Geoffrey M. Jacquez

A k NEAREST NEIGHBOUR TEST FOR SPACE–TIME INTERACTION

This paper describes a k nearest neighbour statistic sensitive to the pattern of cases expected of space-time clusters of health events. The Knox and Mantel tests are frequently used for space-time clustering but have two disadvantages. First, the selection of critical space-time distances for the Knox test and of a data transformation for the Mantel test is subjective. Second, the Mantel statistic is the sum of the products of space and time distances, is linear in form, and is not sensitive to non-linear associations between small space and time distances expected of contagious processes. The k nearest neighbour statistic is the number of case pairs that are k nearest neighbours in both space and time, and is evaluated under the null hypothesis of independent space and time nearest neighbour relationships. The test was applied to simulated and real data and compared to the Knox and Mantel tests using statistical power comparisons. The k nearest neighbour test proved sensitive to the space-time interaction pattern expected of disease clusters, does not require parameters (such as critical distances) to be estimated from the data, and may be used to test hypotheses about the spatial and temporal scale of the cluster process. The method addresses significant weaknesses in existing space-time cluster tests and should prove useful in the quantification and evaluation of clusters of human health events. Additional research is needed to further document the power of the test under different cluster processes.

From fields to objects: A review of geographic boundary analysis

Abstract. Geographic boundary analysis is a relatively new approach unfamiliar to many spatial analysts. It is best viewed as a technique for defining objects – geographic boundaries – on spatial fields, and for evaluating the statistical significance of characteristics of those boundary objects. This is accomplished using null spatial models representative of the spatial processes expected in the absence of boundary-generating phenomena. Close ties to the object-field dialectic eminently suit boundary analysis to GIS data. The majority of existing spatial methods are field-based in that they describe, estimate, or predict how attributes (variables defining the field) vary through geographic space. Such methods are appropriate for field representations but not object representations. As the object-field paradigm gains currency in geographic information science, appropriate techniques for the statistical analysis of objects are required. The methods reviewed in this paper are a promising foundation. Geographic boundary analysis is clearly a valuable addition to the spatial statistical toolbox.¶ This paper presents the philosophy of, and motivations for geographic boundary analysis. It defines commonly used statistics for quantifying boundaries and their characteristics, as well as simulation procedures for evaluating their significance. We review applications of these techniques, with the objective of making this promising approach accessible to the GIS-spatial analysis community. We also describe the implementation of these methods within geographic boundary analysis software: GEM.

Testing inferences about microevolutionary processes by means of spatial autocorrelation analysis

We generated numerous simulated gene‐frequency surfaces subjected to 200 generations of isolation by distance with, in some cases, added migration or selection. From these surfaces we assembled six data sets comprising from 12 to 15 independent allele‐frequency surfaces, to simulate biologically plausible population samples. The purpose of the study was to investigate whether spatial autocorrelation analysis will correctly infer the microevolutionary processes involved in each data set. The correspondence between the simulated processes and the inferences made concerning them is close for five of the six data sets. Errors in inference occurred when the effect of migration was weak, due to low gene frequency differential or low migration strength; when selection was weak and against a background with a complex pattern; and when a random process—isolation by distance—was the only one acting. Spatial correlograms proved more sensitive to detecting trends than inspection of gene‐frequency surfaces by the human eye. Joint interpretation of the correlograms and their clusters proved most reliable in leading to the correct inference. The inspection and clustering of surfaces were useful for determining directional components. Because this method relies on common patterns across loci, as many gene frequencies as feasible should be used. We recommend spatial autocorrelation analysis for the detection of microevolutionary processes in natural populations.

Local clustering in breast, lung and colorectal cancer in Long Island, New York.

BackgroundAnalyses of spatial disease patterns usually employ a univariate approach that uses one technique to identify disease clusters. Because different methods are sensitive to different aspects of spatial pattern, an approach employing a battery of techniques is expected to describe geographic variation in human health more fully. This two-part study employs a multi-method approach to elucidate geographic variation in cancer incidence in Long Island, New York, and to evaluate spatial association with air-borne toxics. This first paper uses the local Moran statistic to identify cancer hotspots and spatial outliers. We evaluated the geographic distributions of breast cancer in females and colorectal and lung cancer in males and females in Nassau, Queens, and Suffolk counties, New York, USA. We calculated standardized morbidity ratios (SMR values) from New York State Department of Health (NYSDOH) data.ResultsWe identified significant local clusters of high and low SMR and significant spatial outliers for each cancer-gender combination. We then compared our results with the study conducted by NYSDOH using Kulldorffs spatial scan statistic. We identified patterns on a smaller spatial scale with different cluster shapes than the NYSDOH analysis did, a consequence of different statistical methods and analysis scale.ConclusionThis is a methodological and comparative study to evaluate whether there is substantial benefit added by using a variety of techniques for geographic pattern detection at different spatial scales. We located significant spatial pattern in cancer morbidity in Nassau, Queens, and Suffolk counties. These results broadly agree with the results of other studies that used different techniques, but differ in specifics. The differences in our results and that of the NYSDOH underscore the need for an exploratory, integrative, and multi-scalar approach to assessing geographic patterns of disease, as different methods identify different patterns. We recommend that future studies of geographic patterns use a concordance of evidence from a multiscalar integrative geographic approach to assure that 1) different aspects of spatial pattern are fully identified and 2) the results from the suite of analyses are logically consistent.

Accounting for regional background and population size in the detection of spatial clusters and outliers using geostatistical filtering and spatial neutral models: the case of lung cancer in Long Island, New York

BackgroundComplete Spatial Randomness (CSR) is the null hypothesis employed by many statistical tests for spatial pattern, such as local cluster or boundary analysis. CSR is however not a relevant null hypothesis for highly complex and organized systems such as those encountered in the environmental and health sciences in which underlying spatial pattern is present. This paper presents a geostatistical approach to filter the noise caused by spatially varying population size and to generate spatially correlated neutral models that account for regional background obtained by geostatistical smoothing of observed mortality rates. These neutral models were used in conjunction with the local Moran statistics to identify spatial clusters and outliers in the geographical distribution of male and female lung cancer in Nassau, Queens, and Suffolk counties, New York, USA.ResultsWe developed a typology of neutral models that progressively relaxes the assumptions of null hypotheses, allowing for the presence of spatial autocorrelation, non-uniform risk, and incorporation of spatially heterogeneous population sizes. Incorporation of spatial autocorrelation led to fewer significant ZIP codes than found in previous studies, confirming earlier claims that CSR can lead to over-identification of the number of significant spatial clusters or outliers. Accounting for population size through geostatistical filtering increased the size of clusters while removing most of the spatial outliers. Integration of regional background into the neutral models yielded substantially different spatial clusters and outliers, leading to the identification of ZIP codes where SMR values significantly depart from their regional background.ConclusionThe approach presented in this paper enables researchers to assess geographic relationships using appropriate null hypotheses that account for the background variation extant in real-world systems. In particular, this new methodology allows one to identify geographic pattern above and beyond background variation. The implementation of this approach in spatial statistical software will facilitate the detection of spatial disparities in mortality rates, establishing the rationale for targeted cancer control interventions, including consideration of health services needs, and resource allocation for screening and diagnostic testing. It will allow researchers to systematically evaluate how sensitive their results are to assumptions implicit under alternative null hypotheses.

Spatial analysis in epidemiology: Nascent science or a failure of GIS?

Abstract. This paper summarizes contributions of GIS in epidemiology, and identifies needs required to support spatial epidemiology as science. The objective of spatial epidemiology is to identify disease causes and correlates by relating spatial disease patterns to geographic variation in health risks. GIS supports disease mapping, location analysis, the characterization of populations, and spatial statistics and modeling. Although laudable, these accomplishments are not sufficient to fully identify disease causes and correlates. One reason is the failure of present-day GIS to provide tools appropriate for epidemiology. Two needs are most pressing. First, we must reject the static view: meaningful inference about the causes of disease is impossible without both spatial and temporal information. Second, we need models that translate space-time data on health outcomes and putative exposures into epidemiologically meaningful measures. The first need will be met by the design and implementation of space-time information systems for epidemiology; the second by process-based disease models.

Quantification of the spatial co-occurrences of ecological boundaries

In this paper, we investigate spatial relationships between vegetation boundaries and environmental boundaries from a second-growth forest in southwestern Quebec, Canada. Four statistics that quantify the amount of direct spatial overlap and the mean minimum distance between boundaries are introduced and used to compute the degree of spatial co-occurrences between boundaries. The significance of these statistics is determined using randomized and restricted permutation tests. Boundaries based on tree species density are found to significantly overlap the locations of boundaries delineated by the environmental data at the study site. Significant overlap is also found using boundaries defined by tree presence-absence data and environmental variables. Vegetation boundaries based on tree species density and on tree presence-absence data are not, however, at the same locations. This suggests that for the study site the two types of vegetation boundaries (tree density and presence-absence) reflect different responses to underlying environmental processes. Vegetation boundaries determined using species diversity and species richness, although spatially related to the presence absence boundaries, did not overlap the environmental boundaries. Results of the two permutation tests (randomized and restricted) agree only when the spatial relationship between the two boundary types is strong. Overall, randomization is found to be a more conservative test for detecting boundary spatial relationships, rejecting the null hypothesis of no spatial relationship fewer times than the restricted permutation test.

Disease models implicit in statistical tests of disease clustering.

State and local health departments investigate an increasing number of cluster allegations, for which the selection of appropriate statistical methods is an important problem. Many of the methods for the spatial analysis of health data assume, either implicitly or explicitly, some model of disease occurrence, and comparisons of methods can be difficult when their underlying disease models differ. We review some of the issues involved in the statistical analysis of spatial disease patterns and describe several methods recently proposed to detect areas of increased disease rates. The disease models upon which the methods are based are explicitly described, and they provide a useful basis for comparing alternative clustering methods.

Geographic boundaries in breast, lung and colorectal cancers in relation to exposure to air toxics in Long Island, New York

BackgroundThis two-part study employs several statistical techniques to evaluate the geographic distribution of breast cancer in females and colorectal and lung cancers in males and females in Nassau, Queens, and Suffolk counties, New York, USA. In this second paper, we compare patterns in standardized morbidity ratios (SMR values), calculated from New York State Department of Health (NYSDOH) data, to geographic patterns in overall predicted risk (OPR) from air toxics using exposures estimated in the USEPA National Air Toxics Assessment database.ResultsWe identified significant geographic boundaries in SMR and OPR. We found little or no association between the SMR of colorectal and breast cancers and the OPR for each cancer from exposure to the air toxics. We did find boundaries in male and female lung cancer SMR and boundaries in lung cancer OPR to be closer to one another than expected.ConclusionWhile consistent with a causal relationship between air toxics and lung cancer incidence, the boundary analysis does not demonstrate the existence of a causal relationship. However, now that the areas of overlap between boundaries in lung cancer incidence and potential airborne exposures have been identified, we can begin to evaluate local- as well as large-scale determinants of lung cancer.

Detection of temporal changes in the spatial distribution of cancer rates using local Moran's I and geostatistically simulated spatial neutral models

Abstract.This paper presents the first application of spatially correlated neutral models to the detection of changes in mortality rates across space and time using the local Moran’s I statistic. Sequential Gaussian simulation is used to generate realizations of the spatial distribution of mortality rates under increasingly stringent conditions: 1) reproduction of the sample histogram, 2) reproduction of the pattern of spatial autocorrelation modeled from the data, 3) incorporation of regional background obtained by geostatistical smoothing of observed mortality rates, and 4) incorporation of smooth regional background observed at a prior time interval. The simulated neutral models are then processed using two new spatio-temporal variants of the Moran’s I statistic, which allow one to identify significant changes in mortality rates above and beyond past spatial patterns. Last, the results are displayed using an original classification of clusters/outliers tailored to the space-time nature of the data. Using this new methodology the space-time distribution of cervix cancer mortality rates recorded over all US State Economic Areas (SEA) is explored for 9 time periods of 5 years each. Incorporation of spatial autocorrelation leads to fewer significant SEA units than obtained under the traditional assumption of spatial independence, confirming earlier claims that Type I errors may increase when tests using the assumption of independence are applied to spatially correlated data. Integration of regional background into the neutral models yields substantially different spatial clusters and outliers, highlighting local patterns which were blurred when local Moran’s I was applied under the null hypothesis of constant risk.