Risk Q2 = 1.012, 95% Credible Interval 0.991–1.033; Q3 = 1.026, 1.004–1.048; Q4 = 1.053, 1.029–1.077; Q5 = 1.068, 1.042–1.095). Summing up, we updated the index of socioeconomic deprivation for Portuguese small-areas, and we showed that the EDI-PT constitutes a sensitive measure to capture health inequalities, since it was consistently associated with a key measure of population health/development, all-cause mortality. We strongly believe this updated version will be widely employed by social and medical researchers and regional planners.

Spatial analysis of macro-level bicycle crashes using the class of conditional autoregressive models

The objective of this study was to investigate the relationship between bicycle crash frequency and their contributing factors at the census block group level in Florida, USA. Crashes aggregated over the census block groups tend to be clustered (i.e., spatially dependent) rather than randomly distributed. To account for the effect of spatial dependence across the census block groups, the class of conditional autoregressive (CAR) models were employed within the hierarchical Bayesian framework. Based on four years (2011-2014) of crash data, total and fatal-and-severe injury bicycle crash frequencies were modeled as a function of a large number of variables representing demographic and socio-economic characteristics, roadway infrastructure and traffic characteristics, and bicycle activity characteristics. This study explored and compared the performance of two CAR models, namely the Besag's model and the Leroux's model, in crash prediction. The Besag's models, which differ from the Leroux's models by the structure of how spatial autocorrelation are specified in the models, were found to fit the data better. A 95% Bayesian credible interval was selected to identify the variables that had credible impact on bicycle crashes. A total of 21 variables were found to be credible in the total crash model, while 18 variables were found to be credible in the fatal-and-severe injury crash model. Population, daily vehicle miles traveled, age cohorts, household automobile ownership, density of urban roads by functional class, bicycle trip miles, and bicycle trip intensity had positive effects in both the total and fatal-and-severe crash models. Educational attainment variables, truck percentage, and density of rural roads by functional class were found to be negatively associated with both total and fatal-and-severe bicycle crash frequencies.

An intuitive Bayesian spatial model for disease mapping that accounts for scaling

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM (Besag, York and Mollié) model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding; however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. The hyperparameters themselves are used to define flexible extensions of simple base models. Consequently, penalised complexity priors for these parameters can be derived based on the information-theoretic distance from the flexible model to the base model, giving priors with clear interpretation. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning.

A two-stage approach to estimate spatial and spatio-temporal disease risks in the presence of local discontinuities and clusters

Disease risk maps for areal unit data are often estimated from Poisson mixed models with local spatial smoothing, for example by incorporating random effects with a conditional autoregressive prior distribution. However, one of the limitations is that local discontinuities in the spatial pattern are not usually modelled, leading to over-smoothing of the risk maps and a masking of clusters of hot/coldspot areas. In this paper, we propose a novel two-stage approach to estimate and map disease risk in the presence of such local discontinuities and clusters. We propose approaches in both spatial and spatio-temporal domains, where for the latter the clusters can either be fixed or allowed to vary over time. In the first stage, we apply an agglomerative hierarchical clustering algorithm to training data to provide sets of potential clusters, and in the second stage, a two-level spatial or spatio-temporal model is applied to each potential cluster configuration. The superiority of the proposed approach with regard to a previous proposal is shown by simulation, and the methodology is applied to two important public health problems in Spain, namely stomach cancer mortality across Spain and brain cancer incidence in the Navarre and Basque Country regions of Spain.

The influence of socioeconomic, biogeophysical and built environment on old-age survival in a Southern European city

Old-age survival is a good indicator of population health and regional development. We evaluated the spatial distribution of old-age survival across Porto neighbourhoods and its relation with physical (biogeophysical and built) and socioeconomic factors (deprivation). Smoothed survival rates and odds ratio (OR) were estimated using Bayesian spatial models. There were important geographical differentials in the chances of survival after 75 years of age. Socioeconomic deprivation strongly impacted old-age survival (Men: least deprived areas OR=1.31(1.05-1.63); Women OR=1.53(1.24-1.89)), explaining over 40% of the spatial variance. Walkability and biogeophysical environment were unrelated to old-age survival and also unrelated to socioeconomic deprivation, being fairly evenly distributed through the city.

Age-space-time CAR models in Bayesian disease mapping

Mortality counts are usually aggregated over age groups assuming similar effects of both time and region, yet the spatio-temporal evolution of cancer mortality rates may depend on changing age structures. In this paper, mortality rates are analyzed by region, time period and age group, and models including space-time, space-age, and age-time interactions are considered. The integrated nested Laplace approximation method, known as INLA, is adopted for model fitting and inference in order to reduce computing time in comparison with Markov chain Monte Carlo (McMC) methods. The methodology provides full posterior distributions of the quantities of interest while avoiding complex simulation techniques. The proposed models are used to analyze prostate cancer mortality data in 50 Spanish provinces over the period 1986-2010. The results reveal a decline in mortality since the late 1990s, particularly in the age group [65,70), probably because of the inclusion of the PSA (prostate-specific antigen) test and better treatment of early-stage disease. The decline is not clearly observed in the oldest age groups. Copyright © 2016 John Wiley & Sons, Ltd.

On fitting spatio-temporal disease mapping models using approximate Bayesian inference

Spatio-temporal disease mapping comprises a wide range of models used to describe the distribution of a disease in space and its evolution in time. These models have been commonly formulated within a hierarchical Bayesian framework with two main approaches: an empirical Bayes (EB) and a fully Bayes (FB) approach. The EB approach provides point estimates of the parameters relying on the well-known penalized quasi-likelihood (PQL) technique. The FB approach provides the posterior distribution of the target parameters. These marginal distributions are not usually available in closed form and common estimation procedures are based on Markov chain Monte Carlo (MCMC) methods. However, the spatio-temporal models used in disease mapping are often very complex and MCMC methods may lead to large Monte Carlo errors and a huge computation time if the dimension of the data at hand is large. To circumvent these potential inconveniences, a new technique called integrated nested Laplace approximations (INLA), based on nested Laplace approximations, has been proposed for Bayesian inference in latent Gaussian models. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with PQL via a simulation study. The spatio-temporal distribution of male brain cancer mortality in Spain during the period 1986-2010 is also analysed.

Modelling risks in disease mapping

In this article, we propose a strategy of analysis of mortality data with the aim of providing a guideline for epidemiologists and public health researchers to choose a reasonable model for estimating mortality (or incidence) risks. Maps displaying the crude mortality rates or ratios are usually misleading because of the instability of the estimators in low populated areas. As an alternative, many smoothing methods have been presented in the literature based on Poisson inference. They account for the extra-Poisson variation (overdispersion), frequently present in the homogeneous Poisson model, by incorporating random effects. Here, we recommend to test for the potential sources of extra-Poisson variation because, depending on them, the models which fit better the data may be different. Overdispersion can be mainly due to spatial autocorrelation, unstructured heterogeneity or to a combination of these two, and also, when studying very rare diseases, it can be due to an excess of zeros in the data. In this article, different situations the analyst may encounter are detailed and appropriate procedures for each case are presented. The alternative models are illustrated using mortality data provided by the Statistical Institute of Navarra, Spain.

The use of score tests for inference on variance components

Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.