A primer on disease mapping and ecological regression using $${\texttt{INLA}}$$

Spatiotemporal varying coefficient model for respiratory disease mapping in Taiwan

Respiratory diseases have been global public health problems for a long time. In recent years, air pollutants as important risk factors have drawn lots of attention. In this study, we investigate the influence of $\pm2.5$ (particulate matters in diameter less than 2.5 ${\rm{\mu }} m$) on hospital visit rates for respiratory diseases in Taiwan. To reveal the spatiotemporal pattern of data, we propose a Bayesian disease mapping model with spatially varying coefficients and a parametric temporal trend. Model fitting is conducted using the integrated nested Laplace approximation, which is a widely applied technique for large-scale data sets due to its high computational efficiency. The finite sample performance of the proposed method is studied through a series of simulations. As demonstrated by simulations, the proposed model can improve both the parameter estimation performance and the prediction performance. We apply the proposed model on the respiratory disease data in 328 third-level administrative regions in Taiwan and find significant associations between hospital visit rates and $\pm2.5$.

Spatial Analysis on Supply and Demand of Adult Surgical Masks in Taipei Metropolitan Areas in the Early Phase of the COVID-19 Pandemic

This study aimed to assess the gap between the supply and demand of adult surgical masks under limited resources. Owing to the implementation of the real-name mask rationing system, the historical inventory data of aggregated mask consumption in a pharmacy during the early period of the COVID-19 outbreak (April and May 2020) in Taiwan were analyzed for supply-side analysis. We applied the Voronoi diagram and areal interpolation methods to delineate the average supply of customer counts from a pharmacy to a village (administrative level). On the other hand, the expected number of demand counts was estimated from the population data. The relative risk (RR) of supply, which is the average number of adults served per day divided by the expected number in a village, was modeled under a Bayesian hierarchical framework, including Poisson, negative binomial, Poisson spatial, and negative binomial spatial models. We observed that the number of pharmacies in a village is associated with an increasing supply, whereas the median annual per capita income of the village has an inverse relationship. Regarding land use percentages, percentages of the residential and the mixed areas in a village are negatively associated, while the school area percentage is positively associated with the supply in the Poisson spatial model. The corresponding uncertainty measurement: villages where the probability exceeds the risk of undersupply, that is, Pr (RR < 1), were also identified. The findings of the study may help health authorities to evaluate the spatial allocation of anti-epidemic resources, such as masks and rapid test kits, in small areas while identifying priority areas with the suspicion of undersupply in the beginning stages of outbreaks.

Identificação de áreas de risco e fatores associados à epidemia de sarampo de 2019 no Estado de São Paulo, Brasil

O objetivo foi analisar a ocorrência de clusters e fatores associados ao ressurgimento de casos de sarampo da maior epidemia do período pós-eliminação, ocorrida no Estado de São Paulo, Brasil, em 2019. Fatores sociossanitários e assistenciais foram analisados por modelos de Poisson inflacionado de zero (ZIP) e ZIP com efeito espacial estruturado e não estruturado. A estatística de varredura SCAN foi usada para analisar a ocorrência de clusters de casos. Foram identificados clusters de casos de alto risco em municípios que compõem a região intermediária de São Paulo. No modelo ZIP, foram observadas como fatores de risco no nível municipal as variáveis chefes de domicílio menores de 18 anos (RR ajustado = 1,39; ICr95%: 1,27-1,53), desigualdade na distribuição de renda (RR ajustado = 36,67; ICr95%: 26,36-51,15), desocupação em maiores de 18 anos (RR ajustado = 1,10; ICr95%: 1,08-1,12) e iluminação pública inexistente (RR ajustado = 1,05; ICr95%: 1,04-1,05). Nos modelos ZIP com efeito espacial estruturado e não estruturado, foram identificados como fatores de risco os indicadores chefes de domicílio menores de 18 anos (RR ajustado = 1,36; ICr95%: 1,04-1,90) e desigualdade na distribuição dos rendimentos do trabalho (RR ajustado = 3,12; ICr95%: 1,02-9,48). Em ambos os modelos, a cobertura de agentes de saúde se apresentou como fator de proteção. Os achados reforçam a importância de intensificar as ações de vigilância de sarampo articuladas à Estratégia Saúde da Família, especialmente em áreas de maior vulnerabilidade social, para garantir coberturas vacinais equânimes e satisfatórias e reduzir o risco de reemergência da doença.

Trends of amenable deaths due to healthcare within the European Union countries. Exploring the association with the economic crisis and education

The study of premature deaths from causes that are generally preventable given the current availability of healthcare - called amenable deaths due to healthcare - provides information on the quality of services. However, they are not only impacted by healthcare characteristics: other factors are also likely to influence. Therefore, identifying the association between amenable deaths due to healthcare and health determinants, such as education, might be the key to preventing these deaths in the future. Still unclear however, is how this works and how amenable deaths due to healthcare are distributed and evolve within the European Union (EU) below the national level. We therefore studied the geographical and temporal patterns of amenable deaths due to healthcare in the 259 EU regions from 1999 to 2016, including the 2007-2008 financial crisis and the post-2008 economic downturn, and identified whether any association with education exists. A cross-sectional ecological study was carried out. Using a hierarchical Bayesian model, we estimated the average smoothed Standardized Mortality Ratios (sSMR). A regression model was also applied to measure the relative risks (RR) at 95% credible intervals for cause-specific mortality association with education. Results show that amenable deaths due to healthcare decreased globally. Nevertheless, the decrease is not the same across all regions, and inequalities within countries do persist, with lower mortality ratios seen in regions from Central European countries and higher mortality ratios in regions from Eastern European countries. Also, the evolution trend reveals that after the financial crisis, the number of these deaths increased in regions across almost all EU countries. Moreover, educational disparities in mortality emerged, and a statistical association was found between amenable deaths due to healthcare and early exit from education and training. These results confirm that identifying and understanding the background of regional differences may lead to a better understanding of the amenable deaths due to healthcare and allow for the application of more effective policies.

Community vulnerability and mobility: What matters most in spatio-temporal modeling of the COVID-19 pandemic?

Community vulnerability is widely viewed as an important aspect to consider when modeling disease. Although COVID-19 does disproportionately impact vulnerable populations, human behavior as measured by community mobility is equally influential in understanding disease spread. In this research, we seek to understand which of four composite measures perform best in explaining disease spread and mortality, and we explore the extent to which mobility account for variance in the outcomes of interest. We compare two community mobility measures, three composite measures of community vulnerability, and one composite measure that combines vulnerability and human behavior to assess their relative feasibility in modeling the US COVID-19 pandemic. Extensions – via temporally dependent fixed effect coefficients – of the commonly used Bayesian spatio-temporal Poisson disease mapping models are implemented and compared in terms of goodness of fit as well as estimate precision and viability. A comparison of goodness of fit measures nearly unanimously suggests the human behavior-based models are superior. The duration at residence mobility measure indicates two unique and seemingly inverse relationships between mobility and the COVID-19 pandemic: the findings indicate decreased COVID-19 presence with decreased mobility early in the pandemic and increased COVID-19 presence with decreased mobility later in the pandemic. The early indication is likely influenced by a large presence of state-issued stay at home orders and self-quarantine, while the later indication likely emerges as a consequence of holiday gatherings in a country under limited restrictions. This study implements innovative statistical methods and furnishes results that challenge the generally accepted notion that vulnerability and deprivation are key to understanding disparities in health outcomes. We show that human behavior is equally, if not more important to understanding disease spread. We encourage researchers to build upon the work we start here and continue to explore how other behaviors influence the spread of COVID-19.

Massive GNSS data for road safety analysis: Comparing crash models for several Canadian cities and data sources

Mobile sensors are a useful data source with applications in several transportation fields. Though cost of collection, transmission, and storage has limited studies on driving data and safety, this can be overcome through usage-based insurance (UBI). In UBI programs, drivers are monitored, and their premiums are adjusted based on driver-level surrogate safety measures (SSMs) related to exposure and driving style. Contextual link-level SSMs (volume, speed, or density) could further improve discount calibration. This study quantifies relationships between contextual SSMs and crashes and includes the validation of previous results (correlations between SSMs and crashes and statistical models estimated using smartphone-collected data from Quebec City) and the comparison of three Canadian cities (using UBI data from Quebec City, Montreal, and Ottawa). Extracted SSMs were compared to large volumes of historical crash frequency data using Spearman's Rank Correlation Coefficient and then implemented into spatial Bayesian crash models. Results from the UBI data generally matched those from the previous study, with observed correlations mirroring previous results in direction (braking, congestion, and speed variation are positively associated with crash frequency while mean speed is negatively associated) while correlation strength was slightly higher. Furthermore, these results were consistent between cities. For the crash modelling, repeatability of previous results in Quebec City was moderately good for the UBI data. Importantly for large-scale implementation, models estimated using UBI data were largely consistent between cities. This work provides an important contribution to the existing literature, clearly demonstrating how contextual safety measures could be applied to benefit UBI practices.

Using spatial and temporal modeling to visualize the effects of U.S. state issued stay at home orders on COVID-19

Coronavirus disease 2019 dominated and augmented many aspects of life beginning in early 2020. Related research and data generation developed alongside its spread. We developed a Bayesian spatio-temporal Poisson disease mapping model for estimating real-time characteristics of the coronavirus disease in the United States. We also created several dashboards for visualization of the statistical model for fellow researchers and simpler spatial and temporal representations of the disease for consumption by analysts and data scientists in the policymaking community in our region. Findings suggest that the risk of confirmed cases is higher for health regions under partial stay at home orders and lower in health regions under full stay at home orders, when compared to before stay at home orders were declared. These results confirm the benefit of state-issued stay at home orders as well as suggest compliance to the directives towards the older population for adhering to social distancing guidelines.

Addressing challenges in routine health data reporting in Burkina Faso through Bayesian spatiotemporal prediction of weekly clinical malaria incidence

Sub-Saharan African (SSA) countries’ health systems are often vulnerable to unplanned situations that can hinder their effectiveness in terms of data completeness and disease control. For instance, in Burkina Faso following a workers' strike, comprehensive data on several diseases were unavailable for a long period in 2019. Weather, seasonal-malaria-chemoprevention (SMC), free healthcare, and other contextual data, which are purported to influence malarial disease, provide opportunities to fit models to describe the clinical malaria data and predict the disease spread. Bayesian spatiotemporal modeling was applied to weekly malaria surveillance data from Burkina Faso (2011–2018) while considering the effects of weather, health programs and contextual factors. Then, a prediction was used to deal with weekly missing data for the entire year of 2019, and SMC and free healthcare effects were quantified. Our proposed model accurately predicted weekly clinical malaria incidence (correlation coefficient, r = 0.90). The distribution of clinical malaria incidence was heterogeneous across the country. Overall, national predicted clinical malaria incidence in 2019 (605 per 1000 [95% CrI: 360–990]) increased by 24.7% compared with the year 2015. SMC and the interaction between free healthcare and health facility attendance were associated with a reduction in clinical malaria incidence. Our modeling approach could be a useful tool for strengthening health systems’ resilience by addressing data completeness and could support SSA countries in developing appropriate targets and indicators to facilitate the subnational control effort.

An Introductory Framework for Choosing Spatiotemporal Analytical Tools in Population-Level Eco-Epidemiological Research

Spatiotemporal visualization and analytical tools (SATs) are increasingly being applied to risk-based surveillance/monitoring of adverse health events affecting humans, animals, and ecosystems. Different disciplines use diverse SATs to address similar research questions. The juxtaposition of these diverse techniques provides a list of options for researchers who are new to population-level spatial eco-epidemiology. Here, we are conducting a narrative review to provide an overview of the multiple available SATs, and introducing a framework for choosing among them when addressing common research questions across disciplines. The framework is comprised of three stages: (a) pre-hypothesis testing stage, in which hypotheses regarding the spatial dependence of events are generated; (b) primary hypothesis testing stage, in which the existence of spatial dependence and patterns are tested; and (c) secondary-hypothesis testing and spatial modeling stage, in which predictions and inferences were made based on the identified spatial dependences and associated covariates. In this step-wise process, six key research questions are formulated, and the answers to those questions should lead researchers to select one or more methods from four broad categories of SATs: (T1) visualization and descriptive analysis; (T2) spatial/spatiotemporal dependence and pattern recognition; (T3) spatial smoothing and interpolation; and (T4) geographic correlation studies (i.e., spatial modeling and regression). The SATs described here include both those used for decades and also other relatively new tools. Through this framework review, we intend to facilitate the choice among available SATs and promote their interdisciplinary use to support improving human, animal, and ecosystem health.

Bayesian hierarchical modeling of joint spatiotemporal risk patterns for Human Immunodeficiency Virus (HIV) and Tuberculosis (TB) in Kenya

The simultaneous spatiotemporal modeling of multiple related diseases strengthens inferences by borrowing information between related diseases. Numerous research contributions to spatiotemporal modeling approaches exhibit their strengths differently with increasing complexity. However, contributions that combine spatiotemporal approaches to modeling of multiple diseases simultaneously are not so common. We present a full Bayesian hierarchical spatio-temporal approach to the joint modeling of Human Immunodeficiency Virus and Tuberculosis incidences in Kenya. Using case notification data for the period 2012–2017, we estimated the model parameters and determined the joint spatial patterns and temporal variations. Our model included specific and shared spatial and temporal effects. The specific random effects allowed for departures from the shared patterns for the different diseases. The space-time interaction term characterized the underlying spatial patterns with every temporal fluctuation. We assumed the shared random effects to be the structured effects and the disease-specific random effects to be unstructured effects. We detected the spatial similarity in the distribution of Tuberculosis and Human Immunodeficiency Virus in approximately 29 counties around the western, central and southern regions of Kenya. The distribution of the shared relative risks had minimal difference with the Human Immunodeficiency Virus disease-specific relative risk whereas that of Tuberculosis presented many more counties as high-risk areas. The flexibility and informative outputs of Bayesian Hierarchical Models enabled us to identify the similarities and differences in the distribution of the relative risks associated with each disease. Estimating the Human Immunodeficiency Virus and Tuberculosis shared relative risks provide additional insights towards collaborative monitoring of the diseases and control efforts.

Severe-malaria infection and its outcomes among pregnant women in Burkina Faso health-districts: Hierarchical Bayesian space-time models applied to routinely-collected data from 2013 to 2018

Fine-scale hotspots detection is crucial for optimum delivery of essential health-services for reducing severe malaria in pregnancy (MiP) and death cases in Burkina Faso. This study used hierarchical-Bayesian Spatio-temporal modeling to explore space-time patterns and pinpoint health-districts with an exceedance probability of severe MiP incidence and fatality rate. Study also assessed effect of health-district service delivery (readiness) on severe-MiP outcomes.

Severe-MiP fatality rate declined considerably while its incidence rate remained unchanged between January-2013 and December-2018. Severe-MiP cases persisted throughout the year with peaks between August and November. These peaks increased 2.5-fold the fatality rate. Furthermore, severe-MiP fatality was higher in health-districts classified as low-readiness (IRR = 2.469, 95%CrI: 1.632–3.738). However, the fatality rate decreased significantly with proper coverage with three doses for intermittent-preventive-treatment with sulphadoxine-pyrimethamine. Severe-MiP burden was heterogeneous spatially and temporally. The study suggested that health-programs should increase health-districts readiness and optimize resource allocation in high burden areas and months.

Pedestrian safety at signalized intersections: Modelling spatial effects of exposure, geometry and signalization on a large urban network

Intersections represent the most dangerous sites in the road network for pedestrians: not only is modal separation often impossible, but elements of geometry, traffic control, and built environment further exacerbate crash risk. Evaluating the safety impact of intersection features requires methods to quantify relationships between different factors and pedestrian injuries. The purpose of this paper is to model the effects of exposure, geometry, and signalization on pedestrian injuries at urban signalized intersections using a Full Bayes spatial Poisson Log-Normal model that accounts for unobserved heterogeneity and spatial correlation. Using the Integrated Nested Laplace Approximation (INLA) technique, this work leverages a rich database of geometric and signalization variables for 1864 intersections in Montreal, Quebec. To collect exposure data, short-term pedestrian and vehicle counts were extrapolated to AADT using developed expansion factors. Results of the model confirmed the positive relationship between pedestrian and vehicle volumes and pedestrian injuries. Curb extensions, raised medians, and exclusive left turn lanes were all found to reduce pedestrian injuries, while the total number of lanes and the number of commercial entrances were found to increase them. Pedestrian priority phases reduced injuries while the green straight arrow increased injuries. Lastly, the posterior expected number of crashes was used to identify hotspots. The proposed ranking criteria identified many intersections close to the city centre where the expected number of crashes is highest and intersections along arterials with lower pedestrian volumes where individual pedestrian risk is elevated. Understanding the effects of intersection geometry and pedestrian signalization will aid in ensuring the safety of pedestrians at signalized intersections.

Spatiotemporal Analysis of Influenza in China, 2005-2018

Influenza is a major cause of morbidity and mortality worldwide, as well as in China. Knowledge of the spatial and temporal characteristics of influenza is important in evaluating and developing disease control programs. This study aims to describe an accurate spatiotemporal pattern of influenza at the prefecture level and explore the risk factors associated with influenza incidence risk in mainland China from 2005 to 2018. The incidence data of influenza were obtained from the Chinese Notifiable Infectious Disease Reporting System (CNIDRS). The Besag York Mollié (BYM) model was extended to include temporal and space-time interaction terms. The parameters for this extended Bayesian spatiotemporal model were estimated through integrated nested Laplace approximations (INLA) using the package R-INLA in R. A total of 702,226 influenza cases were reported in mainland China in CNIDRS from 2005–2018. The yearly reported incidence rate of influenza increased 15.6 times over the study period, from 3.51 in 2005 to 55.09 in 2008 per 100,000 populations. The temporal term in the spatiotemporal model showed that much of the increase occurred during the last 3 years of the study period. The risk factor analysis showed that the decreased number of influenza vaccines for sale, the new update of the influenza surveillance protocol, the increase in the rate of influenza A (H1N1)pdm09 among all processed specimens from influenza-like illness (ILI) patients, and the increase in the latitude and longitude of geographic location were associated with an increase in the influenza incidence risk. After the adjusting for fixed covariate effects and time random effects, the map of the spatial structured term shows that high-risk areas clustered in the central part of China and the lowest-risk areas in the east and west. Large space-time variations in influenza have been found since 2009. In conclusion, an increasing trend of influenza was observed from 2005 to 2018. The insufficient flu vaccine supplements, the newly emerging influenza A (H1N1)pdm09 and expansion of influenza surveillance efforts might be the major causes of the dramatic changes in outbreak and spatio-temporal epidemic patterns. Clusters of prefectures with high relative risks of influenza were identified in the central part of China. Future research with more risk factors at both national and local levels is necessary to explain the changing spatiotemporal patterns of influenza in China.

Bayesian modeling of spatiotemporal patterns of TB-HIV co-infection risk in Kenya

Background

Tuberculosis (TB) and Human Immunodeficiency Virus (HIV) diseases are globally acknowledged as a public health challenge that exhibits adverse bidirectional relations due to the co-epidemic overlap. To understand the co-infection burden we used the case notification data to generate spatiotemporal maps that described the distribution and exposure hypotheses for further epidemiologic investigations in areas with unusual case notification levels.

Methods

We analyzed the TB and TB-HIV case notification data from the Kenya national TB control program aggregated for forty-seven counties over a seven-year period (2012–2018). Using spatiotemporal poisson regression models within the Integrated Nested Laplace Approach (INLA) paradygm, we modeled the risk of TB-HIV co-infection. Six competing models with varying space-time formulations were compared to determine the best fit model. We then assessed the geographic patterns and temporal trends of coinfection risk by mapping the posterior marginal from the best fit model.

Results

Of the total 608,312 TB case notifications, 194,129 were HIV co-infected. The proportion of TB-HIV co-infection was higher in females (39.7%) than in males (27.0%). A significant share of the co-infection was among adults aged 35 to 44 years (46.7%) and 45 to 54 years (42.1%). Based on the Bayesian Defiance Information (DIC) and the effective number of parameters (pD) comparisons, the spatiotemporal model allowing space-time interaction was the best in explaining the geographical variations in TB-HIV coinfection. The model results suggested that the risk of TB-HIV coinfection was influenced by infrastructure index (Relative risk (RR) = 5.75, Credible Interval (Cr.I) = (1.65, 19.89)) and gender ratio (RR = 5.81e⁻⁰⁴, Cr. I = (1.06e⁻⁰⁴, 3.18e⁻⁰³). The lowest and highest temporal relative risks were in the years 2016 at 0.9 and 2012 at 1.07 respectively. The spatial pattern presented an increased co-infection risk in a number of counties. For the spatiotemporal interaction, only a few counties had a relative risk greater than 1 that varied in different years.

Conclusions

We identified elevated risk areas for TB/HIV co-infection and fluctuating temporal trends which could be because of improved TB case detection or surveillance bias caused by spatial heterogeneity in the co-infection dynamics. Focused interventions and continuous TB-HIV surveillance will ensure adequate resource allocation and significant reduction of HIV burden amongst TB patients.

Network screening for large urban road networks: Using GPS data and surrogate measures to model crash frequency and severity

Crash frequency and injury severity are independent dimensions defining crash risk in road safety management and network screening. Traditional screening techniques model crashes using regression and historical crash data, making them intrinsically reactive. In response, surrogate measures of safety have become a popular proactive alternative. The purpose of this paper is to develop models for crash frequency and severity incorporating GPS-derived surrogate safety measures (SSMs) as predictive variables. SSMs based on vehicle manoeuvres and traffic flow were extracted from data collected in Quebec City. The mixed multivariate outcome is estimated using two models; a Full Bayes Spatial Negative Binomial model for crash frequency estimated using the Integrated Nested Laplace Approximation approach and a fractional Multinomial Logit model for crash severity. Model outcomes are combined to generate posterior expected crash frequency at each severity level and rank sites based on crash cost. The crash frequency model was accurate at the network scale, with the majority of proposed SSMs statistically significant at 95% confidence and the direction of their effect generally consistent with previous research. In the crash severity model, fewer variables were significant, yet the direction of the effect of all significant variables was again consistent with previous research. Correlations between rankings predicted by the mixed multivariate model and by the crash data were adequate for intersections (0.46) but were poorer for links (0.25). The ability to prioritize sites based on GPS data and SSMs rather than historical crash data represents a substantial contribution to the field of road safety.

Surrogate safety and network screening: Modelling crash frequency using GPS travel data and latent Gaussian Spatial Models

Improving road safety requires accurate network screening methods to identify and prioritize sites in order to maximize the effectiveness of implemented countermeasures. In screening, hotspots are commonly identified using statistical models and ranking criteria derived from observed crash data. However, collision databases are subject to errors, omissions, and underreporting. More importantly, crash-based methods are reactive and require years of crash data. With the arrival of new technologies including Global Positioning System (GPS) trajectory data, proactive surrogate safety methods have gained popularity as an alternative approach for screening. GPS-enabled smartphones can collect reliable and spatio-temporally rich driving data from regular drivers using an inexpensive, simple, and user-friendly tool. However, few studies to date have analyzed large volumes of smartphone GPS data and considered surrogate-safety modelling techniques for network screening. The purpose of this paper is to propose a surrogate safety screening approach based on smartphone GPS data and a Full Bayesian modelling framework. After processing crash data and GPS data collected in Quebec City, Canada, several surrogate safety measures (SSMs), including vehicle manoeuvres (hard braking) and measures of traffic flow (congestion, average speed, and speed variation), were extracted. Then, spatial crash frequency models incorporating the extracted SSMs were proposed and validated. A Latent Gaussian Spatial Model was estimated using the Integrated Nested Laplace Approximation (INLA) technique. While the INLA Negative Binomial models outperformed alternative models, incorporating spatial correlations provided the greatest improvement in model fit. Relationships between SSMs and crash frequency established in previous studies were generally supported by the modelling results. For example, hard braking, congestion, and speed variation were all positively linked to crash counts at the intersection level. Network screening based on SSMs presents a substantial contribution to the field of road safety and works towards the elimination of crash data in evaluation and monitoring.

Gaining relevance from the random: Interpreting observed spatial heterogeneity

In Bayesian disease mapping, spatial random effects are used to account for confounding in the data so that reasonable estimates for the fixed effects can be obtained. Typically, the spatial random effects are mapped and qualitative comments are made related to an increase or decrease in risk for certain areas. The approach outlined here illustrates how a quantitative secondary assessment can be applied to make more useful and applicable inference related to these spatial random effects. We are able to recover important but unmeasured or unincluded risk factors via a secondary model fit. Results from the secondary model fit can determine association between spatial region-level risk factors and the estimated spatial random effects. We believe this work presents a useful, quantitative technique highlighting the importance and applicability of spatial random effects as well as illustrates how these methods lead to more interpretable conclusions.

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.

Flexible Bayesian P-splines for smoothing age-specific spatio-temporal mortality patterns

In this paper age-space-time models based on one and two-dimensional P-splines with B-spline bases are proposed for smoothing mortality rates, where both fixed relative scale and scale invariant two-dimensional penalties are examined. Model fitting and inference are carried out using integrated nested Laplace approximations, a recent Bayesian technique that speeds up computations compared to McMC methods. The models will be illustrated with Spanish breast cancer mortality data during the period 1985-2010, where a general decline in breast cancer mortality has been observed in Spanish provinces in the last decades. The results reveal that mortality rates for the oldest age groups do not decrease in all provinces.

A tall order: Small area mapping and modelling of adult height among Swiss male conscripts

Adult height reflects an individual's socio-economic background and offers insights into the well-being of populations. Height is linked to various health outcomes such as morbidity and mortality and has consequences on the societal level. The aim of this study was to describe small-area variation of height and associated factors among young men in Switzerland. Data from 175,916 conscripts (aged between 18.50 and 20.50 years) was collected between 2005 and 2011, which represented approximately 90% of the corresponding birth cohorts. These were analysed using Gaussian hierarchical models in a Bayesian framework to investigate the spatial pattern of mean height across postcodes. The models varied both in random effects and degree of adjustment (professional status, area-based socioeconomic position, and language region). We found a strong spatial structure for mean height across postcodes. The range of height differences between mean postcode level estimates was 3.40cm according to the best fitting model, with the shorter conscripts coming from the Italian and French speaking parts of Switzerland. There were positive socioeconomic gradients in height at both individual and area-based levels. Spatial patterns for height persisted after adjustment for individual factors, but not when language region was included. Socio-economic position and cultural/natural boundaries such as language borders and mountain passes are shaping patterns of height for Swiss conscripts. Small area mapping of height contributes to the understanding of its cofactors.

Spatio-temporal Bayesian model selection for disease mapping

Spatio-temporal analysis of small area health data often involves choosing a fixed set of predictors prior to the final model fit. In this paper, we propose a spatio-temporal approach of Bayesian model selection to implement model selection for certain areas of the study region as well as certain years in the study time line. Here, we examine the usefulness of this approach by way of a large-scale simulation study accompanied by a case study. Our results suggest that a special case of the model selection methods, a mixture model allowing a weight parameter to indicate if the appropriate linear predictor is spatial, spatio-temporal, or a mixture of the two, offers the best option to fitting these spatio-temporal models. In addition, the case study illustrates the effectiveness of this mixture model within the model selection setting by easily accommodating lifestyle, socio-economic, and physical environmental variables to select a predominantly spatio-temporal linear predictor.

Epidemiological and Ecological Characterization of the EHEC O104:H4 Outbreak in Hamburg, Germany, 2011

In 2011, a large outbreak of entero-hemorrhagic E. coli (EHEC) and hemolytic uremic syndrome (HUS) occurred in Germany. The City of Hamburg was the first focus of the epidemic and had the highest incidences among all 16 Federal States of Germany. In this article, we present epidemiological characteristics of the Hamburg notification data. Evaluating the epicurves retrospectively, we found that the first epidemiological signal of the outbreak, which was in form of a HUS case cluster, was received by local health authorities when already 99 EHEC and 48 HUS patients had experienced their first symptoms. However, only two EHEC and seven HUS patients had been notified. Middle-aged women had the highest risk for contracting the infection in Hamburg. Furthermore, we studied timeliness of case notification in the course of the outbreak. To analyze the spatial distribution of EHEC/HUS incidences in 100 districts of Hamburg, we mapped cases' residential addresses using geographic information software. We then conducted an ecological study in order to find a statistical model identifying associations between local socio-economic factors and EHEC/HUS incidences in the epidemic. We employed a Bayesian Poisson model with covariates characterizing the Hamburg districts as well as incorporating structured and unstructured spatial effects. The Deviance Information Criterion was used for stepwise variable selection. We applied different modeling approaches by using primary data, transformed data, and preselected subsets of transformed data in order to identify socio-economic factors characterizing districts where EHEC/HUS outbreak cases had their residence.

Incorporating High-Dimensional Exposure Modelling into Studies of Air Pollution and Health

Performing studies on the risks of environmental hazards on human health requires accurate estimates of exposures that might be experienced by the populations at risk. Often there will be missing data and in many epidemiological studies, the locations and times of exposure measurements and health data do not match. To a large extent this will be due to the health and exposure data having arisen from completely different data sources and not as the result of a carefully designed study, leading to problems of both ‘change of support’ and ‘misaligned data’. In such cases, a direct comparison of the exposure and health outcome is often not possible without an underlying model to align the two in the spatial and temporal domains. The Bayesian approach provides the natural framework for such models; however, the large amounts of data that can arise from environmental networks means that inference using Markov Chain Monte Carlo might not be computationally feasible in this setting. Here we adapt the integrated nested Laplace approximation to implement spatio–temporal exposure models. We also propose methods for the integration of large-scale exposure models and health analyses. It is important that any model structure allows the correct propagation of uncertainty from the predictions of the exposure model through to the estimates of risk and associated confidence intervals. The methods are demonstrated using a case study of the levels of black smoke in the UK, measured over several decades, and respiratory mortality.

Geography and social distribution of malaria in Indonesian Papua: a cross-sectional study

Background

Despite being one of the world’s most affected regions, only little is known about the social and spatial distributions of malaria in Indonesian Papua. Existing studies tend to be descriptive in nature; their inferences are prone to confounding and selection biases. At the same time, there remains limited malaria-cartographic activity in the region. Analysing a subset (N = 22,643) of the National Basic Health Research 2007 dataset (N = 987,205), this paper aims to quantify the district-specific risk of malaria in Papua and to understand how socio-demographic/economic factors measured at individual and district levels are associated with individual’s probability of contracting the disease.

Methods

We adopt a Bayesian hierarchical logistic regression model that accommodates not only the nesting of individuals within the island’s 27 administrative units but also the spatial autocorrelation among these locations. Both individual and contextual characteristics are included as predictors in the model; a normal conditional autoregressive prior and an exchangeable one are assigned to the random effects. Robustness is then assessed through sensitivity analyses using alternative hyperpriors.

Results

We find that rural Papuans as well as those who live in poor, densely forested, lowland districts are at a higher risk of infection than their counterparts. We also find age and gender differentials in malaria prevalence, if only to a small degree. Nine districts are estimated to have higher-than-expected malaria risks; the extent of spatial variation on the island remains notable even after accounting for socio-demographic/economic risk factors.

Conclusions

Although we show that malaria is geography-dependent in Indonesian Papua, it is also a disease of poverty. This means that malaria eradication requires not only biological (proximal) interventions but also social (distal) ones.

Finding big shots: small-area mapping and spatial modelling of obesity among Swiss male conscripts

BACKGROUND

In Switzerland, as in other developed countries, the prevalence of overweight and obesity has increased substantially since the early 1990s. Most of the analyses so far have been based on sporadic surveys or self-reported data and did not offer potential for small-area analyses. The goal of this study was to investigate spatial variation and determinants of obesity among young Swiss men using recent conscription data.

METHODS

A complete, anonymized dataset of conscription records for the 2010-2012 period were provided by Swiss Armed Forces. We used a series of Bayesian hierarchical logistic regression models to investigate the spatial pattern of obesity across 3,187 postcodes, varying them by type of random effects (spatially unstructured and structured), level of adjustment by individual (age and professional status) and area-based [urbanicity and index of socio-economic position (SEP)] characteristics.

RESULTS

The analysed dataset consisted of 100,919 conscripts, out of which 5,892 (5.8 %) were obese. Crude obesity prevalence increased with age among conscripts of lower individual and area-based SEP and varied greatly over postcodes. Best model's estimates of adjusted odds ratios of obesity on postcode level ranged from 0.61 to 1.93 and showed a strong spatial pattern of obesity risk across the country. Odds ratios above 1 concentrated in central and north Switzerland. Smaller pockets of elevated obesity risk also emerged around cities of Geneva, Fribourg and Lausanne. Lower estimates were observed in North-East and East as well as south of the Alps. Importantly, small regional outliers were observed and patterning did not follow administrative boundaries. Similarly as with crude obesity prevalence, the best fitting model confirmed increasing risk of obesity with age and among conscripts of lower professional status. The risk decreased with higher area-based SEP and, to a lesser degree - in rural areas.

CONCLUSION

In Switzerland, there is a substantial spatial variation in obesity risk among young Swiss men. Small-area estimates of obesity risk derived from conscripts records contribute to its understanding and could be used to design further studies and interventions.

Análise espacial de dados de contagem com excesso de zeros aplicado ao estudo da incidência de dengue em Campinas, São Paulo, Brasil

Resumo: A incidência de dengue ocorre predominantemente em áreas urbanas das cidades. Identificar o padrão de distribuição espacial da doença no nível local contribui na formulação de estratégias de controle e prevenção da doença. A análise espacial de dados de contagem para pequenas áreas comumente viola as suposições dos modelos tradicionais de Poisson, devido à quantidade excessiva de zeros. Neste estudo, comparou-se o desempenho de quatro modelos de contagem utilizados no mapeamento de doenças: Poisson, Binomial negativa, Poisson inflacionado de zeros e Binomial negativa inflacionado de zeros. Os métodos foram comparados em um estudo de simulação. Os modelos analisados no estudo de simulação foram aplicados em um estudo ecológico espacial, aos dados de dengue agregados por setores censitários, do Município de Campinas, São Paulo, Brasil, em 2007. A análise espacial foi conduzida por modelos hierárquicos bayesianos. O modelo de Poisson inflacionado de zeros apresentou melhor desempenho para estimar o risco relativo de incidência de dengue nos setores censitários.

Small-area spatiotemporal analysis of pedestrian and bicyclist injuries in New York City

BACKGROUND

This study quantifies the spatiotemporal risk of pedestrian and bicyclist injury in New York City at the census tract level over a recent 10-year period, identifies areas of increased risk, and evaluates the role of socioeconomic and traffic-related variables in injury risk.

METHODS

Crash data on 140,835 pedestrian and bicyclist injuries in 1908 census tracts from 2001 to 2010 were obtained from the New York City Department of Transportation. We analyzed injury counts within census tracts with Bayesian hierarchical spatial models using integrated nested Laplace approximations. The model included variables for social fragmentation, median household income, and average vehicle speed and traffic density, as well as a spatially unstructured random effect term, a spatially structured conditional autoregression term, a first-order random walk-correlated time variable, and an interaction term for time and place. Incidence density ratios, credible intervals, and probability exceedances were calculated and mapped.

RESULTS

The yearly rate of crashes involving injuries to "pedestrians" (including bicyclists) decreased 16.2% over the study period, from 23.7 per 10,000 population to 16.2 per 10,000. The temporal term in the spatiotemporal model indicated that much of the decrease over the study period occurred during the first 4 years of the study period. Despite an overall decrease, the model identified census tracts that were at persistently high risk of pedestrian injury throughout the study period, as well as areas that experienced sporadic annual increases in risk. Aggregate social, economic, and traffic-related measures were associated with pedestrian injury risk at the ecologic level. Every 1-unit increase in a standardized social fragmentation index was associated with a 19% increase in pedestrian injury risk (incidence density ratio = 1.19 [95% credible interval = 1.16 - 1.23]), and every 1 standardized unit increase in traffic density was associated with a 20% increase in pedestrian injury risk (1.20 [1.15 - 1.26]). Each 10-mile-per-hour increase in average traffic speed in a census tract was associated with a 24% decrease in pedestrian injury risk (0.76 [0.69 - 0.83]).

CONCLUSIONS

The risk of a pedestrian or bicyclist being struck by a motor vehicle in New York City decreased from 2001 to 2004 and held fairly steady thereafter. Some census tracts in the city did not benefit from overall reductions or experienced sporadic years of increased risk compared with the city as a whole. Injury risk at the census tract level was associated with social, economic, and traffic-related factors.

An examination of disparities in cancer incidence in Texas using Bayesian random coefficient models

Disparities in cancer risk exist between ethnic groups in the United States. These disparities often result from differential access to healthcare, differences in socioeconomic status and differential exposure to carcinogens. This study uses cancer incidence data from the population based Texas Cancer Registry to investigate the disparities in digestive and respiratory cancers from 2000 to 2008. A Bayesian hierarchical regression approach is used. All models are fit using the INLA method of Bayesian model estimation. Specifically, a spatially varying coefficient model of the disparity between Hispanic and Non-Hispanic incidence is used. Results suggest that a spatio-temporal heterogeneity model best accounts for the observed Hispanic disparity in cancer risk. Overall, there is a significant disadvantage for the Hispanic population of Texas with respect to both of these cancers, and this disparity varies significantly over space. The greatest disparities between Hispanics and Non-Hispanics in digestive and respiratory cancers occur in eastern Texas, with patterns emerging as early as 2000 and continuing until 2008.

Application of Bayesian Multilevel Space-Time Models to Study Relative Risk of Esophageal Cancer in Iran 2005-2007 at a County Level

BACKGROUND

Reported age standardized incidence rates for esophageal cancer in Iran are 0.88 and 6.15 for females and males, at fifth and the eighth ranks, respectively, of cancers overall. The present study aimed to map relative risk using more realistic and less problematic methods than common estimators.

MATERIALS AND METHODS

In this ecological investigation, the studied population consisted of all esophageal cancer patients in Iran from 2005 to 2007. The Bayesian multilevel space-time model with three levels of county, province, and time was used to measure the relative risk of esophageal cancer. Analyses were conducted using R package INLA.

RESULTS

The total number of registered patients was 7,160. According to the results, the three-level model with adjustment for risk factors of physical activity and smoking had the best fit among all models .The overall temporal trend was significantly increasing. At county level, Ahar, Marand, Salmas, Bojnoord, Saghez, Sarakhs, Shahroud and Torbatejam had the highest relative risks. Physical activity was found to have significant direct association with risk of developing esophageal cancer.

CONCLUSIONS

Given to great variation across geographical areas, many different factors affect the incidence of esophageal cancer. Conducting further studies at the individual level in areas with high incidence could provide more detailed information on risk factors of esophageal cancer.

Comparing INLA and OpenBUGS for hierarchical Poisson modeling in disease mapping

The recently developed R package INLA (Integrated Nested Laplace Approximation) is becoming a more widely used package for Bayesian inference. The INLA software has been promoted as a fast alternative to MCMC for disease mapping applications. Here, we compare the INLA package to the MCMC approach by way of the BRugs package in R, which calls OpenBUGS. We focus on the Poisson data model commonly used for disease mapping. Ultimately, INLA is a computationally efficient way of implementing Bayesian methods and returns nearly identical estimates for fixed parameters in comparison to OpenBUGS, but falls short in recovering the true estimates for the random effects, their precisions, and model goodness of fit measures under the default settings. We assumed default settings for ground truth parameters, and through altering these default settings in our simulation study, we were able to recover estimates comparable to those produced in OpenBUGS under the same assumptions.

Space-time airborne disease mapping applied to detect specific behaviour of varicella in Valencia, Spain

Airborne diseases are one of humanity's most feared sicknesses and have regularly caused concern among specialists. Varicella is an airborne disease which usually affects children before the age of 10. Because of its nature, varicella gives rise to interesting spatial, temporal and spatio-temporal patterns. This paper studies spatio-temporal exploratory analysis tools to detect specific behaviour of varicella in the city of Valencia, Spain, from 2008 to 2013. These methods have shown a significant association between the spatial and the temporal component, confirmed by the space-time models applied to the data. High relative risk of varicella is observed in economically disadvantaged regions, areas less involved in vaccination programmes.

Estimation of district-level under-5 mortality in Zambia using birth history data, 1980-2010

Birth history data-the primary source of data on under-5 mortality in developing countries-are infrequently used for subnational estimates due to concerns over small sample sizes. In this study we consider different methods for analyzing birth history data in combination with various small area models. We construct a simulation environment to assess the performance of different combinations of birth history methods and small area models in terms of bias, efficiency, and coverage. We find that performance is highly dependent on the birth history method applied and how temporal trends are accounted for. We estimated trends in district-level under-5 mortality in Zambia from 1980 to 2010 using the best-performing model. We find that under-5 mortality is highly variable within Zambia: there was a 1.8-fold difference between the lowest and highest levels in 2010, and declines over the period 1980 to 2010 ranged from less than 5% to more than 50%.

Geographic variation of failure-to-rescue in public acute hospitals in New South Wales, Australia

Despite the wide acceptance of Failure-to-Rescue (FTR) as a patient safety indicator (defined as the deaths among surgical patients with treatable complications), no study has explored the geographic variation of FTR in a large health jurisdiction. Our study aimed to explore the spatiotemporal variations of FTR rates across New South Wales (NSW), Australia. We conducted a population-based study using all admitted surgical patients in public acute hospitals during 2002-2009 in NSW, Australia. We developed a spatiotemporal Poisson model using Integrated Nested Laplace Approximation (INLA) methods in a Bayesian framework to obtain area-specific adjusted relative risk. Local Government Area (LGA) was chosen as the areal unit. LGA-aggregated covariates included age, gender, socio-economic and remoteness index scores, distance between patient residential postcode and the treating hospital, and a quadratic time trend. We studied 4,285,494 elective surgical admissions in 82 acute public hospitals over eight years in NSW. Around 14% of patients who developed at least one of the six FTR-related complications (58,590) died during hospitalization. Of 153 LGAs, patients who lived in 31 LGAs, accommodating 48% of NSW patients at risk, were exposed to an excessive adjusted FTR risk (10% to 50%) compared to the state-average. They were mostly located in state's centre and western Sydney. Thirty LGAs with a lower adjusted FTR risk (10% to 30%), accommodating 8% of patients at risk, were mostly found in the southern parts of NSW and Sydney east and south. There were significant spatiotemporal variations of FTR rates across NSW over an eight-year span. Areas identified with significantly high and low FTR risks provide potential opportunities for policy-makers, clinicians and researchers to learn from the success or failure of adopting the best care for surgical patients and build a self-learning organisation and health system.

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.

Trends in socioeconomic inequalities in ischemic heart disease mortality in small areas of nine Spanish cities from 1996 to 2007 using smoothed ANOVA

The aim of this study was to analyze the evolution of socioeconomic inequalities in mortality due to ischemic heart diseases (IHD) in the census tracts of nine Spanish cities between the periods 1996-2001 and 2002-2007. Among women, there are socioeconomic inequalities in IHD mortality in the first period which tended to remain stable or even increase in the second period in most of the cities. Among men, in general, no socioeconomic inequalities have been detected for this cause in either of the periods. These results highlight the importance of intra-urban inequalities in mortality due to IHD and their evolution over time.

Comparison of Bayesian methods for flexible modeling of spatial risk surfaces in disease mapping

Bayesian hierarchical models usually model the risk surface on the same arbitrary geographical units for all data sources. Poisson/gamma random field models overcome this restriction as the underlying risk surface can be specified independently to the resolution of the data. Moreover, covariates may be considered as either excess or relative risk factors. We compare the performance of the Poisson/gamma random field model to the Markov random field (MRF)-based ecologic regression model and the Bayesian Detection of Clusters and Discontinuities (BDCD) model, in both a simulation study and a real data example. We find the BDCD model to have advantages in situations dominated by abruptly changing risk while the Poisson/gamma random field model convinces by its flexibility in the estimation of random field structures and by its flexibility incorporating covariates. The MRF-based ecologic regression model is inferior. WinBUGS code for Poisson/gamma random field models is provided.

The impact of spatial scales and spatial smoothing on the outcome of bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matérn correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

Estimation of malaria incidence in northern Namibia in 2009 using Bayesian conditional-autoregressive spatial-temporal models

As malaria transmission declines, it becomes increasingly important to monitor changes in malaria incidence rather than prevalence. Here, a spatio-temporal model was used to identify constituencies with high malaria incidence to guide malaria control. Malaria cases were assembled across all age groups along with several environmental covariates. A Bayesian conditional-autoregressive model was used to model the spatial and temporal variation of incidence after adjusting for test positivity rates and health facility utilisation. Of the 144,744 malaria cases recorded in Namibia in 2009, 134,851 were suspected and 9893 were parasitologically confirmed. The mean annual incidence based on the Bayesian model predictions was 13 cases per 1000 population with the highest incidence predicted for constituencies bordering Angola and Zambia. The smoothed maps of incidence highlight trends in disease incidence. For Namibia, the 2009 maps provide a baseline for monitoring the targets of pre-elimination.

Impact of community-based larviciding on the prevalence of malaria infection in Dar es Salaam, Tanzania

Background

The use of larval source management is not prioritized by contemporary malaria control programs in sub-Saharan Africa despite historical success. Larviciding, in particular, could be effective in urban areas where transmission is focal and accessibility to Anopheles breeding habitats is generally easier than in rural settings. The objective of this study is to assess the effectiveness of a community-based microbial larviciding intervention to reduce the prevalence of malaria infection in Dar es Salaam, United Republic of Tanzania.

Methods and Findings

Larviciding was implemented in 3 out of 15 targeted wards of Dar es Salaam in 2006 after two years of baseline data collection. This intervention was subsequently scaled up to 9 wards a year later, and to all 15 targeted wards in 2008. Continuous randomized cluster sampling of malaria prevalence and socio-demographic characteristics was carried out during 6 survey rounds (2004–2008), which included both cross-sectional and longitudinal data (N = 64,537). Bayesian random effects logistic regression models were used to quantify the effect of the intervention on malaria prevalence at the individual level. Effect size estimates suggest a significant protective effect of the larviciding intervention. After adjustment for confounders, the odds of individuals living in areas treated with larviciding being infected with malaria were 21% lower (Odds Ratio = 0.79; 95% Credible Intervals: 0.66–0.93) than those who lived in areas not treated. The larviciding intervention was most effective during dry seasons and had synergistic effects with other protective measures such as use of insecticide-treated bed nets and house proofing (i.e., complete ceiling or window screens).

Conclusion

A large-scale community-based larviciding intervention significantly reduced the prevalence of malaria infection in urban Dar es Salaam.

A hitchhiker's view on spatial statistics and spatial econometrics for lattice data

Spatial statistics and spatial econometrics fill an impressive body of literature, clearly demonstrating the importance of the corresponding methods. Though the two fields are being referred to in the same breath, they differ substantially as they pursue quite different objectives and hence exhibit different interpretations. In this article we shed some light on the nature and relevance of those to demonstrate how the models can be employed with three data examples in a regional context. The discussion covers models for continuous responses and count data, real data examples and Monte Carlo simulations.

Does the effect of gender modify the relationship between deprivation and mortality?

Background

In this study we propose improvements to the method of elaborating deprivation indexes. First, in the selection of the variables, we incorporated a wider range of both objective and subjective measures. Second, in the statistical methodology, we used a distance indicator instead of the standard aggregating method principal component analysis. Third, we propose another methodological improvement, which consists in the use of a more robust statistical method to assess the relationship between deprivation and health responses in ecological regressions.

Methods

We conducted an ecological small-area analysis based on the residents of the Metropolitan region of Barcelona in the period 1994–2007. Standardized mortality rates, stratified by sex, were studied for four mortality causes: tumor of the bronquial, lung and trachea, diabetes mellitus type II, breast cancer, and prostate cancer. Socioeconomic conditions were summarized using a deprivation index. Sixteen socio-demographic variables available in the Spanish Census of Population and Housing were included. The deprivation index was constructed by aggregating the above-mentioned variables using the distance indicator, DP₂. For the estimation of the ecological regression we used hierarchical Bayesian models with some improvements.

Results

At greater deprivation, there is an increased risk of dying from diabetes for both sexes and of dying from lung cancer for men. On the other hand, at greater deprivation, there is a decreased risk of dying from breast cancer and lung cancer for women. We did not find a clear relationship in the case of prostate cancer (presenting an increased risk but only in the second quintile of deprivation).

Conclusions

We believe our results were obtained using a more robust methodology. First off, we have built a better index that allows us to directly collect the variability of contextual variables without having to use arbitrary weights. Secondly, we have solved two major problems that are present in spatial ecological regressions, i.e. those that use spatial data and, consequently, perform a spatial adjustment in order to obtain consistent estimators.