Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk

Estimation and probabilistic projection of age- and sex-specific mortality rates across Brazilian municipalities between 2010 and 2030

BACKGROUND

Mortality rate estimation in small areas can be difficult due the low number of events/exposure (i.e. stochastic error). If the death records are not completed, it adds a systematic uncertainty on the mortality estimates. Previous studies in Brazil have combined demographic and statistical methods to partially overcome these issues. We estimated age- and sex-specific mortality rates for all 5,565 Brazilian municipalities in 2010 and forecasted probabilistic mortality rates and life expectancy between 2010 and 2030.

METHODS

We used a combination of the Tool for Projecting Age-Specific Rates Using Linear Splines (TOPALS), Bayesian Model, Spatial Smoothing Model and an ad-hoc procedure to estimate age- and sex-specific mortality rates for all Brazilian municipalities for 2010. Then we adapted the Lee-Carter model to forecast mortality rates by age and sex in all municipalities between 2010 and 2030.

RESULTS

The adjusted sex- and age-specific mortality rates for all Brazilian municipalities in 2010 reveal a distinct regional pattern, showcasing a decrease in life expectancy in less socioeconomically developed municipalities when compared to estimates without adjustments. The forecasted mortality rates indicate varying regional improvements, leading to a convergence in life expectancy at birth among small areas in Brazil. Consequently, a reduction in the variability of age at death across Brazil's municipalities was observed, with a persistent sex differential.

CONCLUSION

Mortality rates at a small-area level were successfully estimated and forecasted, with associated uncertainty estimates also generated for future life tables. Our approach could be applied across countries with data quality issues to improve public policy planning.

A Bayesian multistage spatio-temporally dependent model for spatial clustering and variable selection

In spatio-temporal epidemiological analysis, it is of critical importance to identify the significant covariates and estimate the associated time-varying effects on the health outcome. Due to the heterogeneity of spatio-temporal data, the subsets of important covariates may vary across space and the temporal trends of covariate effects could be locally different. However, many spatial models neglected the potential local variation patterns, leading to inappropriate inference. Thus, this article proposes a flexible Bayesian hierarchical model to simultaneously identify spatial clusters of regression coefficients with common temporal trends, select significant covariates for each spatial group by introducing binary entry parameters and estimate spatio-temporally varying disease risks. A multistage strategy is employed to reduce the confounding bias caused by spatially structured random components. A simulation study demonstrates the outperformance of the proposed method, compared with several alternatives based on different assessment criteria. The methodology is motivated by two important case studies. The first concerns the low birth weight incidence data in 159 counties of Georgia, USA, for the years 2007 to 2018 and investigates the time-varying effects of potential contributing covariates in different cluster regions. The second concerns the circulatory disease risks across 323 local authorities in England over 10 years and explores the underlying spatial clusters and associated important risk factors.

Geographic disparities and temporal changes of COVID-19 incidence risks in North Dakota, United States

BACKGROUND

COVID-19 is an important public health concern due to its high morbidity, mortality and socioeconomic impact. Its burden varies by geographic location affecting some communities more than others. Identifying these disparities is important for guiding health planning and service provision. Therefore, this study investigated geographical disparities and temporal changes of the percentage of positive COVID-19 tests and COVID-19 incidence risk in North Dakota.

METHODS

COVID-19 retrospective data on total number of tests and confirmed cases reported in North Dakota from March 2020 to September 2021 were obtained from the North Dakota COVID-19 Dashboard and Department of Health, respectively. Monthly incidence risks of the disease were calculated and reported as number of cases per 100,000 persons. To adjust for geographic autocorrelation and the small number problem, Spatial Empirical Bayesian (SEB) smoothing was performed using queen spatial weights. Identification of high-risk geographic clusters of percentages of positive tests and COVID-19 incidence risks were accomplished using Tango's flexible spatial scan statistic. ArcGIS was used to display and visiualize the geographic distribution of percentages of positive tests, COVID-19 incidence risks, and high-risk clusters.

RESULTS

County-level percentages of positive tests and SEB incidence risks varied by geographic location ranging from 0.11% to 13.67% and 122 to 16,443 cases per 100,000 persons, respectively. Clusters of high percentages of positive tests were consistently detected in the western part of the state. High incidence risks were identified in the central and south-western parts of the state, where significant high-risk spatial clusters were reported. Additionally, two peaks (August 2020-December 2020 and August 2021-September 2021) and two non-peak periods of COVID-19 incidence risk (March 2020-July 2020 and January 2021-July 2021) were observed.

CONCLUSION

Geographic disparities in COVID incidence risks exist in North Dakota with high-risk clusters being identified in the rural central and southwest parts of the state. These findings are useful for guiding intervention strategies by identifying high risk communities so that resources for disease control can be better allocated to communities in need based on empirical evidence. Future studies will investigate predictors of the identified disparities so as to guide planning, disease control and health policy.

Bayesian disease mapping: Past, present, and future

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

The effect of pre-aggregation scale on spatially adaptive filters

Choropleth mapping continues to be a dominant mapping technique despite suffering from the Modifiable Areal Unit Problem (MAUP), which may distort disease risk patterns when different administrative units are used. Spatially adaptive filters (SAF) are one mapping technique that can address the MAUP, but the limitations and accuracy of spatially adaptive filters are not well tested. Our work examines these limitations by using varying levels of data aggregation using a case study of geocoded breast cancer screening data and a synthetic georeferenced population dataset that allows us to calculate SAFs at the individual-level. Data were grouped into four administrative boundaries (i.e., county, Zip Code Tabulated Areas, census tracts, and census blocks) and compared to individual-level data (control). Correlation assessed the similarity of SAFs, and map algebra calculated error maps compared to control. This work describes how pre-aggregation affects the level of spatial detail, map patterns, and over and under-prediction.

Persistence of Schistosomiasis-Related Morbidity in Northeast Brazil: An Integrated Spatio-Temporal Analysis

Objective: To analyze the temporal trend and spatial patterns of schistosomiasis-related morbidity in Northeast Brazil, 2001–2017. Methods: Ecological study, of time series and spatial analysis, based on case notifications and hospital admission data, as provided by the Ministry of Health. Results: Of a total of 15,574,392 parasitological stool examinations, 941,961 (6.0%) were positive, mainly on the coastline of Pernambuco, Alagoas and Sergipe states. There was a reduction from 7.4% (2002) to 3.9% (2017) of positive samples and in the temporal trend of the detection rate (APC—11.6*; Confidence Interval 95%—13.9 to −9.1). There was a total of 5879 hospital admissions, with 40.4% in Pernambuco state. The hospitalization rate reduced from 0.82 (2001) to 0.02 (2017) per 100,000 inhabitants. Conclusion: Despite the reduction in case detection and hospitalizations, the persistence of focal areas of the disease in coastal areas is recognized. This reduction may indicate a possible positive impact of control on epidemiological patterns, but also operational issues related to access to healthcare and the development of surveillance and control actions in the Unified Health System.

Spatial Analysis of Factors Associated with Hospitalizations for Ambulatory Care Sensitive Conditions among Old Adults in Minas Gerais State

AIM

To investigate the geographical variability and factors associated with hospitalizations for ambulatory care sensitive conditions (ACSC) among older adults living in the state of Minas Gerais.

METHODOLOGY

This is an ecological study, based on data from the National Hospital Information System (SIH-SUS). Municipal rates of hospitalization for ACSC were compared to the state's average rate, and analysis of associated factors included sociodemographic characteristics, supply of health services and primary health care (PHC) activities. Data analysis was based on Bayesian spatial modeling.

RESULTS

Most municipalities in Minas Gerais (479 or 56.2%) had a rate of hospitalization for ACSC below the state average. After multivariate analysis, income (β = -0,0008; 95%CI: -0.0014 - -0,0002) and the Family Health Strategy coverage (β = -0.4269; 95%CI: -0.7988 - -0.1116) were negatively associated with the risk of hospitalization for ACSC, while the availability of hospital beds (β = 0.0271; 95%CI 0.0211 - 0.0331) was positively associated. The characteristics of PHC did not show any association with the rate of hospitalization for ACSC.

CONCLUSION

the rates of hospitalization for ACSC in the elderly population were influenced by the PHC coverage, but also by external factors such as income and structure and provision of health services, indicating that the meeting of population health demands passes through actions that go beyond the health sector, including investment in the reduction of poverty and inequality and expansion of access to PHC.

Temporal and spatial trends of adult mortality in small areas of Brazil, 1980–2010

To determine the variations and spatial patterns of adult mortality across regions, over time, and by sex for 137 small areas in Brazil, we first apply TOPALS to estimate and smooth mortality rates and then use death distribution methods to evaluate the quality of the mortality data. Lastly, we employ spatial autocorrelation statistics and cluster analysis to identify the adult mortality trends and variations in these areas between 1980 and 2010. We find not only that regions in Brazil’s South and Southeast already had complete death registration systems prior to the study period, but that the completeness of death count coverage improved over time across the entire nation—most especially in lesser developed regions—probably because of public investment in health data collection. By also comparing adult mortality by sex and by region, we document a mortality sex differential in favor of women that remains high over the entire study period, most probably as a result of increased morbidity from external causes, especially among males. This increase also explains the concentration of high male mortality levels in some areas.

Geographic distribution of staphylococcus spp. infections and antimicrobial resistance among dogs from Gauteng Province presented at a veterinary teaching hospital in South Africa

The objective of this study was to investigate spatial patterns of staphylococcal infections and resistance patterns of clinical isolates among dogs from Gauteng province in South Africa. Data from records of 1497 dog clinical samples submitted to a veterinary teaching hospital between 2007 and 2012 were used in the study. Spatial empirical Bayesian smoothed risk maps were used to investigate spatial patterns of staphylococcal infections, antimicrobial resistance (AMR), and multidrug resistance (MDR). Moran's I and spatial scan statistics were used to investigate spatial clusters at municipal and town spatial scales. Significant clusters of staphylococcal infections were identified at both the municipal (Relative Risk [RR] = 1.71, p = 0.003) and town (RR = 1.65, p = 0.039) scales. However, significant clusters of AMR (p = 0.003) and MDR (p = 0.007) were observed only at the town scale. Future larger studies will need to investigate local determinants of geographical distribution of the clusters so as to guide targeted control efforts.

Application of sandwich spatial estimation method in cancer mapping: A case study for breast cancer mortality in the Chinese mainland, 2005

High-accuracy spatial distribution estimation is crucial for cancer prevention and control. Due to their complicated pathogenic factors, the distributions of many cancers' mortalities appear blocky, and spatial heterogeneity is common. However, most of the commonly used cancer mapping methods are based on spatial autocorrelation theory. Sandwich estimation is a new method based on spatial heterogeneity theory. A modified sandwich estimation method suitable for the estimation of cancer mortality distribution is proposed in this study. The variances of cancer mortality data are used to fuse sandwich estimation results from various auxiliary variables, the feasibility of which in estimating cancer mortality distributions is explained theoretically. The breast cancer (BC) mortality of the Chinese mainland in 2005 was taken as a case, and the accuracy of the modified sandwich estimation method was compared with that of the Hierarchical Bayesian (HB), the Co-Kriging (CK) and the Ordinary Kriging (OK) methods. The accuracy of the modified sandwich estimation method was better than the HB, the CK and the OK methods, and the estimation result from the modified sandwich estimation method was more likely to be acceptable. Therefore, this study represents an attempt to apply the sandwich estimation method to the estimation of cancer mortality distributions with strong spatial heterogeneity, which holds great potential for further application.

Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records

High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with probabilistic prior information on death registration coverage derived from demographic estimation techniques, such as Death Distribution Methods, and from field audits by public health experts. We test the model on small-area data from Brazil. Incorporating external estimates of vital registration coverage though priors improves small-area mortality estimates by accounting for underregistration and automatically producing measures of uncertainty. Bayesian estimates show that when mortality levels in small areas are compared, noise often dominates signal. Differences in local point estimates of life expectancy are often small relative to uncertainty, even for relatively large areas in a populous country like Brazil.

Impact of mammography screening programmes on breast cancer mortality in Switzerland, a country with different regional screening policies

INTRODUCTION

In the past decades, mortality due to breast cancer has declined considerably in Switzerland and other developed countries. The reasons for this decline remain controversial as several factors occurred almost simultaneously, including important advances in treatment approaches, breast cancer awareness and the introduction of mammography screening programmes in many European countries. In Switzerland, mammography screening programmes (MSPs) have existed in some regions for over 20 years but do not yet exist in others. This offers the possibility to analyse its effects with modern spatiotemporal methodology. We aimed to assess the spatiotemporal patterns and the effect of MSPs on breast cancer mortality.

SETTING

Switzerland.

PARTICIPANTS

The study covers breast cancer deaths of the female population of Switzerland during the period 1969-2012. We retrieved data from the Swiss Federal Statistical Office aggregated on a small-area level.

DESIGN

We fitted Bayesian hierarchical spatiotemporal models on death rates indirectly standardised by national references. We used linguistic region, degree of urbanisation, duration of population-based screening programmes and socioeconomic index as covariates.

RESULTS

In Switzerland, breast cancer mortality in women slightly increased until 1989-1992 and declined strongly thereafter. Until 2009-2012, the standardised mortality ratio declined to 57% (95% CI 54% to 60%) of the 1969-1972 value. None of the other coefficients of the spatial regressions had a significant effect on breast cancer mortality. In 2009-2012, no region had significantly elevated or reduced breast cancer mortality at 95% credible interval level compared with the national mean.

CONCLUSION

There has been a strong reduction of breast cancer mortality from the 1990s onwards. No important spatial disparities were observed. The factors studied (urbanisation, language, duration of population-based MSP and socioeconomic characteristics) did not seem to have an influence on them. Low participation rates and opportunistic screening use may have contributed to the low impact of MSPs.

Zero-inflated spatio-temporal models for disease mapping

In this paper, our aim is to analyze geographical and temporal variability of disease incidence when spatio-temporal count data have excess zeros. To that end, we consider random effects in zero-inflated Poisson models to investigate geographical and temporal patterns of disease incidence. Spatio-temporal models that employ conditionally autoregressive smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are proposed. The analysis of these complex models is computationally difficult from the frequentist perspective. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning method provides a frequentist approach to mixed models that is also computationally convenient. We propose to use data cloning, which yields to maximum likelihood estimation, to conduct frequentist analysis of zero-inflated spatio-temporal modeling of disease incidence. One of the advantages of the data cloning approach is that the prediction and corresponding standard errors (or prediction intervals) of smoothing disease incidence over space and time is easily obtained. We illustrate our approach using a real dataset of monthly children asthma visits to hospital in the province of Manitoba, Canada, during the period April 2006 to March 2010. Performance of our approach is also evaluated through a simulation study.

Spatial analysis of common gastrointestinal tract cancers in counties of Iran

BACKGROUND

Gastrointestinal tract cancers are among the most common cancers in Iran and comprise approximately 38% of all the reported cases of cancer. This study aimed to describe the epidemiology and to investigate spatial clustering of common cancers of the gastrointestinal tract across the counties of Iran using full Bayesian smoothing and Moran I Index statistics.

MATERIALS AND METHODS

The data of the national registry cancer were used in this study. Besides, indirect standardized rates were calculated for 371 counties of Iranand smoothed using Winbug 1.4 software with a full Bayesian method. Global Moran I and local Moran I were also used to investigate clustering.

RESULTS

According to the results, 75,644 new cases of cancer were nationally registered in Iran among which 18,019 cases (23.8%) were esophagus, gastric, colorectal, and liver cancers. The results of Global Moran's I test were 0.60 (P=0.001), 0.47 (P=0.001), 0.29 (P=0.001), and 0.40 (P=0.001) for esophagus, gastric, colorectal, and liver cancers, respectively. This shows clustering of the four studied cancers in Iran at the national level.

CONCLUSIONS

High level clustering of the cases was seen in northern, northwestern, western, and northeastern areas for esophagus, gastric, and colorectal cancers. Considering liver cancer, high clustering was observed in some counties in central, northeastern, and southern areas.

40 years of progress in female cancer death risk: a Bayesian spatio-temporal mapping analysis in Switzerland

BACKGROUND

In the past decades, mortality of female gender related cancers declined in Switzerland and other developed countries. Differences in the decrease and in spatial patterns within Switzerland have been reported according to urbanisation and language region, and remain controversial. We aimed to investigate geographical and temporal trends of breast, ovarian, cervical and uterine cancer mortality, assess whether differential trends exist and to provide updated results until 2011.

METHODS

Breast, ovarian, cervical and uterine cancer mortality and population data for Switzerland in the period 1969-2011 was retrieved from the Swiss Federal Statistical office (FSO). Cases were grouped into <55 year olds, 55-74 year olds and 75+ year olds. The geographical unit of analysis was the municipality. To explore age- specific spatio-temporal patterns we fitted Bayesian hierarchical spatio-temporal models on subgroup-specific death rates indirectly standardized by national references. We used linguistic region and degree of urbanisation as covariates.

RESULTS

Female cancer mortality continuously decreased in terms of rates in all age groups and cancer sites except for ovarian cancer in 75+ year olds, especially since 1990 onwards. Contrary to other reports, we found no systematic difference between language regions. Urbanisation as a proxy for access to and quality of medical services, education and health consciousness seemed to have no influence on cancer mortality with the exception of uterine and ovarian cancer in specific age groups. We observed no obvious spatial pattern of mortality common for all cancer sites. Rate reduction in cervical cancer was even stronger than for other cancer sites.

CONCLUSIONS

Female gender related cancer mortality is continuously decreasing in Switzerland since 1990. Geographical differences are small, present on a regional or canton-overspanning level, and different for each cancer site and age group. No general significant association with cantonal or language region borders could be observed.

Health risks due to pre-harvesting sugarcane burning in São Paulo State, Brazil

After 2003, a new period of expansion of the sugarcane culture began in Brazil. Pre-harvesting burning of sugarcane straw is an agricultural practice that, despite the nuisance for the population and pollution generated, still persisted in over 70% of the municipalities of São Paulo State in 2010. In order to study the distribution of this risk factor, an ecological epidemiological study was conducted associating the rates of deaths and hospital admissions for respiratory diseases, for each municipality in the State, with the exposure to the pre-harvesting burning of sugarcane straw. A Bayesian multivariate regression model, controlled for the possible effects of socioeconomic and climate (temperature, humidity, and rainfall) variations, has been used. The effect on health was measured by the standardized mortality and morbidity ratio. The measures of exposure to the pre-harvesting burning used were: percentage of the area of sugarcane harvested with burning, average levels of aerosol, and number of outbreaks of burning. The autocorrelation between data was controlled using a neighborhood matrix. It was observed that the increase in the number of outbreaks of burning was significantly associated with higher rates of hospital admissions for respiratory disease in children under five years old. Pre-harvesting burning of sugarcane effectively imposes risk to population health and therefore it should be eliminated.

Using lung cancer mortality to indirectly approximate smoking patterns in space

Smoking is the leading cause of lung cancer. Non-smoking factors have been associated with the disease. Existing Swiss survey data only capture the country partially and temporal coverage does not allow for a time lag between exposure to tobacco and lung cancer outbreak. Knowledge about the distribution of tobacco-use is essential to estimate its contribution to disease burden. Bayesian regression models were applied to estimate spatial smoking patterns. Data were provided from the Swiss Health Survey (14521 participants). Regression models with spatial random effects (SREs) were employed to obtain smoking proxies based on mortality rates and SREs adjusted for environmental exposures. Population attributable fractions were estimated to assess the burden of tobacco-use on lung cancer mortality. Correlation between observed smoking prevalence with smoking proxies was moderate and stronger in females. In the absence of sufficient survey data, smooth unadjusted mortality rates can be used to assess smoking patterns in Switzerland.

Geographical variation analysis of all-cause hospital readmission cases in Winnipeg, Canada

BACKGROUND

Hospital readmission is costly and potentially avoidable. The concept of virtual wards as a new model of care is intended to reduce hospital readmissions by providing short-term transitional care to high-risk and complex patients in the community. In order to provide information regarding the development of virtual wards in the Winnipeg Health Region, Canada, this study used spatial statistics to identify geographic variations of hospital readmissions in 25 neighborhood clusters.

METHODS

The data were obtained from the Population Health Research Data Repository housed at the Manitoba Centre for Health Policy. We used a Bayesian Disease Mapping approach which applied Markov chain Monte Carlo (MCMC) for cluster detection.

RESULTS

Between 2005/06 and 2008/09, 123,842 patients were hospitalized in all Winnipeg hospitals. Of these, 41,551 (33%) were readmitted to hospital in the year following discharge. Most of these readmitted patients (89.4%) had 1-2 readmissions, while 11.6% of readmitted patients had more than 2 readmissions after initial discharge. The smoothed age- and sex- adjusted relative risk rates of hospital readmission in 25 Winnipeg neighborhood clusters ranged between 0.73 and 1.27. We found that there were spatial cluster variations of hospital readmission across the Winnipeg Health Region. Seven neighborhood clusters are more likely to be significant potential clusters for hospital readmissions (p < .05), while six neighborhood clusters are less likely to be significant potential clusters.

CONCLUSIONS

This study provides the foundation and implementation guide for the Winnipeg Regional Health Authority virtual ward program. The findings will also help to improve long-term condition management in community settings and will help program planners to assure the efficient use of healthcare resources.

Bowel disorders and its spatial trend in Manitoba, Canada

BACKGROUND

Bowel disorders have destructive impacts on the patients social and mental aspects of life and can cause emotional distress. The risk of developing bowel incontinence also increases with age. The rate of incidence of inflammatory bowel disease in Manitoba, Canada, has been unusually raised. Therefore, it is important to identify trends in the incidence of bowel disorders that may suggest further epidemiological studies to identify risk factors and identify any changes in important factors.

METHODS

An important part of spatial epidemiology is cluster detection as it has the potential to identify possible risk factors associated with disease, which in turn may lead to further investigations into the nature of diseases. To test for potential disease clusters many methods have been proposed. The focused detection methods including the circular spatial scan statistic (CSS), flexible spatial scan statistic (FSS), and Bayesian disease mapping (BYM) are among the most popular disease detection procedures. A frequentist approach based on maximum likelihood estimation (MLE) has been recently used to identify potential focused clusters as well. The aforementioned approaches are studied by analyzing a dataset of bowel disorders in the province of Manitoba, Canada, from 2001 to 2010.

RESULTS

The CSS method identified less regions than the FSS method in the south part of the province as potential clusters. The same regions were identified by the BYM and MLE methods as being potential clusters of bowel disorders with a slightly different order of significance. Most of these regions were also detected by the CSS or FSS methods.

CONCLUSIONS

Overall, we recommend using the methods BYM and MLE for cluster detection with the similar population and structure of regions as in Manitoba. The potential clusters of bowel disorders are generally located in the southern part of the province including the eastern part of the city of Winnipeg. These results may represent real increases in bowel disorders or they may be an indication of other covariates that were not adjusted for in the model used here. Further investigation is needed to examine these findings, and also to explore the cause of these increases.

Relative risk of visceral leishmaniasis in Brazil: a spatial analysis in urban area

Background

Visceral leishmaniasis (VL) is a vector-borne disease whose factors involved in transmission are poorly understood, especially in more urban and densely populated counties. In Brazil, the VL urbanization is a challenge for the control program. The goals were to identify the greater risk areas for human VL and the risk factors involved in transmission.

Methodology

This is an ecological study on the relative risk of human VL. Spatial units of analysis were the coverage areas of the Basic Health Units (146 small-areas) of Belo Horizonte, Minas Gerais State, Brazil. Human VL cases, from 2007 to 2009 (n = 412), were obtained in the Brazilian Reportable Disease Information System. Bayesian approach was used to model the relative risk of VL including potential risk factors involved in transmission (canine infection, socioeconomic and environmental features) and to identify the small-areas of greater risk to human VL.

Principal Findings

The relative risk of VL was shown to be correlated with income, education, and the number of infected dogs per inhabitants. The estimates of relative risk of VL were higher than 1.0 in 54% of the areas (79/146). The spatial modeling highlighted 14 areas with the highest relative risk of VL and 12 of them are concentrated in the northern region of the city.

Conclusions

The spatial analysis used in this study is useful for the identification of small-areas according to risk of human VL and presents operational applicability in control and surveillance program in an urban environment with an unequal spatial distribution of the disease. Thus the frequent monitoring of relative risk of human VL in small-areas is important to direct and prioritize the actions of the control program in urban environment, especially in big cities.

Visceral leishmaniasis (VL) is a vector-borne disease whose factors involved in transmission are poorly understood, especially in more urban and densely populated counties. In Brazil, the increasing occurrence of human VL cases in urban centers is a challenge for the control program. We aimed to identify the risk areas for VL and the risk factors involved in transmission in Belo Horizonte, a large urban area of the Brazil. At the same geographical space, we analyzed human VL cases (n = 412), canine infection and socioeconomic and environmental features. We identified a concentration of high-risk small-areas of human VL cases in the northern part of the city, marked by worse levels of education and income, and higher number of infected dogs per inhabitants. The spatial analysis used is useful for the identification of small-areas with a greater risk of VL and displays operational applicability in the control program in an urban environment with an unequal spatial distribution of the disease. Thus, the frequent monitoring of risk of human VL according to small-areas is important to direct and prioritize the actions of the control program in urban environment, especially in big cities.

Bayesian semiparametric model with spatially-temporally varying coefficients selection

In spatiotemporal analysis, the effect of a covariate on the outcome usually varies across areas and time. The spatial configuration of the areas may potentially depend on not only the structured random intercept but also spatially varying coefficients of covariates. In addition, the normality assumption of the distribution of spatially varying coefficients could lead to potential biases of estimations. In this article, we proposed a Bayesian semiparametric space-time model where the spatially-temporally varying coefficient is decomposed as fixed, spatially varying, and temporally varying coefficients. We nonparametrically modeled the spatially varying coefficients of space-time covariates by using the area-specific Dirichlet process prior with weights transformed via a generalized transformation. We modeled the temporally varying coefficients of covariates through the dynamic model. We also took into account the uncertainty of inclusion of the spatially-temporally varying coefficients by variable selection procedure through determining the probabilities of different effects for each covariate. The proposed semiparametric approach shows its improvement compared with the Bayesian spatial-temporal models with normality assumption on spatial random effects and the Bayesian model with the Dirichlet process prior on the random intercept. We presented a simulation example to evaluate the performance of the proposed approach with the competing models. We used an application to low birth weight data in South Carolina as an illustration.

Epidemiology and geographical variation of myasthenia gravis in the province of Pavia, Italy

BACKGROUND AND AIMS

Previous studies have reported a prevalence estimate of myasthenia gravis (MG) from 7.7 to 11.1 per 100,000 inhabitants in Europe. Moreover, the study of the geographical distribution of MG should be useful to generate specific hypotheses. The aims are to estimate MG prevalence and to investigate its geographical variation in a delimited area in Northern Italy.

METHODS

The primary source of data was the MG database of the Neurological Institute of Pavia and all other sources of case collection in and outside the province. We adopted a Bayesian approach to analyze MG geographical variation within the finest geographical grid.

RESULTS

We identified 119 live MG prevalent cases resident in the province of Pavia on December 31, 2008. The overall crude prevalence was 24 per 100,000 inhabitants. The Bayesian analysis identified a small cluster of higher MG prevalence in the northern area of the province.

CONCLUSIONS

The estimated MG prevalence sets the province of Pavia among the high-risk areas. The identification of high/low MG risk areas deserves further investigation of genetic and environmental factors possibly related to a major risk of the disease in that area.

[Patterns of variation in the infant mortality rate in Rio Grande do Sul State, Brazil: comparison of empirical Bayesian and fully Bayesian approaches]

Infant mortality is considered a sensitive health indicator, and knowledge of its geographical profile is essential for formulating appropriate public health policies. Disease mapping aims to describe the geographical distribution of disease incidence and mortality rates. Due to the heavy instability of crude rates in small areas, methods involving Bayesian smoothing of rates are used, drawing on information for the whole area or neighborhood to estimate the event rate. The current study compares empirical Bayesian (EB) and fully Bayesian (FB) methods for infant mortality rates (accumulated data from 2001 to 2004) in Rio Grande do Sul State, Brazil. This study highlights the advantages of Bayesian estimators for viewing and interpreting maps. For the problem at hand, EB and FB methods showed quite similar results and had the great advantage of easy use by health professionals, since they evenly highlight the main spatial patterns in the mortality rate in the State during the target period.

An examination of five spatial disease clustering methodologies for the identification of childhood cancer clusters in Alberta, Canada

Cluster detection is an important part of spatial epidemiology because it may help suggest potential factors associated with disease and thus, guide further investigation of the nature of diseases. Many different methods have been proposed to test for disease clusters. In this paper, we study five popular methods for detecting spatial clusters. These methods are Besag-Newell (BN), circular spatial scan statistic (CSS), flexible spatial scan statistic (FSS), Tango's maximized excess events test (MEET), and Bayesian disease mapping (BYM). We study these five different methods by analyzing a data set of malignant cancer diagnoses in children in the province of Alberta, Canada during 1983-2004. Our results show that the potential clusters are located in the south-central part of the province. Although, all methods performed very well to detect clusters, the BN and MEET methods identified local as well as general clusters.

Mapping under-five mortality in the Wenchuan earthquake using hierarchical Bayesian modeling

More than two years after the 2008 earthquake in Wenchuan, China, the total number of lives lost remains unclear, particularly for children under five years old. Mortality for this age group can be estimated using a variety of techniques, but sample proportion estimates may be unreliable in areas with low populations of children under five. To address this problem, we propose a hierarchical Bayesian model to map the distribution of under-five mortality in Wenchuan at the township scale. This model is based on conditional distributions for data conditioned on a spatial process and parameters to capture uncertainties usually identified as either spatially-correlated effects or heterogeneity effects. The method was adapted to obtain reliable estimates of the under-five mortality rate in townships with low under-five populations. The approach was compared to other models and, despite some limitations, was found to outperform other methods in its smoothing effect as well as in exploration of other aspects of spatial patterns.

Identification of risk areas for visceral leishmaniasis in Teresina, Piaui State, Brazil

This study used spatial analysis to identify areas at greatest risk of visceral leishmaniasis (VL) in the urban area of Teresina, Brazil during 2001-2006. The results from kernel ratios showed that peripheral census tracts were the most heavily affected. Local spatial analysis showed that in the beginning of the study period local clusters of high incidence of VL were mostly located in the southern and northeastern parts of the city, but in subsequent years those clusters also appeared in the northern region of the city, suggesting that the pattern of VL is not static, and the disease may occasionally spread to other areas of the municipality. We also observed a spatial correlation between VL rates and all socioeconomic and demographic indicators evaluated (P < 0.01). The concentration of interventions in high-risk areas could be an effective strategy to control the disease in the urban setting.

Epidemiology of multiple sclerosis in south-western Sardinia

BACKGROUND

Sardinia is a known high-risk area for multiple sclerosis (MS), but no data for south-western Sardinia (SWS) are available. SWS has a genetically homogeneous population, apart from St Peter Island, and represents a peculiar environment related to the industrial, mineralogical and military economy.

OBJECTIVE

To estimate prevalence and incidence and to evaluate temporal trends and geographical distribution of MS in SWS.

METHODS

MS prevalence was evaluated on 31 December 2007 and crude mean annual incidence rate was defined between 2003 and 2007. Temporal trend in MS incidence was assessed using the Armitage test. To identify MS clusters, Standard Morbidity Ratio (SMR) was calculated for each village and geographical distribution prevalence by means of a Bayesian hierarchical model.

RESULTS

Total crude prevalence rate was 210.4 (95% CI 186.3-234.5): 280.3 (95% CI 241.4-319.3) for females, 138 (95% CI 110.1-165.8) for males. The crude mean annual incidence rate was 9.7/100,000 (95% CI 3.4-13.2): 4.7/100,000 (95% CI 2.4-17.0) and 14.6/100,000 (95% CI 11.8-34.8) for males and females respectively. MS incidence has increased over the last 50 years. Cluster analysis showed an SMR of 0.2 (95% CI 0.05-0.68, p = 0.002) on the island of San Pietro, and 2.0 (95% CI 1.35-2.95, p = 0.001) in Domusnovas. Spatial distribution of MS was confirmed by Bayesian geographical analysis.

CONCLUSIONS

Our data confirm Sardinia as a high-risk area for MS and support the relevance of genetic factors in MS, as evidenced in St Peter Island. However, we found an unexpectedly high MS prevalence in one village, in particular in males, suggesting an environmental influence on MS occurrence.

A hierarchical Bayesian approach to multiple testing in disease mapping

We propose a Bayesian approach to multiple testing in disease mapping. This study was motivated by a real example regarding the mortality rate for lung cancer, males, in the Tuscan region (Italy). The data are relative to the period 1995–1999 for 287 municipalities. We develop a tri-level hierarchical Bayesian model to estimate for each area the posterior classification probability that is the posterior probability that the municipality belongs to the set of non-divergent areas. We show also the connections of our model with the false discovery rate approach. Posterior classification probabilities are used to explore areas at divergent risk from the reference while controlling for multiple testing. We consider both the Poisson-Gamma and the Besag, York and Mollié model to account for extra Poisson variability in our Bayesian formulation. Posterior inference on classification probabilities is highly dependent on the choice of the prior. We perform a sensitivity analysis and suggest how to rely on subject-specific information to derive informative a priori distributions. Hierarchical Bayesian models provide a sensible way to model classification probabilities in the context of disease mapping.

The spatial epidemiology and clinical features of reported cases of La Crosse virus infection in West Virginia from 2003 to 2007

BACKGROUND

La Crosse virus (LACV) is a major cause of pediatric encephalitis in the United States. Since the mid-1980s, the number of reported cases of LACV infection in West Virginia has continued to rise and the state currently reports the most cases in the United States. The purpose of this study was to investigate and describe the spatial epidemiology and clinical presentation of LACV infection cases reported in West Virginia, as well as to provide a description of the environmental conditions present at the residences of the LACV infection cases.

METHODS

Descriptive and spatial analyses were performed on LACV infection cases reported to the West Virginia Department of Health from 2003 to 2007. Clinical and environmental variables were available for 96 cases and residence data were available for 68 of these cases. Spatial analyses using the global Moran's I and Kulldorff's spatial scan statistic were performed using the population 15 years and younger at both the county and census tract levels to identify those geographic areas at the highest risk of infection.

RESULTS

Two statistically significant (p < 0.05) high-risk clusters, involving six counties, were detected at the county level. At the census tract level, one statistically significant high-risk cluster involving 41 census tracts spanning over six counties was identified. The county level cumulative incidence for those counties in the primary high-risk cluster ranged from 100.0 to 189.0 cases per 100,000 persons (median 189.0) and the census tract level cumulative incidence for those counties in the high-risk cluster ranged from 61.7 to 505.9 cases per 100,000 persons (median 99.0). The counties and census tracts within high-risk clusters had a relative risk four to nine times higher when compared to those areas not contained within high-risk clusters. The majority of LACV infection cases were reported during the summer months in children 15 years and younger. Fever, vomiting, photophobia, and nausea were the most commonly reported signs and symptoms. A case fatality rate (CFR) of 3.1% was observed. Wooded areas and containers were present at the majority of case residences.

CONCLUSIONS

The cumulative incidences of LACV infection from 2003 to 2007 were considerably higher than previously reported for West Virginia, and statistically significant high-risk clusters for LACV infection were detected at both the county and census tract levels. The finding of a high CFR and the identification of those areas at highest risk for infection will be useful for guiding future research and intervention efforts.

Developing the atlas of cancer in Queensland: methodological issues

BACKGROUND

Achieving health equity has been identified as a major challenge, both internationally and within Australia. Inequalities in cancer outcomes are well documented, and must be quantified before they can be addressed. One method of portraying geographical variation in data uses maps. Recently we have produced thematic maps showing the geographical variation in cancer incidence and survival across Queensland, Australia. This article documents the decisions and rationale used in producing these maps, with the aim to assist others in producing chronic disease atlases.

METHODS

Bayesian hierarchical models were used to produce the estimates. Justification for the cancers chosen, geographical areas used, modelling method, outcome measures mapped, production of the adjacency matrix, assessment of convergence, sensitivity analyses performed and determination of significant geographical variation is provided.

CONCLUSIONS

Although careful consideration of many issues is required, chronic disease atlases are a useful tool for assessing and quantifying geographical inequalities. In addition they help focus research efforts to investigate why the observed inequalities exist, which in turn inform advocacy, policy, support and education programs designed to reduce these inequalities.

Spatial and genetic epidemiology of hookworm in a rural community in Uganda

There are remarkably few contemporary, population-based studies of intestinal nematode infection for sub-Saharan Africa. This paper presents a comprehensive epidemiological analysis of hookworm infection intensity in a rural Ugandan community. Demographic, kinship, socioeconomic and environmental data were collected for 1,803 individuals aged six months to 85 years in 341 households in a cross-sectional community survey. Hookworm infection was assessed by faecal egg count. Spatial variation in the intensity of infection was assessed using a Bayesian negative binomial spatial regression model and the proportion of variation explained by host additive genetics (heritability) and common domestic environment was estimated using genetic variance component analysis. Overall, the prevalence of hookworm was 39.3%, with the majority of infections (87.7%) of light intensity ( Collapse

Key Words Collapse

MESH Headings

• Adolescent
• Analysis of Variance
• Ancylostomatoidea
• Animals
• Bayes Theorem
• Child
• Child, Preschool
• Cluster Analysis
• Female
• Genetic Predisposition to Disease
• Geography
• Hookworm Infections/epidemiology
• Hookworm Infections/genetics
• Humans
• Infant
• Male
• Regression Analysis
• Risk Factors
• Rural Population/statistics & numerical data
• Sex Distribution
• Surveys and Questionnaires
• Uganda/epidemiology

Collapse

Grants

• Wellcome Trust
• 081673 Wellcome Trust
• Medical Research Council

Collapse

Affiliation(s)

Rachel L Pullan Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical Medicine, London, United Kingdom.
Narcis B Kabatereine
Rupert J Quinnell
Simon Brooker

Collapse

[The aids epidemic in the State of São Paulo: application of the full Bayesian space-time model]

The State of São Paulo accounts for approximately 40% of the AIDS cases notified in Brazil and provides a suitable opportunity for space-time analysis aimed at better understanding of the dissemination of HIV/AIDS. Using the AIDS cases notified to the Ministry of Health between 1990 and 2004, among individuals aged 15 years or over, and the Ministry of Health's information system for disease notification (Sistema de Informação de Agravos e Notificação, SINAN) as the information source, the relative risks of AIDS over three-year periods were estimated using full Bayesian models, for each gender. The models used were shown to be adequate for explaining the process of AIDS dissemination in the State of São Paulo and demonstrated the growth among females and in small-sized municipalities. They also suggested that the municipalities currently most affected are in regions of economic growth and have populations of less than 50,000 inhabitants.

The geospatial relation between UV solar radiation and type 1 diabetes in Newfoundland

Type 1 diabetes (T1DM) has been previously associated with northern latitude and vitamin D insufficiency. This study investigates the geospatial association between average daily ultraviolet B (UVB) irradiance and T1DM across the province of Newfoundland (NL), Canada. NL has one of the highest documented incidences of T1DM worldwide. A complete list of patients diagnosed (1987-2005) with T1DM in the province of Newfoundland and Labrador (NL) was constructed using multiple sources. All places of habitation at diagnosis were ascertained. Ecological analysis using Bayesian estimation was performed employing both NASA UVB data and latitude. Correlation of T1DM to both UVB irradiation and latitude was measured. A statistically significant correlation of erythemal UVB irradiance was observed (-0.0284: 95% CI -0.0542 to -0.0096). A more significant correlation of T1DM was observed with erythemal UVB irradiance than with latitude. This study suggests that erythemal UVB radiation may be geospatially associated with the incidence of T1DM in NL.

Mapping the Timing, Pace, and Scale of the Fertility Transition in Brazil

Between 1960 and 2000, fertility fell sharply in Brazil, but this transition was unevenly distributed in space and time. Using Bayesian spatial statistical methods and microdata from five censuses, we develop and apply a procedure for fitting logistic curves to the fertility transitions in more than 500 small regions of Brazil over this 40-year period. Doing so enables us to map the main features of the Brazilian fertility transition in considerable detail. We detect early declines in some regions of the country and document large differences between early and late transitions in regard to both the initial level of fertility and the speed of the transition. We also use our results to test hypotheses regarding changes in the level of development at the onset of the fertility transition and identify a temporary stall in the Brazilian transition that occurred in the late 1990s. A web site with project details is at http://schmert.net/BayesLogistic.

Assessing risk in focal arboviral infections: are we missing the big or little picture?

Background

Focal arboviral infections affecting a subset of the overall population present an often overlooked set of challenges in the assessment and reporting of risk and the detection of spatial patterns. Our objective was to assess the variation in risk when using different at-risk populations and geographic scales for the calculation of incidence risk and the detection of geographic hot-spots of infection. We explored these variations using a pediatric arbovirus, La Crosse virus (LACV), as our model.

Methods and Findings

Descriptive and cluster analyses were performed on probable and confirmed cases of LACV infections reported to the Tennessee Department of Health from 1997 to 2006, using three at-risk populations (the total population, the population 18 years and younger, and the population 15 years and younger) and at two geographic levels (county and census tract) to assess the variation in incidence risk and to investigate evidence of clustering using both global and local spatial statistics. We determined that the most appropriate at-risk population to calculate incidence risk and to assess the evidence of clustering was the population 15 years and younger. Based on our findings, the most appropriate geographical level to conduct spatial analyses and report incidence risk is the census tract level. The incidence risk in the population 15 years and younger at the county level ranged from 0 to 226.5 per 100,000 persons (median 41.5) in those counties reporting cases (n = 14) and at the census tract level it ranged from 50.9 to 673.9 per 100,000 persons (median 126.7) in those census tracts reporting cases (n = 51). To our knowledge, this is the highest reported incidence risk for this population at the county level for Tennessee and at the census tract level nationally.

Conclusion

The results of this study indicate the possibility of missing disease clusters resulting from performing incidence risk investigations of focal diseases using inappropriate at-risk populations and/or at large geographic scales. Improved disease surveillance and health planning will result through the use of well defined at-risk populations and the use of appropriate geographic scales for the analysis and reporting of diseases. The finding of a high incidence risk of LACV infections in eastern Tennessee demonstrates that the vast majority of these infections continue to be under-diagnosed and/or underreported in this region. Persistent prevention and surveillance efforts will be required to reduce exposure to infectious vectors and to detect new cases of infection in this region. Application of this study's observations in future investigations will enhance the quantification of incidence risk and the identification of high-risk groups within the population.

Spatial analysis of notified cryptosporidiosis infections in Brisbane, Australia

PURPOSE

This study explored the spatial distribution of notified cryptosporidiosis cases and identified major socioeconomic factors associated with the transmission of cryptosporidiosis in Brisbane, Australia.

METHODS

We obtained the computerized data sets on the notified cryptosporidiosis cases and their key socioeconomic factors by statistical local area (SLA) in Brisbane for the period of 1996 to 2004 from the Queensland Department of Health and Australian Bureau of Statistics, respectively. We used spatial empirical Bayes rates smoothing to estimate the spatial distribution of cryptosporidiosis cases. A spatial classification and regression tree (CART) model was developed to explore the relationship between socioeconomic factors and the incidence rates of cryptosporidiosis.

RESULTS

Spatial empirical Bayes analysis reveals that the cryptosporidiosis infections were primarily concentrated in the northwest and southeast of Brisbane. A spatial CART model shows that the relative risk for cryptosporidiosis transmission was 2.4 when the value of the social economic index for areas (SEIFA) was over 1028 and the proportion of residents with low educational attainment in an SLA exceeded 8.8%.

CONCLUSIONS

There was remarkable variation in spatial distribution of cryptosporidiosis infections in Brisbane. Spatial pattern of cryptosporidiosis seems to be associated with SEIFA and the proportion of residents with low education attainment.

Space-time variation of malaria incidence in Yunnan province, China

BACKGROUND

Understanding spatio-temporal variation in malaria incidence provides a basis for effective disease control planning and monitoring.

METHODS

Monthly surveillance data between 1991 and 2006 for Plasmodium vivax and Plasmodium falciparum malaria across 128 counties were assembled for Yunnan, a province of China with one of the highest burdens of malaria. County-level Bayesian Poisson regression models of incidence were constructed, with effects for rainfall, maximum temperature and temporal trend. The model also allowed for spatial variation in county-level incidence and temporal trend, and dependence between incidence in June-September and the preceding January-February.

RESULTS

Models revealed strong associations between malaria incidence and both rainfall and maximum temperature. There was a significant association between incidence in June-September and the preceding January-February. Raw standardised morbidity ratios showed a high incidence in some counties bordering Myanmar, Laos and Vietnam, and counties in the Red River valley. Clusters of counties in south-western and northern Yunnan were identified that had high incidence not explained by climate. The overall trend in incidence decreased, but there was significant variation between counties.

CONCLUSION

Dependence between incidence in summer and the preceding January-February suggests a role of intrinsic host-pathogen dynamics. Incidence during the summer peak might be predictable based on incidence in January-February, facilitating malaria control planning, scaled months in advance to the magnitude of the summer malaria burden. Heterogeneities in county-level temporal trends suggest that reductions in the burden of malaria have been unevenly distributed throughout the province.

The incidence risk, clustering, and clinical presentation of La Crosse virus infections in the eastern United States, 2003-2007

BACKGROUND

Although La Crosse virus (LACV) is one of the most common causes of pediatric arboviral infections in the United States, little has been done to assess its geographic distribution, identify areas of higher risk of disease, and to provide a national picture of its clinical presentation. Therefore, the objective of this study was to investigate the geographic distribution of LACV infections reported in the United States, to identify hot-spots of infection, and to present its clinical picture.

METHODS AND FINDINGS

Descriptive and cluster analyses were performed on probable and confirmed cases of LACV infections reported to the Centers for Disease Control and Prevention from 2003-2007. A total of 282 patients had reported confirmed LACV infections during the study period. Of these cases the majority (81 percent) presented during the summer, occurred in children 15 years and younger (83.3 percent), and were found in male children (64.9 percent). Clinically, the infections presented as meningioencephalitis (56.3 percent), encephalitis (20.7 percent), meningitis (17.2 percent), or uncomplicated fever (5 percent). Deaths occurred in 1.9 percent of confirmed cases, and in 8.6 percent of patients suffering from encephalitis. The majority of these deaths were in patients 15 years and younger. The county-level incidence risk among counties (n = 136) reporting both probable and confirmed cases for children 15 years and younger (n = 355) ranged from 0.2 to 228.7 per 100,000 persons. The southern United States experienced a significantly higher (p<0.05) incidence risk during the months of June, July, August, and October then the northern United States. There was significant (p<0.05) clustering of high risk in several geographic regions with three deaths attributed to complications from LAC encephalitis occurring in two of these hot-spots of infections.

CONCLUSIONS

Both the incidence risk and case fatality rates were found to be higher than previously reported. We detected clustering in four geographic regions, a shift from the prior geographic distributions, and developed maps identifying high-risk areas. These findings are useful for raising awareness among health care providers regarding areas at a high risk of infections and for guiding targeted multifaceted interventions by public health officials.

Geographical clustering of lung cancer in the province of Lecce, Italy: 1992-2001

Background

The triennial mortality rates for lung cancer in the two decades 1981–2001 in the province of Lecce, Italy, are significantly higher than those for the entire region of Apulia (to which the Province of Lecce belongs) and the national reference rates. Moreover, analyzing the rates in the three-year periods 1993–95, 1996–98 and 1999–01, there is a dramatic increase in mortality for both males and females, which still remains essentially unexplained: to understand the extent of this phenomenon, it is worth noting that the standardized mortality rate for males in 1999–01 is equal to 13.92 per 10000 person-years, compared to a value of 6.96 for Italy in the 2000–2002 period.

These data have generated a considerable concern in the press and public opinion, which with little scientific reasoning have sometimes identified suspected culprits of the risk excess (for example, the emission caused by a number of large industrial sites located in the provinces of Brindisi and Taranto, bordering the Province of Lecce). The objective of this paper is to study on a scientifically sound basis the spatial distribution of risk for lung cancer mortality in the province of Lecce. Our goal is to demonstrate that most of the previous explanations are not supported by data: to this end, we will follow a hybrid approach that combines both frequentist and Bayesian disease mapping methods. Furthermore, we define a new sequential algorithm based on a modified version of the Besag-York-Mollié (BYM) model, suitably modified to detect geographical clusters of disease.

Results

Standardized mortality ratios (SMRs) for lung cancer in the province of Lecce: For males, the relative risk (measured by means of SMR, i.e. the ratio between observed and expected cases in each area under internal standardization) was judged to be significantly greater than 1 in many municipal areas, the significance being evaluated under the null hypothesis of neutral risk on the ground of area-specific p-values (denoted by ρ_i); in addition, it was seen that high risk areas were not randomly distributed within the province, but showed a sharp clustering. The most perceptible cluster involved a collection of municipalities around the Maglie area (Istat code: 75039), while the association among the municipalities of Otranto, Poggiardo and Santa Cesarea Terme (Istat codes: 75057, 75061, 75072) was more ambiguous. For females, it was noteworthy the significant risk excess in the city of Lecce (Istat code: 75035), where an SMR of 1.83 and ρ_i < 0.01 have been registered. BYM model for the province of Lecce: For males, Bayes estimates of relative risks varied around an overall mean of 1.04 with standard deviation of 0.1, with a minimum of 0.77 and a maximum of 1.25. The posterior relative risks for females, although smoothed, showed more variation than for males, ranging form 0.74 to 1.65, around a mean of 0.90 with standard deviation 0.12. For males, 95% posterior credible intervals of relative risks included unity in every area, whereas significantly elevated risk of mortality was confirmed in the Lecce area for females (95% posterior CI: 1.33 – 2.00). BYM model for the whole Apulia: For males, internally standardized maps showed several high risk areas bordering the province of Lecce, belonging to the province of Brindisi, and the presence of a large high risk region, including the southern part of the province of Brindisi and the eastern and southern part of the Salento peninsula, in which an increasing trend in the north-south direction was found.

Ecological correlation study with deprivation (Cadum Index): For males, posterior mean of the ecological regression coefficient β resulted to be 0.04 with 95% posterior credible interval equal to (-0.01, 0.08); similarly, β was estimated as equal to -0.03 for females (95% posterior credible interval: -0.16, 0.10). Moreover, there was some indication of nonlinearly increasing relative risk with increasing deprivation for higher deprivation levels. For females, it was difficult to postulate the existence of any association between risk and deprivation.

Cluster detection: cluster detection based on a modified BYM model identified two large unexplained increased risk clusters in the central-eastern and southern part of the peninsula. Other secondary clusters, which raise several complex interpretation issues, are present.

Conclusion

Our results reduce the alleged role of the industrial facilities located around the province of Taranto: in particular, air pollution produced around the city of Taranto (which lies to the west of the province of Lecce) has been often identified as the main culprit of the mortality excess, a conclusion that was further supported by a recent study on the direction of prevailing winds on Salento. This hypothesis is contradicted by the finding that those municipalities that directly border on the province of Taranto (belonging to the so-called "Jonico-Salentina" band) are those that present low mortality rates (at least for males). In the same way, the responsibilities of energy production plants located in the province of Brindisi (Brindisi province lies to the north) appear to be of little relevance. For females, given the situation observed in the city of Lecce, and given the substantial increase in mortality observed in younger age classes, further investigation is required into the role played by changes in lifestyle, including greater net propensity to smoke that women have shown since the 80s onwards (a phenomenon which could be amplified in a city traditionally cultured and modern as Lecce, as the tobacco habit is a largely cultural phenomenon). For males, the presence of high levels of deprivation throughout the eastern and southern Salento is likely to play an important role: those with lower socio-economic status smoke more, and gender differences may be explained on the basis of the fact that in less developed areas women have less habit to tobacco smoking and alcohol drinking (and other harmful lifestyles), which are seen as purely masculine behaviour: research into the role of material deprivation and individual lifestyle differences between genders should be further developed.