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Monitoring point patterns for the development of space–time clusters

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  • Peter A. Rogerson

Abstract

Existing statistical methods for the detection of space–time clusters of point events are retrospective, in that they are used to ascertain whether space–time clustering exists among a fixed number of past events. In contrast, prospective methods treat a series of observations sequentially, with the aim of detecting quickly any changes that occur in the series. In this paper, cumulative sum methods of monitoring are adapted for use with Knox's space–time statistic. The result is a procedure for the rapid detection of any emergent space–time interactions for a set of sequentially monitored point events. The approach relies on a ‘local’ Knox statistic that is useful in retrospective analyses to detect when and where space–time interaction occurs. The distribution of the local Knox statistic under the null hypothesis of no space–time interaction is derived. The retrospective local statistic and the prospective cumulative sum monitoring method are illustrated by using previously published data on Burkitt's lymphoma in Uganda.

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  • Peter A. Rogerson, 2001. "Monitoring point patterns for the development of space–time clusters," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 87-96.
    • Handle: RePEc:bla:jorssa:v:164:y:2001:i:1:p:87-96
    DOI: 10.1111/1467-985X.00188
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    Cited by:

    1. Marianne Frisén, 2014. "Spatial outbreak detection based on inference principles for multivariate surveillance," IISE Transactions, Taylor & Francis Journals, vol. 46(8), pages 759-769, August.
    2. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    3. Jingnan Zhang & Yicheng Kang & Yang Yang & Peihua Qiu, 2015. "Statistical monitoring of the hand, foot and mouth disease in China," Biometrics, The International Biometric Society, vol. 71(3), pages 841-850, September.
    4. Alexandre Rodrigues & Peter J. Diggle, 2012. "Bayesian Estimation and Prediction for Inhomogeneous Spatiotemporal Log-Gaussian Cox Processes Using Low-Rank Models, With Application to Criminal Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 93-101, March.
    5. Shino Shiode & Narushige Shiode, 2022. "Network-Based Space-Time Scan Statistics for Detecting Micro-Scale Hotspots," Sustainability, MDPI, vol. 14(24), pages 1-20, December.
    6. Linus Schiöler & Marianne Fris�n, 2012. "Multivariate outbreak detection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 223-242, April.
    7. Tanzina AKHTER & MD NUR-AL-AHAD, 2021. "Influence Of Packaging Elements On The Purchase Decision-Making: A Study On The Bar Soap Users Of Dhaka City, Bangladesh," Management and Marketing Journal, University of Craiova, Faculty of Economics and Business Administration, vol. 0(2), pages 161-180, November.
    8. Thais Paiva & Renato Assunção & Taynãna Simões, 2015. "Prospective space–time surveillance with cumulative surfaces for geographical identification of the emerging cluster," Computational Statistics, Springer, vol. 30(2), pages 419-440, June.
    9. de Lima, Max Sousa & Duczmal, Luiz Henrique, 2014. "Adaptive likelihood ratio approaches for the detection of space–time disease clusters," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 352-370.

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