Testing for homogeneity: II. The Poisson distribution

Potthoff, Richard F.; Whittinghill, Maurice

doi:10.1093/biomet/53.1-2.183

Cited by 129 publications

(34 citation statements)

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“…By using the approach of Potthoff-Whittinghill, a test with reasonable statistical power in a variety of overdispersion models was chosen [33]. It is an appropriate approach to find a general trend of clustering, but not appropriate to locate specific clusters.…”

Section: Discussionmentioning

confidence: 99%

“…Under the null hypothesis, the number of cases in each municipality follows a Poisson distribution, as explained above. The alternative to overdispersion is described by a negative binomial, for which the variance of the mean ratio is 1 + β [32][33][34]. This method expresses overdispersion in relation to the mean by a single parameter β, and β = 0 is tested in a score test.…”

Section: Methodsmentioning

confidence: 99%

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Spatial clustering and space–time clusters of leukemia among children in Germany, 1987–2007

et al. 2010

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Spatial clustering and space–time clusters of leukemia among children in Germany, 1987–2007

et al. 2010

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“…Spatial and spatio-temporal methods have first been developed more than 40 years ago (Moran, 1948;Knox, 1964;Naus, 1965;Potthoff and Whittinghill, 1966). Since then some improvements have been made, new approaches have emerged and several methods are now widely used.…”

Section: Methodsmentioning

confidence: 99%

“…The first one (Potthoff and Whittinghill, 1966) assumes that the number of cases in each area is Poisson distributed under the null hypothesis of no spatial heterogeneity and follows a negative binomial distribution under the alternative hypothesis of overdispersion with a variance to the mean ratio equal to 1 þ b. Based on previous results (Rudant et al, 2005), this method was also applied focusing on isolated communes with more than 50 inhabitants per km 2 .…”

Section: Global Spatial Heterogeneitymentioning

confidence: 99%

Spatial and space–time clustering of childhood acute leukaemia in France from 1990 to 2000: a nationwide study

et al. 2006

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This study aimed to investigate the spatial and space -time distributions of cases of childhood acute leukaemia (CL) during 1990 -2000 over the whole French territory. A global spatial heterogeneity and a spatial autocorrelation were first considered using the methods proposed by Potthoff and Whittinghill, Moran and Rogerson methods. The presence of space -time interaction between the places of residence and the dates of diagnosis was investigated with the Knox's test. Finally, the Kulldorff's statistic permitted to scan the whole territory in search for localised clusters. Two time periods were considered (1990 -1994, 1995 -2000). Overall, a statistically significant spatial heterogeneity of a very small magnitude was observed in the incidence of CL over 1990 -1994, but neither over 1995 -2000 nor over the whole time period. Moreover, a significant overdispersion of 5.5% was evidenced for 0 -4 year children living in isolated areas with more than 50 inhabitants per km 2 . Cases older than 10 years living in the same area at diagnosis also tended to cluster within 6 months.

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“…There are many tests available for testing the significance of disease clustering. Among them are tests for deviation from homogeneity like the usual Pearson's chi-square statistic for quadrat data or PotthoffWhittinghill's test (Potthoff and Whittinghill (1966)). Clustering methods for detection of disease clustering can be grouped into four categories: (i) methods based on regional count data, (ii) individual point data (e.g., case-control data in epidemiology), (iii) adjacencies of high count regional data, and (iv) distance-based methods.…”

Section: Introductionmentioning

confidence: 99%

Segregation indices for disease clustering

Ceyhan

2013

Statistics in Medicine

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Spatial clustering has important implications in various fields. In particular, disease clustering is of major public concern in epidemiology. In this article, we propose the use of two distance-based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population. We derive their asymptotic distributions and compare them with other distance-based disease clustering tests in terms of empirical size and power by extensive Monte Carlo simulations. The null pattern we consider is the random labeling (RL) of cases and controls to the given locations. Along this line, we investigate the sensitivity of the size of these tests to the underlying background pattern (e.g., clustered or homogenous) on which the RL is applied, the level of clustering and number of clusters, or differences in relative abundances of the classes. We demonstrate that differences in relative abundance has the highest impact on the empirical sizes of the tests. We also propose various non-RL patterns as alternatives to the RL pattern and assess the empirical power performance of the tests under these alternatives. We illustrate the methods on two real-life examples from epidemiology.

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Testing for homogeneity: II. The Poisson distribution

Cited by 129 publications

References 0 publications

Spatial clustering and space–time clusters of leukemia among children in Germany, 1987–2007

Spatial clustering and space–time clusters of leukemia among children in Germany, 1987–2007

Spatial and space–time clustering of childhood acute leukaemia in France from 1990 to 2000: a nationwide study

Segregation indices for disease clustering

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