Spatial Cluster Detection Methods Research Articles

Evaluation and comparison of spatial cluster detection methods for improved decision making of disease surveillance: a case study of national dengue surveillance in Thailand

BackgroundDengue is a mosquito-borne disease that causes over 300 million infections worldwide each year with no specific treatment available. Effective surveillance systems are needed for outbreak detection and resource allocation. Spatial cluster detection methods are commonly used, but no general guidance exists on the most appropriate method for dengue surveillance. Therefore, a comprehensive study is needed to assess different methods and provide guidance for dengue surveillance programs.MethodsTo evaluate the effectiveness of different cluster detection methods for dengue surveillance, we selected and assessed commonly used methods: Getis Ord Gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${G}_{i}^{*}$$\\end{document}, Local Moran, SaTScan, and Bayesian modeling. We conducted a simulation study to compare their performance in detecting clusters, and applied all methods to a case study of dengue surveillance in Thailand in 2019 to further evaluate their practical utility.ResultsIn the simulation study, Getis Ord Gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${G}_{i}^{*}$$\\end{document} and Local Moran had similar performance, with most misdetections occurring at cluster boundaries and isolated hotspots. SaTScan showed better precision but was less effective at detecting inner outliers, although it performed well on large outbreaks. Bayesian convolution modeling had the highest overall precision in the simulation study. In the dengue case study in Thailand, Getis Ord Gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${G}_{i}^{*}$$\\end{document} and Local Moran missed most disease clusters, while SaTScan was mostly able to detect a large cluster. Bayesian disease mapping seemed to be the most effective, with adaptive detection of irregularly shaped disease anomalies.ConclusionsBayesian modeling showed to be the most effective method, demonstrating the best accuracy in adaptively identifying irregularly shaped disease anomalies. In contrast, SaTScan excelled in detecting large outbreaks and regular forms. This study provides empirical evidence for the selection of appropriate tools for dengue surveillance in Thailand, with potential applicability to other disease control programs in similar settings.

Geographic footprints of life expectancy inequalities in the state of Geneva, Switzerland

Though Switzerland has one of the highest life expectancies in the world, this global indicator may mask significant disparities at a local level. The present study used a spatial cluster detection approach based on individual death records to investigate the geographical footprint of life expectancy inequalities in the state of Geneva, Switzerland. Individual-level mortality data (n = 22,751) were obtained from Geneva’s official death notices (2009–2016). We measured life expectancy inequalities using the years of potential life lost or gained (YPLLG) metric, defined as the difference between an individual’s age at death and their life expectancy at birth. We assessed the spatial dependence of YPLLG across the state of Geneva using spatial autocorrelation statistics (Local Moran’s I). To ensure the robustness of the patterns discovered, we ran the analyses for ten random subsets of 10,000 individuals taken from the 22,751 deceased. We also repeated the spatial analysis for YPLLG before and after controlling for individual-level and neighborhood-level covariates. The results showed that YPLLG was not randomly distributed across the state of Geneva. The ten random subsets revealed no significant difference with the geographic footprint of YPLLG and the population characteristics within Local Moran cluster types, suggesting robustness for the observed spatial structure. The proportion of women, the proportion of Swiss, the neighborhood median income, and the neighborhood median age were all significantly lower for populations in low YPLLG clusters when compared to populations in high YPLLG clusters. After controlling for individual-level and neighborhood-level covariates, we observed a reduction of 43% and 39% in the size of low and high YPLLG clusters, respectively. To our knowledge, this is the first study in Switzerland using spatial cluster detection methods to investigate inequalities in life expectancy at a local scale and based on individual data. We identified clear geographic footprints of YPLLG, which may support further investigations and guide future public health interventions at the local level.

Statistical methods for spatial cluster detection in childhood cancer incidence: A simulation study

Background and objectiveThe potential existence of spatial clusters in childhood cancer incidence is a debated topic. Identification of such clusters may help to better understand etiology and develop preventive strategies. We evaluated widely used statistical approaches to cluster detection in this context. MethodsIncidence of newly diagnosed childhood cancer (140/1,000,000 children under 15 years) and nephroblastoma (7/1,000,000) was simulated. Clusters of defined size (1–50) were randomly assembled on the district level in Germany. Each cluster was simulated with different relative risk levels (1–100). For each combination 2000 iterations were done. Simulated data was then analyzed by three local clustering tests: Besag-Newell method, spatial scan statistic and Bayesian Besag-York-Mollié with Integrated Nested Laplace Approximation approach. The operating characteristics (sensitivity, specificity, predictive values, power and correct classification) of all three methods were systematically described. ResultsPerformance varied considerably within and between methods, depending on the simulated setting. Sensitivity of all methods was positively associated with increasing size, incidence and RR of the high-risk area. Besag-York-Mollié showed highest specificity for minimally increased RR in most scenarios. The performance of all methods was lower in the nephroblastoma scenario compared with the scenario including all cancer cases. ConclusionThis study illustrates the challenge to make reliable inferences on the existence of spatial clusters based on single statistical approaches in childhood cancer. Application of multiple methods, ideally with known operating characteristics, and a critical discussion of the joint evidence seems recommendable when aiming to identify high-risk clusters.

Support vector subset scan for spatial pattern detection

Discovery of localized and irregularly shaped anomalous patterns in spatial data provides useful context for operational decisions across many policy domains. The support vector subset scan (SVSS) integrates the penalized fast subset scan with a kernel support vector machine classifier to accurately detect spatial clusters without imposing hard constraints on the shape or size of the pattern. The method iterates between (1) efficiently maximizing a penalized log-likelihood ratio over subsets of locations to obtain an anomalous pattern, and (2) learning a high-dimensional decision boundary between locations included in and excluded from the anomalous subset. On each iteration, location-specific penalties to the log-likelihood ratio are assigned according to distance to the decision boundary, encouraging patterns which are spatially compact but potentially highly irregular in shape. SVSS outperforms competing methods for spatial cluster detection at the task of detecting randomly generated patterns in simulated experiments. SVSS enables discovery of practically-useful anomalous patterns for disease surveillance in Chicago, IL, crime hotspot detection in Portland, OR, and pothole cluster detection in Pittsburgh, PA, as demonstrated by experiments using publicly available data sets from these domains.

Cluster Detection of Cancer Incidence: Analyzing Childhood Residential Location Linked to Later Life Cancer Records

BackgroundChildhood environmental exposures are now recognized contributors to cancer later in life. However, direct measurement of environmental contaminants is not feasible using most retrospective datasets and potentially long latency periods exist between exposures and cancer incidence. Investigating the spatiotemporal patterns of cancer clustering is one useful approach to evaluate the importance of childhood environment on adult cancer risk. We assessed spatial clustering of cancer incidence in 1966-2017 based on early life location defined by household Enumeration District (ED) at the 1940 US Census.MethodsA cohort of all individuals born 1930-1939 was selected from the Utah Population Database. Incident cancer cases for 25 cancer types were identified beginning in 1966 from the Utah Cancer Registry or by death records and linked to geocoded population-weighted ED centroids. Follow-up time was measured as years from 1940 to first primary cancer diagnosis, death, or last known residence in Utah. Spatial scan statistic with a purely elliptic scanning window was used to identify spatial clustering of EDs with high rates of cancer assuming the discrete Poisson model. Separate analyses were completed for each cancer type. Our analysis included 92,279 individuals who contributed 4,674,932 person-years representing 826 EDs.ResultsAverage follow-up time was 50.9 years (range 0.58-78 years). Cancer was diagnosed in 21% of individuals on follow-up. The number of individuals in an ED ranged from 11-518 (mean = 111). We detected four clusters of excess risk of breast (Relative Risk [RR]=1.27, p=0.028), leukemia (RR=1.92, p=0.033), lung (RR=1.89, p=0.013), and prostate cancers (RR=1.27, p=0.0089).ConclusionsWhile this study was hypothesis generating and did not test for environmental contaminants directly, we demonstrate that early life location may contribute to later health outcomes. With the growing availability of longitudinal databases that compile records across the lifespan, spatial cluster detection methods offer unique opportunities to improve understanding of chronic disease etiology.

Abstract A11: Neighborhood clustering of bladder cancer incidence in Utah: Analyzing census data linked to cancer records

Abstract Evaluating risk factors across the lifespan (using the life course perspective) is important when considering the role of environment on BCa risk. Spatial cluster detection methods offer unique opportunities to identify shared exposures of individuals with BCa on the local level and formulate hypotheses about the potential role of environmental exposures. This study tests for evidence of spatial clustering of BCa incidence based on neighborhoods defined as 1940 US Census enumeration districts (ED). Data were extracted from the Utah Population Database (UPDB). UPDB holds birth, death, historic US Census, and driver license records that allow tracking of an individual’s location across the lifespan. UPDB is linked to the Utah Cancer Registry, an original member of the Surveillance, Epidemiology, and End Results program. Incident BCa cases from 1966 to 2017 were identified in the UCR or by death records and linked to UPDB. We geocoded all 1940 US Census ED centroids in Utah using US Census maps and ArcGIS software. The cohort comprises all individuals age 0–40 years at the time of the 1940 Census (Ncohort=343,521). We excluded individuals with an absence of follow-up information (Nexcluded=82,726). Our final cohort size was 260,795 individuals who contributed 13,816,670 person-years. SatScan software was used to identify spatial clustering of EDs with high rates of BCa. BCa was diagnosed in 2,654 individuals during follow-up (rate=19.2 cases per 100,000 person-years). Approximately 78.4% of cases were male. Average follow-up time was 53 years (range 1-78 years). We identified a circular cluster of 1.54 kilometers in diameter containing 23 ED centroids in an urban area, with a rate of 32.7 cases per 100,000 person-years (relative risk = 1.73, p=0.0023). We found evidence of spatial clustering of BCa incidence in an urban area of Salt Lake City, Utah for individuals in early life (0-40 years) at the time of the 1940 US Census. Individuals residing in this shared space were significantly more likely to develop BCa later in life, with a 73% increase in the incidence rate. Shared space in this context is presumed to be a proxy for environmental exposures. Environmental exposures including arsenic in drinking water and exposure to carcinogenic chemicals are associated with bladder cancer incidence. While this study was hypothesis generating and did not test for contaminants directly, future studies would benefit from the inclusion of contamination data. Additionally, we were limited by the use of residential history at a single time point and lack of data on personal behaviors (e.g., smoking). Strengths of this study include large cohort size, long follow-up time, and ability to expand to an early census. A life course perspective on cancer incidence provides for innovative methods to explore the environmental contexts of disease. Citation Format: Claire L. Leiser, Marissa Taddie, Rebecca Richards-Steed, James A. VanDerslice, Brock O’Neil, Heidi A. Hanson. Neighborhood clustering of bladder cancer incidence in Utah: Analyzing census data linked to cancer records [abstract]. In: Proceedings of the AACR Special Conference on Environmental Carcinogenesis: Potential Pathway to Cancer Prevention; 2019 Jun 22-24; Charlotte, NC. Philadelphia (PA): AACR; Can Prev Res 2020;13(7 Suppl): Abstract nr A11.

Asymptotic properties of spatial scan statistics under the alternative hypothesis

A common challenge for most spatial cluster detection methods is the lack of asymptotic properties to support their validity. As the spatial scan test is the most often used cluster detection method, we investigate two important properties in the method: the consistency and asymptotic local efficiency. We address the consistency by showing that the detected cluster converges to the true cluster in probability. We address the asymptotic local efficiency by showing that the spatial scan statistic asymptotically converges to the square of the maximum of a Gaussian random field, where the mean and covariance functions of the Gaussian random field depends on a function of at-risk population within and outside of the cluster. These conclusions, which are also supported by simulation and case studies, make it practical to precisely detect and characterize a spatial cluster.

Spatial parameterization of infant mortality in Anhui Province, China

The study is motivated by an unexplained and relatively high infant mortality in Anhui Province, where a suspected unknown source may contribute to it. However, spatially focused disease clustering tests tend to base on a known location, and in many cases, use the point source as the referent. When elevated risks in some areas are caused by unknown sources, it becomes necessary to infer these sources spatially. The paper extends spatial cluster parameterization models from known sources to unknown sources by a profile likelihood method. In both simulation and extended case study, we show that the spatial parameterization method is able to effectively identify the cluster influence center and measure cluster strength. We found that the center is located where the borders of several counties met in a relatively well-to-do part of the province. In addition to its ability to identify cluster influence away from the traditional centroid point, the parameterized method tends to perform better than the common spatial cluster detection method in terms of goodness of fit statistic and location specificity.

The spatial clustering of obesity: does the built environment matter?

Obesity rates in the USA show distinct geographical patterns. The present study used spatial cluster detection methods and individual-level data to locate obesity clusters and to analyse them in relation to the neighbourhood built environment. The 2008-2009 Seattle Obesity Study provided data on the self-reported height, weight, and sociodemographic characteristics of 1602 King County adults. Home addresses were geocoded. Clusters of high or low body mass index were identified using Anselin's Local Moran's I and a spatial scan statistic with regression models that searched for unmeasured neighbourhood-level factors from residuals, adjusting for measured individual-level covariates. Spatially continuous values of objectively measured features of the local neighbourhood built environment (SmartMaps) were constructed for seven variables obtained from tax rolls and commercial databases. Both the Local Moran's I and a spatial scan statistic identified similar spatial concentrations of obesity. High and low obesity clusters were attenuated after adjusting for age, gender, race, education and income, and they disappeared once neighbourhood residential property values and residential density were included in the model. Using individual-level data to detect obesity clusters with two cluster detection methods, the present study showed that the spatial concentration of obesity was wholly explained by neighbourhood composition and socioeconomic characteristics. These characteristics may serve to more precisely locate obesity prevention and intervention programmes.

Spatial Cluster Detection for Longitudinal Outcomes Using Administrative Regions

This article proposes a new spatial cluster detection method for longitudinal outcomes that detects neighborhoods and regions with elevated rates of disease while controlling for individual level confounders. The proposed method, CumResPerm, utilizes cumulative geographic residuals through a permutation test to detect potential clusters which are defined as sets of administrative regions, such as a town or group of administrative regions. Previous cluster detection methods are not able to incorporate individual level data including covariate adjustment, while still being able to define potential clusters using informative neighborhood or town boundaries. Often, it is of interest to detect such spatial clusters because individuals residing in a town may have similar environmental exposures or socioeconomic backgrounds due to administrative reasons, such as zoning laws. Therefore, these boundaries can be very informative and more relevant than arbitrary clusters such as the standard circle or square. Application of the CumResPerm method will be illustrated by the Home Allergens and Asthma prospective cohort study analyzing the relationship between area or neighborhood residence and repeated measured outcome, occurrence of wheeze in the last six months, while taking into account mobile locations.

Exploring Hotspots of Drug Offences in Toronto: A Comparison of Four Local Spatial Cluster Detection Methods

Spatial cluster detection is an exploratory spatial data analysis technique that identifies areas or groups of areas with disproportionately high risk. Several local cluster detection methods have been developed; yet no research has critiqued these methods as they contribute to spatial studies of crime. This study aims to identify the locations of drug offence hotspots in Toronto and compare the clusters detected through four methods: (1) spatial scan statistic – Euclidean distance, (2) spatial scan statistic – non-Euclidean contiguity, (3) flexibly shaped scan statistic, and (4) local Moran's I. It was found that all methods detected clusters in the downtown, with fewer methods detecting clusters in the west and east of Toronto. It was observed that the spatial scan statistic detected the largest and most circular clusters, making it a suitable tool to inform general policing initiatives and highlight possible variables to be included in confirmatory research. The local Moran's I method, in contrast, found the smallest and most compact clusters, indicating that it is an appropriate test for identifying areas where resource intensive crime prevention and policing efforts should be targeted.

Spatial cluster detection using dynamic programming

BackgroundThe task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster.MethodsWe present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data.ResultsWhen compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging.ConclusionsWe conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm.

Multiple Spatio-Temporal Cluster Detection for Case Event Data: An Ordering-Based Approach

This article introduces a spatio-temporal distance which allows the extension of the spatial cluster detection methods of Demattei et al. (2007) and Cucala (2009). A review of these methods is given before we define a spatio-temporal distance. Then this distance is used for detecting spatio-temporal clusters. These ordering-based methods are compared to the scan statistic by a simulation study. The scan procedure is more powerful but it detects fewer true positives due to its lack of flexibility. Those techniques are applied to a seismic data set. This article highlights two advantages of the ordering-based methods: their flexibility and their low computational demand.

Local Indicators of Network-Constrained Clusters in Spatial Patterns Represented by a Link Attribute

Clustering in a spatially distributed phenomenon is an important focus of spatial analysis because it not only suggests characteristics of the pattern itself but also of its background processes. Traditional methods of spatial cluster detection mostly rely on the planar space assumption, yet a variety of spatial phenomena do not support its logic. This article expounds on an exploratory spatial data analysis methodology named local indicators of network-constrained clusters (LINCS) introduced elsewhere for detecting local-scale clustering in a spatial phenomenon that is constrained by a network space. In particular, this article focuses on two types of LINCS methods that are network extensions of traditional methods for analyzing spatial associations in zone-based planar-space data, namely, the local Moran I statistic and the local Getis and Ord G statistic. They are designed for phenomena that are represented by attribute values of individual network links. Examples of such phenomena include traffic volume, traffic speed, and the number of vehicle crashes aggregated at the link level. When the phenomenon of interest can be seen as a subset of a more generic spatial phenomenon, for example, vehicle crashes in relation to the entire traffic observed in a study region, the LINCS methods are capable of taking into account the distribution of such a base phenomenon so that one can avoid the detection of spurious clusters merely reflecting the base distribution. The article illustrates the application of the two LINCS methods using data on highway vehicle crashes in the Buffalo, New York, area in 1997.

Spatial Cluster Detection for Repeatedly Measured Outcomes while Accounting for Residential History

Spatial cluster detection has become an important methodology in quantifying the effect of hazardous exposures. Previous methods have focused on cross-sectional outcomes that are binary or continuous. There are virtually no spatial cluster detection methods proposed for longitudinal outcomes. This paper proposes a new spatial cluster detection method for repeated outcomes using cumulative geographic residuals. A major advantage of this method is its ability to readily incorporate information on study participants relocation, which most cluster detection statistics cannot. Application of these methods will be illustrated by the Home Allergens and Asthma prospective cohort study analyzing the relationship between environmental exposures and repeated measured outcome, occurrence of wheeze in the last 6 months, while taking into account mobile locations.

Spatial Cluster Detection for Weighted Outcomes Using Cumulative Geographic Residuals

Spatial cluster detection is an important methodology for identifying regions with excessive numbers of adverse health events without making strong model assumptions on the underlying spatial dependence structure. Previous work has focused on point or individual-level outcome data and few advances have been made when the outcome data are reported at an aggregated level, for example, at the county- or census-tract level. This article proposes a new class of spatial cluster detection methods for point or aggregate data, comprising of continuous, binary, and count data. Compared with the existing spatial cluster detection methods it has the following advantages. First, it readily incorporates region-specific weights, for example, based on a region's population or a region's outcome variance, which is the key for aggregate data. Second, the established general framework allows for area-level and individual-level covariate adjustment. A simulation study is conducted to evaluate the performance of the method. The proposed method is then applied to assess spatial clustering of high Body Mass Index in a health maintenance organization population in the Seattle, Washington, USA area.

Geovisual analytics to enhance spatial scan statistic interpretation: an analysis of U.S. cervical cancer mortality

BackgroundKulldorff's spatial scan statistic and its software implementation – SaTScan – are widely used for detecting and evaluating geographic clusters. However, two issues make using the method and interpreting its results non-trivial: (1) the method lacks cartographic support for understanding the clusters in geographic context and (2) results from the method are sensitive to parameter choices related to cluster scaling (abbreviated as scaling parameters), but the system provides no direct support for making these choices. We employ both established and novel geovisual analytics methods to address these issues and to enhance the interpretation of SaTScan results. We demonstrate our geovisual analytics approach in a case study analysis of cervical cancer mortality in the U.S.ResultsWe address the first issue by providing an interactive visual interface to support the interpretation of SaTScan results. Our research to address the second issue prompted a broader discussion about the sensitivity of SaTScan results to parameter choices. Sensitivity has two components: (1) the method can identify clusters that, while being statistically significant, have heterogeneous contents comprised of both high-risk and low-risk locations and (2) the method can identify clusters that are unstable in location and size as the spatial scan scaling parameter is varied. To investigate cluster result stability, we conducted multiple SaTScan runs with systematically selected parameters. The results, when scanning a large spatial dataset (e.g., U.S. data aggregated by county), demonstrate that no single spatial scan scaling value is known to be optimal to identify clusters that exist at different scales; instead, multiple scans that vary the parameters are necessary. We introduce a novel method of measuring and visualizing reliability that facilitates identification of homogeneous clusters that are stable across analysis scales. Finally, we propose a logical approach to proceed through the analysis of SaTScan results.ConclusionThe geovisual analytics approach described in this manuscript facilitates the interpretation of spatial cluster detection methods by providing cartographic representation of SaTScan results and by providing visualization methods and tools that support selection of SaTScan parameters. Our methods distinguish between heterogeneous and homogeneous clusters and assess the stability of clusters across analytic scales.MethodWe analyzed the cervical cancer mortality data for the United States aggregated by county between 2000 and 2004. We ran SaTScan on the dataset fifty times with different parameter choices. Our geovisual analytics approach couples SaTScan with our visual analytic platform, allowing users to interactively explore and compare SaTScan results produced by different parameter choices. The Standardized Mortality Ratio and reliability scores are visualized for all the counties to identify stable, homogeneous clusters. We evaluated our analysis result by comparing it to that produced by other independent techniques including the Empirical Bayes Smoothing and Kafadar spatial smoother methods. The geovisual analytics approach introduced here is developed and implemented in our Java-based Visual Inquiry Toolkit.

Détection de clusters spatiaux sans point source prédéfini : utilisation de cinq méthodes et comparaison de leurs résultats

Background Various statistical methods have been developed to describe spatial heterogeneity, in terms of high risk zones. If no source can be determined, this heterogeneity can be globally or locally described. Global methods test a statistic estimated over the whole studied geographical area, whereas local methods estimate a statistic on each spatial unit (or regrouping unit). This paper aimed to present, and to compare results of an epidemiological application, of five methods of spatial cluster detection. Methods The two global detection methods were: 1) Moran's coefficient, a classically used autocorrelation coefficient; 2) Tango's statistic, a spatial generalization of the Chi 2 statistic. The three local methods were: 1) the local application of Moran's coefficient, proposed by Anselin; 2) the scan statistic, which searches for grouping of spatial units; 3) the oblique regression tree, which splits the studied zone into sub-zones of different risks. These five methods were applied to the description of the spatial heterogeneity of the malaria risk over a hyperendemic village, in Mali. Results All the methods highlighted a significant spatial heterogeneity. Both global methods (Moran's coefficient and Tango's statistic) showed weak spatial correlations. Local Moran's coefficient (with Bonferronis' adjustment) highlighted five spatial units. The scan statistic identified a single high risk cluster. The regression oblique tree split the study area into six sub-zones; the sub-zone with the higher risk was consistent with the cluster identified by the scan statistic. Conclusion These presented methods do not require any previous knowledge of a source. They allow evaluating spatial risk heterogeneity over the entire geographical area under study. It is noteworthy that shape, size, and spatial heterogeneity characteristics (either global or local) of the study area, as well as the definition of the proximity, significantly influence the spatial risk analysis' outcome. Although their results should be cautiously interpreted, these methods are useful for preliminary field studies or epidemiological surveys.

A spatial hazard model for cluster detection on continuous indicators of disease: application to somatic cell score

Methods for spatial cluster detection dealing with diseases quantified by continuous variables are few, whereas several diseases are better approached by continuous indicators. For example, subclinical mastitis of the dairy cow is evaluated using a continuous marker of udder inflammation, the somatic cell score (SCS). Consequently, this study proposed to analyze spatialized risk and cluster components of herd SCS through a new method based on a spatial hazard model. The dataset included annual SCS for 34 142 French dairy herds for the year 2000, and important SCS risk factors: mean parity, percentage of winter and spring calvings, and herd size. The model allowed the simultaneous estimation of the effects of known risk factors and of potential spatial clusters on SCS, and the mapping of the estimated clusters and their range. Mean parity and winter and spring calvings were significantly associated with subclinical mastitis risk. The model with the presence of 3 clusters was highly significant, and the 3 clusters were attractive, i.e. closeness to cluster center increased the occurrence of high SCS. The three localizations were the following: close to the city of Troyes in the northeast of France; around the city of Limoges in the center-west; and in the southwest close to the city of Tarbes. The semi-parametric method based on spatial hazard modeling applies to continuous variables, and takes account of both risk factors and potential heterogeneity of the background population. This tool allows a quantitative detection but assumes a spatially specified form for clusters.

Spatial Cluster Detection for Censored Outcome Data

While numerous methods have been proposed to test for spatial cluster detection, in particular for discrete outcome data (e.g., disease incidence), few have been available for continuous data that are subject to censoring. This article provides an extension of the spatial scan statistic (Kulldorff, 1997, Communications in Statistics 26, 1481-1496) for censored outcome data and further proposes a simple spatial cluster detection method by utilizing cumulative martingale residuals within the framework of the Cox's proportional hazards models. Simulations have indicated good performance of the proposed methods, with the practical applicability illustrated by an ongoing epidemiology study which investigates the relationship of environmental exposures to asthma, allergic rhinitis/hayfever, and eczema.