The Knox Method and Other Tests for Space‐Time Interaction

Kulldorff, Martin; Hjalmars, Ulf

doi:10.1111/j.0006-341x.1999.00544.x

Cited by 140 publications

(122 citation statements)

References 13 publications

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“…Some authors have suggested that shifts in the underlying population may artefactually cause space-time clustering. 27,28 We are not able to investigate population shifts, because this would require small area level population data for short time periods, which are not available in the United Kingdom. However, because space-time clustering was present in both the earlier and later parts of the study period (1987-1994 and 1995-2003), population shifts are unlikely to explain our results.…”

Section: Discussionmentioning

confidence: 99%

Are transient environmental agents involved in the cause of primary biliary cirrhosis? Evidence from space-time clustering analysis

2009

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The cause of primary biliary cirrhosis (PBC) is unclear. Both genetic and environmental factors are likely to contribute. Some studies have suggested that one or more infectious agents may be involved. To examine whether infections may contribute to the cause of PBC, we have analyzed for space-time clustering using population-based data from northeast England over a defined period (1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003). Space-time clustering is observed when excess cases of a disease are found within limited geographical areas at limited periods of time. If present, it is suggestive of the involvement of one or more environmental components in the cause of a disease and is especially supportive of infections. A second-order procedure based on K-functions was used to test for global space-time clustering using residential addresses at the time of diagnosis. The Knox method determined the spatiotemporal range over which global clustering was strongest. K-function tests were repeated using nearest neighbor thresholds to adjust for variations in population density. Individual space-time clusters were identified using Kulldorff's scan statistic. Analysis of 1015 cases showed highly statistically significant space-time clustering (P < 0.001). Clustering was most marked for cases diagnosed within 1-4 months of one another. A number of specific space-time clusters were identified. In conclusion, these novel results suggest that transient environmental agents may play a role in the cause of PBC. (HEPATOLOGY 2009;50:1169-1174

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Section: Discussionmentioning

confidence: 99%

Are transient environmental agents involved in the cause of primary biliary cirrhosis? Evidence from space-time clustering analysis

2009

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“…Knox's method is known to be subject to possible bias in case of nonuniform population shifts over the time period (Besag and Newell, 1991;Kulldorff and Hjalmars, 1999) and the probability to detect space -time clustering due to population shifts increases with the number of close pairs observed (Kulldorff and Hjalmars, 1999).…”

Section: Discussionmentioning

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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“…If the population increases or decreases with different rates in different geographical areas, the test will be biased, and it is necessary to incorporate population-at-risk data in order to have a valid test (Kulldorff & Hjalmars 1999). Mantel (1967) generalized the Knox test to allow for an arbitrary decaying function of the spatial and temporal distance between events.…”

Section: Inferential Approaches For Space-time Clustersmentioning

confidence: 99%

Space‐time cluster identification in point processes

et al. 2007

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Abstract:The authors propose a new type of scan statistic to test for the presence of space-time clusters in point processes data, when the goal is to identify and evaluate the statistical significance of localized clusters. Their method is based only on point patterns for cases; it does not require any specific knowledge of the underlying population. The authors propose to scan the three-dimensional space with a score test statistic under the null hypothesis that the underlying point process is an inhomogeneous Poisson point process with space and time separable intensity. The alternative is that there are one or more localized space-time clusters. Their method has been implemented in a computationally efficient way so that it can be applied routinely. They illustrate their method with space-time crime data from Belo Horizonte, a Brazilian city, in addition to presenting a Monte Carlo study to analyze the power of their new test. Identification d'agrégation spatio-temporelle dans des processus ponctuelsRésumé : Les auteurs proposent une statistique permettant de détecter la présence d'agrégation spatiotemporelle dans des données issues de processus ponctuels, l'objectifétant d'identifier des regroupements et d'évaluer s'ils sont statistiquement significatifs. Leur méthode ne dépend que de la disposition des observations ; elle ne nécessite aucune connaissance particulière de la population sous-jacente. Une statistique de type score mesurée sur l'ensemble de l'espaceà trois dimensions leur permet de tester l'hypothèse nullè a l'effet que le processus ponctuel sous-jacent est un processus de Poisson hétérogène dont les composantes spatiale et temporelle de l'intensité sont séparables. La contre-hypothèse està l'effet qu'il existe un ou des regroupements spatio-temporels localisés. L'implantation informatique de leur méthode est efficace au plan calcul et facile d'emploi. Les auteurs l'illustrentà l'aide de données sur la répartition spatio-temporelle de la criminalité dans la ville brésilienne de Belo Horizonte, en plus de présenter uneétude de Monte-Carlo investigant la puissance de leur test.

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The Knox Method and Other Tests for Space‐Time Interaction

Cited by 140 publications

References 13 publications

Are transient environmental agents involved in the cause of primary biliary cirrhosis? Evidence from space-time clustering analysis

Are transient environmental agents involved in the cause of primary biliary cirrhosis? Evidence from space-time clustering analysis

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

Space‐time cluster identification in point processes

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