Spatial Data Analysis of Regional Counts

Differentiating anomalous disease intensity with confounding variables in space

Background

The investigation of perceived geographical disease clusters serves as a preliminary step that expedites subsequent etiological studies and analysis of epidemicity. With the identification of disease clusters of statistical significance, to determine whether or not the detected disease clusters can be explained by known or suspected risk factors is a logical next step. The models allowing for confounding variables permit the investigators to determine if some risk factors can explain the occurrence of geographical clustering of disease incidence and to investigate other hidden spatially related risk factors if there still exist geographical disease clusters, after adjusting for risk factors.

Methods

We propose to develop statistical methods for differentiating incidence intensity of geographical disease clusters of peak incidence and low incidence in a hierarchical manner, adjusted for confounding variables. The methods prioritize the areas with the highest or lowest incidence anomalies and are designed to recognize hierarchical (in intensity) disease clusters of respectively high-risk areas and low-risk areas within close geographic proximity on a map, with the adjustment for known or suspected risk factors. The data on spatial occurrence of sudden infant death syndrome with a confounding variable of race in North Carolina counties were analyzed, using the proposed methods.

Results

The proposed Poisson model appears better than the one based on SMR, particularly at facilitating discrimination between the 13 counties with no cases. Our study showed that the difference in racial distribution of live births explained, to a large extent, the 3 previously identified hierarchical high-intensity clusters, and a small region of 4 mutually adjacent counties with the higher race-adjusted rates, which was hidden previously, emerged in the southwest, indicating that unobserved spatially related risk factors may cause the elevated risk. We also showed that a large geographical cluster with the low race-adjusted rates, which was hidden previously, emerged in the mid-east.

Conclusion

With the information on hierarchy in adjusted intensity levels, epidemiologists and public health officials can better prioritize the regions with the highest rates for thorough etiologic studies, seeking hidden spatially related risk factors and precisely moving resources to areas with genuine highest abnormalities.

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

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

Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing

BACKGROUND

Many methods of spatial smoothing have been developed, for both point data as well as areal data. In Bayesian spatial models, this is achieved by purposefully designed prior(s) or smoothing functions which smooth estimates towards a local or global mean. Smoothing is important for several reasons, not least of all because it increases predictive robustness and reduces uncertainty of the estimates. Despite the benefits of smoothing, this attribute is all but ignored when it comes to model selection. Traditional goodness-of-fit measures focus on model fit and model parsimony, but neglect "goodness-of-smoothing", and are therefore not necessarily good indicators of model performance. Comparing spatial models while taking into account the degree of spatial smoothing is not straightforward because smoothing and model fit can be viewed as opposing goals. Over- and under-smoothing of spatial data are genuine concerns, but have received very little attention in the literature.

METHODS

This paper demonstrates the problem with spatial model selection based solely on goodness-of-fit by proposing several methods for quantifying the degree of smoothing. Several commonly used spatial models are fit to real data, and subsequently compared using the goodness-of-fit and goodness-of-smoothing statistics.

RESULTS

The proposed goodness-of-smoothing statistics show substantial agreement in the task of model selection, and tend to avoid models that over- or under-smooth. Conversely, the traditional goodness-of-fit criteria often don't agree, and can lead to poor model choice. In particular, the well-known deviance information criterion tended to select under-smoothed models.

CONCLUSIONS

Some of the goodness-of-smoothing methods may be improved with modifications and better guidelines for their interpretation. However, these proposed goodness-of-smoothing methods offer researchers a solution to spatial model selection which is easy to implement. Moreover, they highlight the danger in relying on goodness-of-fit measures when comparing spatial models.

Spatializing Area-Based Measures of Neighborhood Characteristics for Multilevel Regression Analyses: An Areal Median Filtering Approach

Area-based measures of neighborhood characteristics simply derived from enumeration units (e.g., census tracts or block groups) ignore the potential of spatial spillover effects, and thus incorporating such measures into multilevel regression models may underestimate the neighborhood effects on health. To overcome this limitation, we describe the concept and method of areal median filtering to spatialize area-based measures of neighborhood characteristics for multilevel regression analyses. The areal median filtering approach provides a means to specify or formulate "neighborhoods" as meaningful geographic entities by removing enumeration unit boundaries as the absolute barriers and by pooling information from the neighboring enumeration units. This spatializing process takes into account for the potential of spatial spillover effects and also converts aspatial measures of neighborhood characteristics into spatial measures. From a conceptual and methodological standpoint, incorporating the derived spatial measures into multilevel regression analyses allows us to more accurately examine the relationships between neighborhood characteristics and health. To promote and set the stage for informative research in the future, we provide a few important conceptual and methodological remarks, and discuss possible applications, inherent limitations, and practical solutions for using the areal median filtering approach in the study of neighborhood effects on health.

Local population characteristics and hemoglobin A1c testing rates among diabetic medicare beneficiaries

BACKGROUND

Proposed payment reforms in the US healthcare system would hold providers accountable for the care delivered to an assigned patient population. Annual hemoglobin A1c (HbA1c) tests are recommended for all diabetics, but some patient populations may face barriers to high quality healthcare that are beyond providers' control. The magnitude of fine-grained variations in care for diabetic Medicare beneficiaries, and their associations with local population characteristics, are unknown.

METHODS

HbA1c tests were recorded for 480,745 diabetic Medicare beneficiaries. Spatial analysis was used to create ZIP code-level estimated testing rates. Associations of testing rates with local population characteristics that are outside the control of providers--population density, the percent African American, with less than a high school education, or living in poverty--were assessed.

RESULTS

In 2009, 83.3% of diabetic Medicare beneficiaries received HbA1c tests. Estimated ZIP code-level rates ranged from 71.0% in the lowest decile to 93.1% in the highest. With each 10% increase in the percent of the population that was African American, associated HbA1c testing rates were 0.24% lower (95% CI -0.32--0.17); for identical increases in the percent with less than a high school education or the percent living in poverty, testing rates were 0.70% lower (-0.95--0.46) and 1.6% lower (-1.8--1.4), respectively. Testing rates were lowest in the least and most densely populated ZIP codes. Population characteristics explained 5% of testing rate variations.

CONCLUSIONS

HbA1c testing rates are associated with population characteristics, but these characteristics fail to explain the vast majority of variations. Consequently, even complete risk-adjustment may have little impact on some process of care quality measures; much of the ZIP code-related variations in testing rates likely result from provider-based differences and idiosyncratic local factors not related to poverty, education, or race.

Spatial clusters in a global-dependence model

Spatial data often possess multiple components, such as local clusters and global clustering, and these effects are not easy to be separated. In this study, we propose an approach to deal with the cases where both global clustering and local clusters exist simultaneously. The proposed method is a two-stage approach, estimating the autocorrelation by an EM algorithm and detecting the clusters by a generalized least square method. It reduces the influence of global dependence on detecting local clusters and has lower false alarms. Simulations and the sudden infant disease syndrome data of North Carolina are used to illustrate the difference between the proposed method and the spatial scan statistic.

Bacterial meningitis and living conditions

INTRODUCTION

Bacterial meningitis has great social relevance due to its ability to produce sequelae and cause death. It is most frequently found in developing countries, especially among children. Meningococcal meningitis occurs at a high frequency in populations with poor living conditions. This study describes the temporal evolution of bacterial meningitis in Salvador, Brazil, 1995-2009, and verifies the association between its spatial variation and the living conditions of the population.

METHODS

This was an ecological study in which the areas of information were classified by an index of living conditions. It examined fluctuations using a trend curve, and the relationship between this index and the spatial distribution of meningitis was verified using simple linear regression.

RESULTS

From 1995-2009, there were 3,456 confirmed cases of bacterial meningitis in Salvador. We observed a downward trend during this period, with a yearly incidence of 9.1 cases/100,000 population and fatality of 16.7%. Children aged <5 years old and male were more affected. There was no significant spatial autocorrelation or pattern in the spatial distribution of the disease. The areas with the worst living conditions had higher fatality from meningococcal disease (β = 0.0078117, p < 0.005).

CONCLUSIONS

Bacterial meningitis reaches all social strata; however, areas with poor living conditions have a greater proportion of cases that progress to death. This finding reflects the difficulties for ready access and poor quality of medical care faced by these populations.

Geographical mapping and Bayesian spatial modeling of malaria incidence in Sistan and Baluchistan province, Iran

OBJECTIVE

To present the geographical map of malaria and identify some of the important environmental factors of this disease in Sistan and Baluchistan province, Iran.

METHODS

We used the registered malaria data to compute the standard incidence rates (SIRs) of malaria in different areas of Sistan and Baluchistan province for a nine-year period (from 2001 to 2009). Statistical analyses consisted of two different parts: geographical mapping of malaria incidence rates, and modeling the environmental factors. The empirical Bayesian estimates of malaria SIRs were utilized for geographical mapping of malaria and a Poisson random effects model was used for assessing the effect of environmental factors on malaria SIRs.

RESULTS

In general, 64,926 new cases of malaria were registered in Sistan and Baluchistan Province from 2001 to 2009. Among them, 42,695 patients (65.8%) were male and 22,231 patients (34.2%) were female. Modeling the environmental factors showed that malaria incidence rates had positive relationship with humidity, elevation, average minimum temperature and average maximum temperature, while rainfall had negative effect on malaria SIRs in this province.

CONCLUSIONS

The results of the present study reveals that malaria is still a serious health problem in Sistan and Baluchistan province, Iran. Geographical map and related environmental factors of malaria can help the health policy makers to intervene in high risk areas more efficiently and allocate the resources in a proper manner.

Análise da distribuição espacial da mortalidade neonatal e de fatores associados, em Salvador, Bahia, Brasil, no período 2000-2006

Realizou-se estudo de agregados espaciais visando a identificar padrões na distribuição espacial da mortalidade neonatal, bem como fatores associados, em Salvador, Bahia, Brasil, 2000-2006. Foram construídos mapas temáticos e usadas técnicas para apreciação formal de dependência espacial. Mediante modelos de regressão linear múltipla (espacial e não espacial) verificou-se a relação entre distribuição espacial dessa mortalidade e fatores selecionados. Evidenciou-se autocorrelação espacial para a mortalidade neonatal (I = 0,17; p = 0,0100), não havendo, portanto, aleatoriedade em sua distribuição. Foi delineado um padrão espacial em que os maiores riscos (> 9,0/1.000 nascidos vivos) concentraram-se em áreas do centro e subúrbio, onde reside a população de menor condição socioeconômica, mostrando-se esta distribuição associada aos fatores de risco analisados. A proporção de nascidos vivos com baixo peso foi a única variável significativamente associada à mortalidade neonatal. Possivelmente, as condições de vida da população contribuíram para a desigual distribuição espacial da mortalidade neonatal nesse município.

Georeferenced data in epidemiologic research

This paper reviews some conceptual and practical issues regarding the application of georeferenced data in epidemiologic research. Starting with the disease mapping tradition of geographical medicine, topics such as types of georeferenced data, implications for data analysis, spatial autocorrelation and main analytical approaches are heuristically discussed, relying on examples from the epidemiologic literature, most of them concerning mapping disease distribution, detection of disease spatial clustering, evaluation of exposure in environmental health investigation and ecological correlation studies. As for concluding remarks, special topics that deserve further development, including the misuses of the concept of space in epidemiologic research, issues related to data quality and confidentiality, the role of epidemiologic designs for spatial research, sensitivity analysis and spatiotemporal modeling, are presented.

Exploratory spatial data analysis for the identification of risk factors to birth defects

BACKGROUND

Birth defects, which are the major cause of infant mortality and a leading cause of disability, refer to "Any anomaly, functional or structural, that presents in infancy or later in life and is caused by events preceding birth, whether inherited, or acquired (ICBDMS)". However, the risk factors associated with heredity and/or environment are very difficult to filter out accurately. This study selected an area with the highest ratio of neural-tube birth defect (NTBD) occurrences worldwide to identify the scale of environmental risk factors for birth defects using exploratory spatial data analysis methods.

METHODS

By birth defect registers based on hospital records and investigation in villages, the number of birth defects cases within a four-year period was acquired and classified by organ system. The neural-tube birth defect ratio was calculated according to the number of births planned for each village in the study area, as the family planning policy is strictly adhered to in China. The Bayesian modeling method was used to estimate the ratio in order to remove the dependence of variance caused by different populations in each village. A recently developed statistical spatial method for detecting hotspots, Getis's 7, was used to detect the high-risk regions for neural-tube birth defects in the study area.

RESULTS

After the Bayesian modeling method was used to calculate the ratio of neural-tube birth defects occurrences, Getis's statistics method was used in different distance scales. Two typical clustering phenomena were present in the study area. One was related to socioeconomic activities, and the other was related to soil type distributions.

CONCLUSION

The fact that there were two typical hotspot clustering phenomena provides evidence that the risk for neural-tube birth defect exists on two different scales (a socioeconomic scale at 6.84 km and a soil type scale at 22.8 km) for the area studied. Although our study has limited spatial exploratory data for the analysis of the neural-tube birth defect occurrence ratio and for finding clues to risk factors, this result provides effective clues for further physical, chemical and even more molecular laboratory testing according to these two spatial scales.

Spatial analysis of disease--applications

The application of spatial statistical analysis to health data has reached adolescence. The theory and the software are both still maturing. We are drawing upon the experiences of the geostatisticians in modeling surfaces and the econometricians in modeling time series. "New and improved" computer algorithms are constantly being provided to implement the evolving theory or to improve the processing in terms of stability, reliability, and efficiency. We will come of age when we have the theory, the software, and the process to reliably produce "generalized spatio-temporal" models suitable for health data. In the meantime, biostatisticians need to acknowledge when their data is not independently distributed and to consider the spatial correlation in their analysis. This chapter provided examples using four available methods. The methods were spatial filtering, identifying clusters using the spatial scan statistic, hierarchical modeling, and conditional autoregression modeling.

Spatial analysis of disease

In this chapter, we have reviewed the history of the spatial analysis of disease and the statistical methods used for the exploratory analysis, testing and modeling of spatial patterns. In the next chapter, the principles described here will be illustrated.

Spatial modeling using mixed models: an ecologic study of visceral leishmaniasis in Teresina, Piauí State, Brazil

Most ecologic studies use geographical areas as units of observation. Because data from areas close to one another tend to be more alike than those from distant areas, estimation of effect size and confidence intervals should consider spatial autocorrelation of measurements. In this report we demonstrate a method for modeling spatial autocorrelation within a mixed model framework, using data on environmental and socioeconomic determinants of the incidence of visceral leishmaniasis (VL) in the city of Teresina, Piauí, Brazil. A model with a spherical covariance structure indicated significant spatial autocorrelation in the data and yielded a better fit than one assuming independent observations. While both models showed a positive association between VL incidence and residence in a favela (slum) or in areas with green vegetation, values for the fixed effects and standard errors differed substantially between the models. Exploration of the data's spatial correlation structure through the semivariogram should precede the use of these models. Our findings support the hypothesis of spatial dependence of VL rates and indicate that it might be useful to model spatial correlation in order to obtain more accurate point and standard error estimates.

The urban spread of visceral leishmaniasis: clues from spatial analysis

BACKGROUND

The pattern of spread of visceral leishmaniasis in Brazilian cities is poorly understood.

METHODS

We used geographic information systems and spatial statistics to evaluate the distribution of 1061 cases of visceral leishmaniasis in Teresina, Brazil, in 1993 through 1996.

RESULTS

A locally weighted (LOESS) regression model, which was fit as a smoothed function of spatial coordinates, demonstrated large-scale variation, with high incidence rates in peripheral neighborhoods that bordered forest land and pastures. Moran's I indicated small-scale variation and clustering up to 300 m, roughly the flight range of the sand fly vector.

CONCLUSIONS

Spatial analytical techniques can identify high-risk areas for targeting control interventions.

Spatial associations among density of cattle, abundance of wild canids, and seroprevalence to Neospora caninum in a population of beef calves

OBJECTIVE

To determine the epidemiologic plausibility of a sylvatic transmission cycle for Neospora caninum between wild canids and beef cattle.

DESIGN

Spatial analysis study.

ANIMALS

1,009 weaned beef steers from 94 beef herds in Texas.

PROCEDURE

Calves were grouped on the basis of seroprevalence for N caninum and ecologic region in Texas. The Morans I test was used to evaluate spatial interdependence for adjusted seroprevalence by ecologic region. Cattle density (Number of cattle/259 km2 [Number of cattle/100 mile2] of each ecologic region) and abundance indices for gray foxes and coyotes (Number of animals/161 spotlight-transect [census] km [Number of animals/100 census miles] of each ecologic region) were used as covariates in spatial regression models, with adjusted seroprevalence as the outcome variable. A geographic information system (GIS) that used similar covariate information for each county was used to validate spatial regression models. Results-Spatial interdependence was not detected for ecologic regions. Three spatial regression models were tested. Each model contained a variable for cattle density for the ecologic regions. Results for the 3 models revealed that seroprevalence was associated with cattle density and abundances of gray foxes, coyotes, or both. Abundances of gray foxes and coyotes were collinear. Results of a GIS-generated model validated these spatial models.

CONCLUSIONS AND CLINICAL RELEVANCE

In Texas, beef cattle are at increased risk of exposure to N caninum as a result of the abundance of wild canids and the density of beef cattle. It is plausible that a sylvatic transmission cycle for neosporosis exists.

Simultaneous smoothing and adjusting mortality rates in U.S. counties: melanoma in white females and white males

Detecting patterns in health-related data for geographic areas is facilitated with the use of exploratory methods, especially smoothing. In addition, these data often must be adjusted for known prognostic factors such as age and gender. The analysis in this paper focuses on mortality rates due to malignant melanoma in White males and White females; these data are adjusted for both age and latitude, separately for males and females, and then smoothed using (a) a non-linear smoother known as weighted head-banging, and (b) a new method that incorporates the adjustment and the smoothing simultaneously. Maps of the continental United States show regions of high rates, even after having adjusted for age and latitude, and suggest the possibility of other variables that may influence the rates.

A study of the breast cancer dynamics in North Carolina

This work is concerned with the study of breast cancer incidence in the State of North Carolina. Methodologically, the current analysis illustrates the importance of spatiotemporal random field modelling and introduces a mode of reasoning that is based on a combination of inductive and deductive processes. The composite space/time analysis utilizes the variability characteristics of incidence and the mathematical features of the random field model to fit it to the data. The analysis is significantly general and can efficiently represent non-homogeneous and non-stationary characteristics of breast cancer variation. Incidence predictions are produced using data at the same time period as well as data from other time periods and disease registries. The random field provides a rigorous and systematic method for generating detailed maps, which offer a quantitative description of the incidence variation from place to place and from time to time, together with a measure of the accuracy of the incidence maps. Spatiotemporal mapping accounts for the geographical locations and the time instants of the incidence observations, which is not usually the case with most empirical Bayes methods. It is also more accurate than purely spatial statistics methods, and can offer valuable information about the breast cancer risk and dynamics in North Carolina. Field studies could be initialized in high-rate areas identified by the maps in an effort to uncover environmental or life-style factors that might be responsible for the high risk rates. Also, the incidence maps can help elucidate causal mechanisms, explain disease occurrences at a certain scale, and offer guidance in health management and administration.

[Characteristics of neonatal mortality in the State of Rio de Janeiro, Brazil, in the 1980's: a spatio-temporal analysis]

OBJECTIVE

The spatial distribution of neonatal mortality by age-group (0-23 hours, 1-6 days and 7-27 days) in the State of Rio de Janeiro, Brazil, for two periods of time 1979-81 and 1990-92, is analysed.

METHODOLOGY

A methodology was used to perform the spatial analysis which took the counties of Rio de Janeiro as the spatial units and "first-nearest-neighbors" as the neighborhood criterion. For the purpose of detecting anisotropy, the connection matrix was defined through "first-nearest-neighbors" in a particular direction. To understand the spatial behavior of neonatal mortality, social and environmental indicators and indicators of medical assistance by county for both periods of time were constructed.

RESULTS AND CONCLUSIONS

At the beginning of the 80's, the neonatal mortality for the age group 7-27 days showed the presence of clusters in the East and Southeast in direct association with the poorest conditions of life in the State, characteristics that had vanished by the next decade. Spatial dependence for the mortality rates for the first day of life, for 1991, was identified clusters in two different regions beings detected, followed by a positive correlation with "number of private hospital beds per inhabitant". Some of the cluster counties were, in particular, death receivers from neighboring counties and showed hospital case fatality rates much greater than the overall mean rate.

Linking public health data using geographic information system techniques: Alaskan community characteristics and infant mortality

This article identifies geographical contexts important in differentiating infant mortality in Alaska and uses spatial processing models to link and analyse multi-source data. Information characterizing geographical locations are collected from Alaska's vital statistics for the years 1982-91 and the 1990 Census. Geographic information system (GIS) techniques are applied to identify spatially homogeneous regions, assess spatial compatibility across databases, and allocate geographical units across boundaries. A primary goal of this paper is to encourage spatial linkage and analysis techniques for vital statistics and census data. By demonstrating the interplay of tabular, graphical, and mapping techniques on Alaskan infant mortality, this analysis describes procedures for conducting epidemiological research with data spatially defined at distinct geographical levels.

A constrained empirical Bayes estimator for incidence rates in areas with small populations

Maps that show the geographic distribution of incidence rates can be useful tools for analysing spatial variation in mortality and morbidity. To attain the necessary geographic resolution, however, production of such maps often requires estimation of incidence in areas with small populations where the observed rates may be highly unstable. Manton et al. have presented an empirical Bayes stabilization procedure in which the observed rate is combined with an area-specific estimate of the underlying incidence. The approach allows for the mapping of outcomes with varied and possibly unknown etiologies without necessitating covariate dependent modelling of the expected rate. The empirical distribution of a collection of these estimates, however, may not provide an adequate description of the dispersion among the true rates. As a result, decisions based on the histogram of the empirical Bayes estimates may be suspect. We propose a modified version of the approach in which the mean and sample variance of the ensemble of estimates are constrained to equal the appropriate moments of the posterior distribution. The resulting collection of constrained empirical Bayes estimators has nearly the stability of the unconstrained approach and provides an improved estimator of the true rate distribution. We illustrate use of the estimator by producing stabilized county-level maps of U.S. fire- and burn-related mortality rates and validate the analytic results using a simulation analysis.

Spatial distribution of neurons in tissue culture wells: implications for sampling methods to estimate population size

Many laboratory procedures require the counting of cells in culture. While many cultured cells may be counted by automated methods, neuronal cultures often require manual cell counting methods that are prohibitively time-consuming. This paper examines methods of sampling from tissue culture wells for estimating total cell counts. Performance of sampling and estimation schemes will depend in part on how the cells distribute themselves within a well. Spatial statistical analysis techniques are applied to the known total number and distribution of neurons in two wells counted in a grid scheme to demonstrate some important features of the neuron distributional patterns. Based on these two wells and simulated realizations from other point processes, a new sampling and estimation technique using open wedge-shaped sampling regions radiating from the centre of the well is proposed. This method is shown to result in more accurate estimates of the total number of neurons in the well than standard methods.