Empirical Bayes methods for disease mapping

Investigation of geographic disparities of diabetes-related hospitalizations in Florida using flexible spatial scan statistics: An ecological study

BACKGROUND

Hospitalizations due to diabetes complications are potentially preventable with effective management of the condition in the outpatient setting. Diabetes-related hospitalization (DRH) rates can provide valuable information about access, utilization, and efficacy of healthcare services. However, little is known about the local geographic distribution of DRH rates in Florida. Therefore, the objectives of this study were to investigate the geographic distribution of DRH rates at the ZIP code tabulation area (ZCTA) level in Florida, identify significant local clusters of high hospitalization rates, and describe characteristics of ZCTAs within the observed spatial clusters.

METHODS

Hospital discharge data from 2016 to 2019 were obtained from the Florida Agency for Health Care Administration through a Data Use Agreement with the Florida Department of Health. Raw and spatial empirical Bayes smoothed DRH rates were computed at the ZCTA level. High-rate DRH clusters were identified using Tango's flexible spatial scan statistic. Choropleth maps were used to display smoothed DRH rates and significant high-rate spatial clusters. Demographic, socioeconomic, and healthcare-related characteristics of cluster and non-cluster ZCTAs were compared using the Wilcoxon rank sum test for continuous variables and Chi-square test for categorical variables.

RESULTS

There was a total of 554,133 diabetes-related hospitalizations during the study period. The statewide DRH rate was 8.5 per 1,000 person-years, but smoothed rates at the ZCTA level ranged from 0 to 101.9. A total of 24 significant high-rate spatial clusters were identified. High-rate clusters had a higher percentage of rural ZCTAs (60.9%) than non-cluster ZCTAs (41.8%). The median percent of non-Hispanic Black residents was significantly (p < 0.0001) higher in cluster ZCTAs than in non-cluster ZCTAs. Populations of cluster ZCTAs also had significantly (p < 0.0001) lower median income and educational attainment, and higher levels of unemployment and poverty compared to the rest of the state. In addition, median percent of the population with health insurance coverage and number of primary care physicians per capita were significantly (p < 0.0001) lower in cluster ZCTAs than in non-cluster ZCTAs.

CONCLUSIONS

This study identified geographic disparities of DRH rates at the ZCTA level in Florida. The identification of high-rate DRH clusters provides useful information to guide resource allocation such that communities with the highest burdens are prioritized to reduce the observed disparities. Future research will investigate determinants of hospitalization rates to inform public health planning, resource allocation and interventions.

Analysis of the association between areal socioeconomic deprivation levels and viral hepatitis B and C infections in Japanese municipalities

Background

We investigated the association between municipal socioeconomic deprivation levels and the positivity of hepatitis B surface antigen (HBsAg) and the prevalence of hepatitis C virus (HCV) among individuals who have never participated in hepatitis screening using Japanese national screening data.

Methods

The hepatitis virus screening data analyzed included the 5-year age group-specific number of participants aged 40 years or older, number of HBsAg-positive persons, and number of HCV carriers for each municipality from 2013 to 2017. Principal component analysis was used to derive a socioeconomic deprivation level using the socioeconomic characteristics of municipalities. Bayesian spatial Poisson regression analysis was conducted to investigate the association between the socioeconomic deprivation level and the results of screening. Data on 1,660 municipalities were used in the analysis.

Results

The data of 4,233,819 participants in the HBV screening and 4,216,720 in the HCV screening were used in the analysis. A principal component interpreted as level of rurality (principal component 1) and another principal component interpreted as level of low socioeconomic status among individuals (principal component 2) were extracted as the major principal components. Their principal component scores were used as the deprivation levels of municipalities. Spatial regression analysis showed that the deprivation level derived from the sum of the scores of principal components 1 and 2 was significantly and positively associated with HBsAg positivity and HCV prevalence. In addition, the deprivation level derived only from the score of principal component 2 was also significantly and positively associated with the outcomes. Conversely, the deprivation level derived only from the score of principal component 1 was not associated with the outcomes. Moreover, population density was significantly and positively associated with HBsAg positivity and HCV prevalence.

Conclusions

This study suggested that participation in hepatitis virus screening is important and meaningful, particularly for areas with a higher lower socioeconomic level in Japan.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-022-13089-w.

Estimating Country-Specific Incidence Rates of Rare Cancers: Comparative Performance Analysis of Modeling Approaches Using European Cancer Registry Data

Estimating incidence of rare cancers is challenging for exceptionally rare entities and in small populations. In a previous study, investigators in the Information Network on Rare Cancers (RARECARENet) provided Bayesian estimates of expected numbers of rare cancers and 95% credible intervals for 27 European countries, using data collected by population-based cancer registries. In that study, slightly different results were found by implementing a Poisson model in integrated nested Laplace approximation/WinBUGS platforms. In this study, we assessed the performance of a Poisson modeling approach for estimating rare cancer incidence rates, oscillating around an overall European average and using small-count data in different scenarios/computational platforms. First, we compared the performance of frequentist, empirical Bayes, and Bayesian approaches for providing 95% confidence/credible intervals for the expected rates in each country. Second, we carried out an empirical study using 190 rare cancers to assess different lower/upper bounds of a uniform prior distribution for the standard deviation of the random effects. For obtaining a reliable measure of variability for country-specific incidence rates, our results suggest the suitability of using 1 as the lower bound for that prior distribution and selecting the random-effects model through an averaged indicator derived from 2 Bayesian model selection criteria: the deviance information criterion and the Watanabe-Akaike information criterion.

Geographical Differences and Their Associated Factors in Chronic Obstructive Pulmonary Disease Mortality in Japan: An Ecological Study Using Nationwide Data

Geographical differences in chronic obstructive pulmonary disease (COPD) mortality have not been determined using municipal-specific data in Japan. This study determined the geographical differences in COPD mortality in Japan using municipal-specific data and identified associated factors. Data on COPD mortality from 2013 to 2017 for each municipality were obtained from the Vital Statistics of Japan. We calculated the standardized mortality ratio (SMR) of COPD by an empirical Bayes method for each municipality and located the SMRs on a map of Japan. In addition, an ecological study was conducted to identify factors associated with the SMR using demographic, socioeconomic, and medical characteristics of municipalities by a spatial statistics model. Geographical differences in the SMR were different in men and women, and municipalities with a low SMR tended to be more frequent in women. Spatial regression analysis identified that the total population and taxable income per capita were negatively associated with the SMR in men. In women, population density, the proportion of fatherless households, and the number of clinics per capita were positively associated with the SMR, whereas taxable income per capita was negatively associated with the SMR. There were some differences in regional characteristics associated with COPD mortality by sex.

Socioeconomic Predictors of Diabetes Mortality in Japan: An Ecological Study Using Municipality-specific Data

OBJECTIVES

The aim of this study was to examine the geographic distribution of diabetes mortality in Japan and identify socioeconomic factors affecting differences in municipality-specific diabetes mortality.

METHODS

Diabetes mortality data by year and municipality from 2013 to 2017 were extracted from Japanese Vital Statistics, and the socioeconomic characteristics of municipalities were obtained from government statistics. We calculated the standardized mortality ratio (SMR) of diabetes for each municipality using the empirical Bayes method and represented geographic differences in SMRs in a map of Japan. Multiple linear regression was conducted to identify the socioeconomic factors affecting differences in SMR. Statistically significant socioeconomic factors were further assessed by calculating the relative risk of mortality of quintiles of municipalities classified according to the degree of each socioeconomic factor using Poisson regression analysis.

RESULTS

The geographic distribution of diabetes mortality differed by gender. Of the municipality-specific socioeconomic factors, high rates of single-person households and unemployment and a high number of hospital beds were associated with a high SMR for men. High rates of fatherless households and blue-collar workers were associated with a high SMR for women, while high taxable income per-capita income and total population were associated with low SMR for women. Quintile analysis revealed a complex relationship between taxable income and mortality for women. The mortality risk of quintiles with the highest and lowest taxable per-capita income was significantly lower than that of the middle-income quintile.

CONCLUSIONS

Socioeconomic factors of municipalities in Japan were found to affect geographic differences in diabetes mortality.

Socioeconomic Predictors of Trends in Cancer Mortality among Municipalities in Japan, 2010-2019

Background:

A study investigating associations between various socioeconomic factors and standardized mortality ratios (SMR) of each type of cancer among municipalities in Japan has not been conducted using the data of the past decade. Herein, we investigated the predictors of a recent trend of municipal SMRs of cancer using the Vital Statistics in Japan and revealed the change in the SMRs depending on the identified predictors.

Methods:

Data on cancer mortality for each municipality in 2010 and 2019 were used. We calculated empirical Bayes SMR (EBSMR) for each municipality by type of cancer and sex and then fitted a multiple linear regression model using possible predictors in 2010 as explanatory variables and the EBSMR in 2019 as the outcome variable. We also classified municipalities into quintiles based on the values of an identified predictor in 2010, and SMRs of each type of cancer in 2010 and 2019 were calculated for each quintile.

Results:

The total population was positively associated with EMSMRs of multiple cancer types, whereas educational level was negatively associated with EMSMRs of multiple cancer types. In addition, SMRs of municipalities with the lowest educational level deteriorated from 2010 to 2019 for many cancer types among men and women, and the difference between municipalities with the highest and lowest educational level for the SMR of cancer in all sites widened in 2019 for men. On the other hand, the SMR of municipalities with the highest educational level or the largest total population tended to be higher than municipalities with lower counterparts in both 2010 and 2019 for women.

Conclusion:

There was a difference in the trend of the SMRs of multiple types of cancer depending on municipal educational level, whereas municipalities with larger population or educational level continued to have higher SMRs of cancer in all sites for women.

POISSON COKRIGING AS A GENERALIZED LINEAR MIXED MODEL

It is often of interest to predict spatially correlated count outcomes that follow a Poisson distribution. For example, in the environmental sciences we may want to predict pollen counts using temperature or precipitation data as auxiliary variables. To predict a Poisson outcome variable in the presence of an auxiliary variable, Poisson cokriging as a Generalized Linear Mixed Model (GLMM) is proposed. This model has a bivariate structure with a Poisson outcome variable and an auxiliary variable. A covariance matrix similar to that used in cokriging is assumed. A simulation study and a real data example using the number of microplastics in the digestive tracts of fish are presented. The results showed that Poisson cokriging methodology can be applied successfully in practice with small average errors and coverage close to 95%. The Poisson cokriging model can be a useful tool for spatial prediction.

Epidemiology and spatial distribution of bluetongue virus in Xinjiang, China

Bluetongue (BT) is a non-contagious disease affecting domestic and wild ruminants. Outbreaks of BT can cause serious economic losses. To investigate the distribution characteristics of bluetongue virus (BTV), two large-scale censuses of BTV prevalence in Xinjiang, China were collected. Spatial autocorrelation analysis, including global spatial autocorrelation and local spatial autocorrelation, was performed. Risk areas for BTV occurrence in Xinjiang were detected using the presence-only maximum entropy model. The global spatial autocorrelation of BTV distribution in Xinjiang in 2012 showed a random pattern. In contrast, the spatial distribution of BTV from 2014 to 2015 was significantly clustered. The hotspot areas for BTV infection included Balikun County (p < 0.05), Yiwu County (p < 0.05) and Hami City (p < 0.05) in 2012. These three regions were also hotspot areas during 2014 and 2015. Sheep distribution (25.6% contribution), precipitation seasonality (22.1% contribution) and mean diurnal range (16.2% contribution) were identified as the most important predictors for BTV occurrence in Xinjiang. This study demonstrated the presence of high-risk areas for BTV infection in Xinjiang, which can serve as a tool to aid in the development of preventative countermeasures of BT outbreaks.

Detection of Epistasis for Flowering Time Using Bayesian Multilocus Estimation in a Barley MAGIC Population

Gene-by-gene interactions, also known as epistasis, regulate many complex traits in different species. With the availability of low-cost genotyping it is now possible to study epistasis on a genome-wide scale. However, identifying genome-wide epistasis is a high-dimensional multiple regression problem and needs the application of dimensionality reduction techniques. Flowering Time (FT) in crops is a complex trait that is known to be influenced by many interacting genes and pathways in various crops. In this study, we successfully apply Sure Independence Screening (SIS) for dimensionality reduction to identify two-way and three-way epistasis for the FT trait in a Multiparent Advanced Generation Inter-Cross (MAGIC) barley population using the Bayesian multilocus model. The MAGIC barley population was generated from intercrossing among eight parental lines and thus, offered greater genetic diversity to detect higher-order epistatic interactions. Our results suggest that SIS is an efficient dimensionality reduction approach to detect high-order interactions in a Bayesian multilocus model. We also observe that many of our findings (genomic regions with main or higher-order epistatic effects) overlap with known candidate genes that have been already reported in barley and closely related species for the FT trait.

Women and HIV in the United States

BACKGROUND

The demographic and geographic characteristics of the HIV epidemic in the US has changed substantially since the disease emerged, with women in the South experiencing a particularly high HIV incidence. In this study, we identified and described counties in the US in which the prevalence of HIV is particularly high in women compared to men.

METHODS

Using data from AIDSVu, a public dataset of HIV cases in the US in 2012, we categorized counties by their decile of the ratio of female to male HIV prevalence. The demographic and socioeconomic characteristics of counties in the highest decile were compared to those of counties in the lower deciles.

RESULTS

Most of the counties in the highest decile were located in the Deep South. These counties had a lower median income, higher percentage of people in poverty, and lower percentage of people with a high school education. Additionally, people with HIV in these counties were more likely to be non-Hispanic black.

CONCLUSIONS

Counties with the highest ratios of female-to-male HIV prevalence are concentrated in the Southern US, and residents of these counties tend to be of lower socioeconomic status. Identifying and describing these counties is important for developing public health interventions.

Type and Proximity of Green Spaces Are Important for Preventing Cardiovascular Morbidity and Diabetes--A Cross-Sectional Study for Quebec, Canada

This study aimed at determining the role of proximity to specific types of green spaces (GSes) as well as their spatial location in the relationship with the most morbid cardiovascular diseases (CVD) and diabetes. We measured the accessibility to various types of GS and used a cross-sectional approach at census Dissemination Area (DA) levels in the Montreal and Quebec City metropolitan zones for the period 2006–2011. Poisson and negative binomial regression models were fitted to quantify the relationship between distances to specific types of GS and CVD morbidity as well as some risk factors (diabetes and hypertension) while controlling for several social and environmental confounders. GSes that have sports facilities showed a significant relationship to cerebrovascular diseases: the most distant population had an 11% higher prevalence rate ratio (PRR) compared to the nearest, as well as higher diabetes risk (PRR 9%) than the nearest. However, the overall model performance and the understanding of the role of GSes with sport facilities may be substantially achieved with lifestyle factors. Significantly higher prevalence of diabetes and cerebrovascular diseases as well as lower access to GSes equipped with sports facilities were found in suburban areas. GSes can advantageously be used to prevent some CVDs and their risk factors, but there may be a need to reconsider their types and location.

Integrated health service delivery networks and tuberculosis avoidable hospitalizations: is there a relation between them in Brazil?

BACKGROUND

The early identification of the Breathing Symptoms within the scope of Primary Health Care is recommended, and is also one of the strategies of national sanitary authorities for reaching the elimination of tuberculosis. The purpose of this study is to consider which attributes and which territories have shown the most significant progress in Primary Health Care, in terms of coordination of Health Care Networks, and also check if those areas of Primary Health Care that are most critical regarding coordination, there were more or less cases of avoidable hospitalizations for tuberculosis.

METHODS

This is an ecological study that uses primary and secondary data. For analysis, coropletic maps were developed through the ArcGIS software, version 10.2. There was also the calculation of gross annual and Bayesian rates for hospitalizations for tuberculosis, for each Primary Health Care territory.

RESULTS

There were satisfactory results for attributes such as Population (n = 37; 80.4 %), Primary Health Care (n = 43; 93.5 %), Support System (n = 45; 97.8 %); the exceptions were Logistics System (n = 32; 76.0 %) and Governance System, with fewer units in good condition (n = 31; 67.3 %). There is no evidence of any connection between networks' coordination by Primary Health Care and tuberculosis avoidable admissions.

CONCLUSION

The results show that progress has been made regarding the coordination of the Health Care Networks, and a positive trend has been shown, even though the levels are not excellent. It was found no relationship between the critical areas of Primary Health Care and tuberculosis avoidable hospitalizations, possibly because other variables necessary to comprehend the phenomena.

Comparison of estimation methods for creating small area rates of acute myocardial infarction among Medicare beneficiaries in California

Creating local population health measures from administrative data would be useful for health policy and public health monitoring purposes. While a wide range of options--from simple spatial smoothers to model-based methods--for estimating such rates exists, there are relatively few side-by-side comparisons, especially not with real-world data. In this paper, we compare methods for creating local estimates of acute myocardial infarction rates from Medicare claims data. A Bayesian Monte Carlo Markov Chain estimator that incorporated spatial and local random effects performed best, followed by a method-of-moments spatial Empirical Bayes estimator. As the former is more complicated and time-consuming, spatial linear Empirical Bayes methods may represent a good alternative for non-specialist investigators.

Spatial and statistical methodologies to determine the distribution of dengue in Brazilian municipalities and relate incidence with the Health Vulnerability Index

Dengue fever is among the most important emerging infectious diseases in the world, and in recent years it has been a source of public concern for the public health control systems of many tropical and subtropical countries. Thus, the purpose of this study was to apply spatial and statistical methodologies to analyze the geographic distribution of dengue and to relate its incidence to the Health Vulnerability Index (HVI), an indicator that integrates different socioeconomic variables to estimate the degree of health vulnerability in different Brazilian cities. The cases of dengue, incidence rates and Bayesian incidence rates were determined using census tracts covering a period of 3 years in a city with socioeconomic and administrative characteristics typical of Brazilian municipalities. Distribution plots, descriptive statistics, kernel density maps, test of global and local spatial autocorrelation and Spearman correlation were used. No association was found between the incidence of dengue and the HVI. Conversely, statistically significant high-incidence clusters were found over the 3 years in an area identified as having lower health vulnerability. The finding that HVI was not a good indicator of dengue in the city studied may be explained by the complexity of the disease. Administrative and financial problems in the municipalities, environmental factors, cultural changes and the emergence of new serotypes are other factors that hinder the understanding and control of the disease. However, the spatial and statistical methodologies used here are suitable and useful tools for the accurate understanding of dengue and other infectious epidemiological processes.

A brief review of spatial analysis concepts and tools used for mapping, containment and risk modelling of infectious diseases and other illnesses

Fast response and decision making about containment, management, eradication and prevention of diseases, are increasingly important aspects of the work of public health officers and medical providers. Diseases and the agents causing them are spatially and temporally distributed, and effective countermeasures rely on methods that can timely locate the foci of infection, predict the distribution of illnesses and their causes, and evaluate the likelihood of epidemics. These methods require the use of large datasets from ecology, microbiology, health and environmental geography. Geodatabases integrating data from multiple sets of information are managed within the frame of geographic information systems (GIS). Many GIS software packages can be used with minimal training to query, map, analyse and interpret the data. In combination with other statistical or modelling software, predictive and spatio-temporal modelling can be carried out. This paper reviews some of the concepts and tools used in epidemiology and parasitology. The purpose of this review is to provide public health officers with the critical tools to decide about spatial analysis resources and the architecture for the prevention and surveillance systems best suited to their situations.

Relating land cover and spatial distribution of nephropathia epidemica and Lyme borreliosis in Belgium

Lyme borreliosis (LB) and nephropathia epidemica (NE) are zoonoses resulting from two different transmission mechanisms and the action of two different pathogens: the bacterium Borrelia burgdorferi and the Puumala virus, respectively. The landscape configuration is known to influence the spatial spread of both diseases by affecting vector demography and human exposure to infection. Yet, the connections between landscape and disease have rarely been quantified, thereby hampering the exploitation of land cover data sources to segment areas in function of risk. This study implemented a data-driven approach to relate land cover metrics and an indicator of NE/LB risk at different scales of observation of the landscape. Our results showed the suitability of the modeling approach (r² > 0.75, ρ < 0.001) and highlighted the relevance of the scale of observation in the set of landscape attributes found to influence disease risk as well as common and specific risk factors of NE and LB.

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping

BACKGROUND

Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level.

RESULTS

In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing.

CONCLUSIONS

Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset.

[Spatial pattern of legionellosis in Spain, 2003-2007]

OBJECTIVES

To analyze the spatial pattern of legionellosis in Spain for men and women during the period 2003-2007 and to identify spatial clustering of risk.

METHODS

We identified the spatial pattern of the distribution of legionellosis rates based on calculation of rates by municipality through the direct method. Smoothing of these rates was performed by the Empirical Bayes method for studying the spatial pattern of disease for both sexes. We used Morańs index to analyze spatial autocorrelation rates globally. To calculate local rates, the Local Moran's Index [known as local indicators of spatial association (LISA)], was used to analyze the clusters of municipalities with the highest risk.

RESULTS

After smoothing the risk, the highest rates (over 50 per 100,000 inhabitants) were grouped in the eastern Mediterranean coastal areas and the north of the mainland, as well as in the Mediterranean islands. Moran's index smoothed rates were 0.15 for men and 0.23 for women. The spatial clusters of statistically significant higher rates calculated by the LISA index were distributed in the north and east for both sexes.

CONCLUSIONS

These methods of spatial analysis allow patterns of disease distribution to be identified. All the methods used yielded similar results. These techniques are a complementary tool for epidemiological surveillance of infectious diseases.

Mapping health data: improved privacy protection with donut method geomasking

A major challenge in mapping health data is protecting patient privacy while maintaining the spatial resolution necessary for spatial surveillance and outbreak identification. A new adaptive geomasking technique, referred to as the donut method, extends current methods of random displacement by ensuring a user-defined minimum level of geoprivacy. In donut method geomasking, each geocoded address is relocated in a random direction by at least a minimum distance, but less than a maximum distance. The authors compared the donut method with current methods of random perturbation and aggregation regarding measures of privacy protection and cluster detection performance by masking multiple disease field simulations under a range of parameters. Both the donut method and random perturbation performed better than aggregation in cluster detection measures. The performance of the donut method in geoprivacy measures was at least 42.7% higher and in cluster detection measures was less than 4.8% lower than that of random perturbation. Results show that the donut method provides a consistently higher level of privacy protection with a minimal decrease in cluster detection performance, especially in areas where the risk to individual geoprivacy is greatest.

Power Evaluation of Focused Cluster Tests

Many statistical tests have been developed to assess the significance of clusters of disease located around known sources of environmental contaminants, also known as focused disease clusters. The majority of focused-cluster tests were designed to detect a particular spatial pattern of clustering, one in which the disease cluster centers around the pollution source and declines in a radial fashion with distance. However, other spatial patterns of environmentally related disease clusters are likely given that the spatial dispersion patterns of environmental contaminants, and thus human exposure, depend on a number of factors (i.e., meteorology and topography). For this study, data were simulated with five different spatial patterns of disease clusters, reflecting potential pollutant dispersion scenarios: 1) a radial effect decreasing with increasing distance, 2) a radial effect with a defined peak and decreasing with distance, 3) a simple angular effect, 4) an angular effect decreasing with increasing distance and 5) an angular effect with a defined peak and decreasing with distance. The power to detect each type of spatially distributed disease cluster was evaluated using Stone's Maximum Likelihood Ratio Test, Tango's Focused Test, Bithell's Linear Risk Score Test, and variations of the Lawson-Waller Score Test. Study findings underscore the importance of considering environmental contaminant dispersion patterns, particularly directional effects, with respect to focused-cluster test selection in cluster investigations. The effect of extra variation in risk also is considered, although its effect is not substantial in terms of the power of tests.

Cancer incidence in men: a cluster analysis of spatial patterns

BACKGROUND

Spatial clustering of different diseases has received much less attention than single disease mapping. Besides chance or artifact, clustering of different cancers in a given area may depend on exposure to a shared risk factor or to multiple correlated factors (e.g. cigarette smoking and obesity in a deprived area). Models developed so far to investigate co-occurrence of diseases are not well-suited for analyzing many cancers simultaneously. In this paper we propose a simple two-step exploratory method for screening clusters of different cancers in a population.

METHODS

Cancer incidence data were derived from the regional cancer registry of Umbria, Italy. A cluster analysis was performed on smoothed and non-smoothed standardized incidence ratios (SIRs) of the 13 most frequent cancers in males. The Besag, York and Mollie model (BYM) and Poisson kriging were used to produce smoothed SIRs.

RESULTS

Cluster analysis on non-smoothed SIRs was poorly informative in terms of clustering of different cancers, as only larynx and oral cavity were grouped, and of characteristic patterns of cancer incidence in specific geographical areas. On the other hand BYM and Poisson kriging gave similar results, showing cancers of the oral cavity, larynx, esophagus, stomach and liver formed a main cluster. Lung and urinary bladder cancers clustered together but not with the cancers mentioned above. Both methods, particularly the BYM model, identified distinct geographic clusters of adjacent areas.

CONCLUSION

As in single disease mapping, non-smoothed SIRs do not provide reliable estimates of cancer risks because of small area variability. The BYM model produces smooth risk surfaces which, when entered into a cluster analysis, identify well-defined geographical clusters of adjacent areas. It probably enhances or amplifies the signal arising from exposure of more areas (statistical units) to shared risk factors that are associated with different cancers. In Umbria the main clusters were characterized by high risks for cancers with alcohol and tobacco both as risk factors. Tobacco-only related cancers formed a separate cluster to the alcohol- and tobacco-related sites. Joint spatial analysis or investigation of hypothesized exposures might be used for further investigation into interesting geographical clusters.

Modeling spatial patterns in fisheries bycatch: improving bycatch maps to aid fisheries management

Fisheries bycatch, or incidental take, of large vertebrates such as sea turtles, seabirds, and marine mammals, is a pressing conservation and fisheries management issue. Identifying spatial patterns of bycatch is an important element in managing and mitigating bycatch occurrences. Because bycatch of these taxa involves rare events and fishing effort is highly variable in space and time, maps of raw bycatch rates (the ratio of bycatch to fishing effort) can be misleading. Here we show how mapping bycatch can be enhanced through the use of Bayesian hierarchical spatial models. We compare model-based estimates of bycatch rates to raw rates. The model-based estimates were more precise and fit the data well. Using these results, we demonstrate the utility of this approach for providing information to managers on bycatch probabilities and cross-taxa bycatch comparisons. To illustrate this approach, we present an analysis of bycatch data from the U.S. gill net fishery for groundfish in the northwest Atlantic. The goals of this analysis are to produce more reliable estimates of bycatch rates, assess similarity of spatial patterns between taxa, and identify areas of elevated risk of bycatch.

How does Poisson kriging compare to the popular BYM model for mapping disease risks?

Background

Geostatistical techniques are now available to account for spatially varying population sizes and spatial patterns in the mapping of disease rates. At first glance, Poisson kriging represents an attractive alternative to increasingly popular Bayesian spatial models in that: 1) it is easier to implement and less CPU intensive, and 2) it accounts for the size and shape of geographical units, avoiding the limitations of conditional auto-regressive (CAR) models commonly used in Bayesian algorithms while allowing for the creation of isopleth risk maps. Both approaches, however, have never been compared in simulation studies, and there is a need to better understand their merits in terms of accuracy and precision of disease risk estimates.

Results

Besag, York and Mollie's (BYM) model and Poisson kriging (point and area-to-area implementations) were applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. The spatial support (i.e. point versus area) has a much smaller impact on the results than the statistical methodology (i.e. geostatistical versus Bayesian models). Differences between methods are particularly pronounced in the Western US dataset: BYM model yields smoother risk surface and prediction variance that changes mainly as a function of the predicted risk, while the Poisson kriging variance increases in large sparsely populated counties. Simulation studies showed that the geostatistical approach yields smaller prediction errors, more precise and accurate probability intervals, and allows a better discrimination between counties with high and low mortality risks. The benefit of area-to-area Poisson kriging increases as the county geography becomes more heterogeneous and when data beyond the adjacent counties are used in the estimation. The trade-off cost for the easier implementation of point Poisson kriging is slightly larger kriging variances, which reduces the precision of the model of uncertainty.

Conclusion

Bayesian spatial models are increasingly used by public health officials to map mortality risk from observed rates, a preliminary step towards the identification of areas of excess. More attention should however be paid to the spatial and distributional assumptions underlying the popular BYM model. Poisson kriging offers more flexibility in modeling the spatial structure of the risk and generates less smoothing, reducing the likelihood of missing areas of high risk.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Modelling multiple hospital outcomes: the impact of small area and primary care practice variation

BACKGROUND

Appropriate management of care--for example, avoiding unnecessary attendances at, or admissions to, hospital emergency units when they could be handled in primary care--is an important part of health strategy. However, some variations in these outcomes could be due to genuine variations in health need. This paper proposes a new method of explaining variations in hospital utilisation across small areas and the general practices (GPs) responsible for patient primary care. By controlling for the influence of true need on such variations, one may identify remaining sources of excess emergency attendances and admissions, both at area and practice level, that may be related to the quality, resourcing or organisation of care. The present paper accordingly develops a methodology that recognises the interplay between population mix factors (health need) and primary care factors (e.g. referral thresholds), that allows for unobserved influences on hospitalisation usage, and that also reflects interdependence between hospital outcomes. A case study considers relativities in attendance and admission rates at a North London hospital involving 149 small areas and 53 GP practices.

RESULTS

A fixed effects model shows variations in attendances and admissions are significantly related (positively) to area and practice need, and nursing home patients, and related (negatively) to primary care access and distance of patient homes from the hospital. Modelling the impact of known factors alone is not sufficient to produce a satisfactory fit to the observations, and random effects at area and practice level are needed to improve fit and account for overdispersion.

CONCLUSION

The case study finds variation in attendance and admission rates across areas and practices after controlling for need, and remaining differences between practices may be attributable to referral behaviour unrelated to need, or to staffing, resourcing, and access issues. In managerial terms, the analysis points to the utility of formal statistical analysis of hospitalisation rates as a prelude to non-statistical investigation of primary care resourcing and organisation. For example, there may be implications for the location of staff involved in community management of chronic conditions; health managers may also investigate whether some practices have unusual populations (homeless, asylum seekers, students) that explain different hospital use patterns.

Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging

Background

Cancer mortality maps are used by public health officials to identify areas of excess and to guide surveillance and control activities. Quality of decision-making thus relies on an accurate quantification of risks from observed rates which can be very unreliable when computed from sparsely populated geographical units or recorded for minority populations. This paper presents a geostatistical methodology that accounts for spatially varying population sizes and spatial patterns in the processing of cancer mortality data. Simulation studies are conducted to compare the performances of Poisson kriging to a few simple smoothers (i.e. population-weighted estimators and empirical Bayes smoothers) under different scenarios for the disease frequency, the population size, and the spatial pattern of risk. A public-domain executable with example datasets is provided.

Results

The analysis of age-adjusted mortality rates for breast and cervix cancers illustrated some key features of commonly used smoothing techniques. Because of the small weight assigned to the rate observed over the entity being smoothed (kernel weight), the population-weighted average leads to risk maps that show little variability. Other techniques assign larger and similar kernel weights but they use a different piece of auxiliary information in the prediction: global or local means for global or local empirical Bayes smoothers, and spatial combination of surrounding rates for the geostatistical estimator. Simulation studies indicated that Poisson kriging outperforms other approaches for most scenarios, with a clear benefit when the risk values are spatially correlated. Global empirical Bayes smoothers provide more accurate predictions under the least frequent scenario of spatially random risk.

Conclusion

The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of mortality rates into the mapping of risk values and the quantification of the associated uncertainty, while being easier to implement than a full Bayesian model. The availability of a public-domain executable makes the geostatistical analysis of health data, and its comparison to traditional smoothers, more accessible to common users. In future papers this methodology will be generalized to the simulation of the spatial distribution of risk values and the propagation of the uncertainty attached to predicted risks in local cluster analysis.

Municipal health expectancy in Japan: decreased healthy longevity of older people in socioeconomically disadvantaged areas

BACKGROUND

Little is known about small-area variation in healthy longevity of older people and its socioeconomic correlates. This study aimed to estimate health expectancy at 65 years (HE65) at the municipal level in Japan, and to examine its relation to area socio-demographic conditions.

METHODS

HE65 of municipalities (N = 3361) across Japan was estimated by a linear regression formula with life expectancy at 65 years and the prevalence of those certificated as needing nursing care. The relation between HE65 and area socio-demographic indicators was examined using correlation coefficients.

RESULTS

The estimated HE65 (years) ranged from 13.13 to 17.39 for men and from 14.84 to 20.53 for women. HE65 was significantly positively correlated with the proportion of elderly and per capita income, and negatively correlated with the percentage of households of a single elderly person, divorce rate, and unemployment rate. These relations were stronger in large municipalities (with a population of more than 100,000) than in small and medium-size municipalities.

CONCLUSION

A decrease in healthy longevity of older people was associated with a higher percentage of households of a single elderly person and divorce rate, and lower socioeconomic conditions. This study suggests that older people in urban areas are susceptible to socio-demographic factors, and a social support network for older people living in socioeconomically disadvantaged conditions should be encouraged.