Space‐time cluster identification in point processes

Abstract

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.

Characterizing Spatial and Chronological Target Selection of Serial Offenders

“…However, in any test for space–time clustering, such as Assunção et al . (), the required intensity estimate could vary in both space and time, so bandwidths in time, the x ‐co‐ordinates and y ‐co‐ordinates could all be different, and residual diagnostics would need to be extended to handle this three‐dimensional case. Significant programming efforts would be required to implement such extensions.…”

“…The methodology that was used in Section 3 would require extending the inhomogeneous K-function to three dimensions in which the third dimension is time, which is not technically difficult. However, in any test for space-time clustering, such as Assunção et al (2007), the required intensity estimate could vary in both space and time, so bandwidths in time, the x-co-ordinates and y-co-ordinates could all be different, and residual diagnostics would need to be extended to handle this three-dimensional case. Significant programming efforts would be required to implement such extensions.…”

Space-time prospective surveillance based on Knox local statistics

“…This is appropriate when the test is aimed at finding evidence of disease contagion or infection. However, when the interest is in spatially localized episodic or epidemic outbreak, the identification of clusters is important as the space–time interaction appears in the form of raised incidence on localized regions over a short time period . We focus on this problem of identifying as early as possible the emergence of a space–time disease cluster when point events are under monitoring.…”

An up-to-date review of scan statistics

“…Although there are many applications of the "space-time scan statistic", Tango, Takahashi and Kohriyama (2011); Correa, Assunção and Costa (2015); Gangnon (2010b); Tango (2016) criticized the use of the prospective space-time scan statistic. To improve some of its problems, Assunção et al (2007) proposed a score-based space-time scan statistic which is discussed in the next subsection. Also, Prates, Kulldorff and Assuncao (2014) presented a simulation study showing that the relative risk estimates for the space-time scan statistic must be defined with care and presented bias in its estimation, while the relative risk estimator is well defined for the purely spatial scan situations being not biased as the true relative risk of the cluster increases.…”

“…To find spatio-temporal clusters, Assunção et al (2007) proposed a new scan statistic that detects clusters in time and space in a point process by scanning three dimensions (two dimensions for space and one dimension for time). As before, a hypothesis testing method is applied such that the null hypothesis is that the underlying point process is a homogeneous Poisson point process with separable space-time intensity versus the alternative hypothesis of the existence of at least one space-time cluster.…”