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Multiple Window and Cluster Size Scan Procedures

Author

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  • Joseph I. Naus

    (Rutgers the State University of New Jersey, Hill Center, Busch Campus)

  • Sylvan Wallenstein

    (Mount Sinai School of Medicine)

Abstract

Researchers apply scan statistics to test for unusually large clusters of events within a time window of specified length w, or alternatively an unusually small window w that contains a specified number of events. In some cases, the researcher is interested in testing for a range of specified window lengths, or a set of several specified number of events k (cluster sizes). In this paper, we derive accurate approximations for the joint distributions of scan statistics for a range of values of w, or of k, that can be used to set an experiment-wide level of significance that takes into account the multiple comparisons involved. We use these methods to compare different ways of choosing the window sizes for the different cluster sizes. One special case is a multiple comparison procedure based on a generalized likelihood ratio test (GLRT) for a range of window sizes. We compare the power of the GLRT with another method for allocating the window sizes. We find that the GLRT is sensitive for very small window sizes at the expense of moderate and larger window sizes. We illustrate these results on two examples, one involving clustering of translocation breakpoints in DNA, and the other involving disease clusters.

Suggested Citation

  • Joseph I. Naus & Sylvan Wallenstein, 2004. "Multiple Window and Cluster Size Scan Procedures," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 389-400, December.
    • Handle: RePEc:spr:metcap:v:6:y:2004:i:4:d:10.1023_b:mcap.0000045087.33227.8c
    DOI: 10.1023/B:MCAP.0000045087.33227.8c
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    References listed on IDEAS

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    1. Segal M. R. & Wiemels J. L., 2002. "Clustering of Translocation Breakpoints," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 66-76, March.
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    Cited by:

    1. Wu, Tung-Lung & Glaz, Joseph, 2015. "A new adaptive procedure for multiple window scan statistics," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 164-172.
    2. Markos V. Koutras & Demetrios P. Lyberopoulos, 2018. "Asymptotic results for jump probabilities associated to the multiple scan statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 951-968, October.
    3. Yi-Shen Lin & Xenos Chang-Shuo Lin & Daniel Wei-Chung Miao & Yi-Ching Yao, 2020. "Corrected Discrete Approximations for Multiple Window Scan Statistics of One-Dimensional Poisson Processes," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 237-265, March.
    4. Guenther Walther & Andrew Perry, 2022. "Calibrating the scan statistic: Finite sample performance versus asymptotics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1608-1639, November.

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