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Adaptive Likelihood Ratio Scans for the Detection of Space-Time Clusters

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Handbook of Scan Statistics

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Abstract

This work presents a methodology to detect space-time clusters, based on adaptive likelihood ratios (ALRs), which preserves the martingale structure of the regular likelihood ratio. Monte Carlo simulations are not required to validate the procedure’s statistical significance, because the upper limit for the false alarm rate of the proposed method depends only on the quantity of evaluated cluster candidates, thus allowing the construction of a fast computational algorithm. The quantity of evaluated clusters is also significantly reduced, by using another adaptive scheme to prune many unpromising clusters, further increasing the computational speed. Performance is evaluated through simulations to measure the average detection delay and the probability of correct cluster detection. Applications for thyroid cancer in New Mexico and hanseniasis in children in the Brazilian Amazon are shown.

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Acknowledgements

The authors were funded with grants from the Brazilian agencies CAPES, UFAM, CNPq, and FAPEMIG.

Author information

Authors and Affiliations

  1. Department of Statistics, Universidade Federal do Amazonas, 69077-000, Manaus, AM, Brazil

    Max S. deLima

  2. Campus Pampulha, Department of Statistics, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, MG, Brazil

    Lui H. Duczmal

Authors
  1. Max S. deLima
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  2. Lui H. Duczmal
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Corresponding author

Correspondence to Max S. deLima .

Editor information

Editors and Affiliations

  1. University of Connecticut Dept. Statistics, Storrs, Connecticut, USA

    Joseph Glaz

  2. University of Pireaus Dept. Statistics & Insurance Sciences, Piraeus, Greece

    Markos V. Koutras

Section Editor information

  1. Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, 06269-4120, Storrs, CT, USA

    Joseph Glaz

  2. Dept. of Statistics and Insurance Science, University of Piraeus, 18534, Piraeus, Greece

    Markos V. Koutras

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deLima, M.S., Duczmal, L.H. (2017). Adaptive Likelihood Ratio Scans for the Detection of Space-Time Clusters. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_37-1

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  • DOI: https://doi.org/10.1007/978-1-4614-8414-1_37-1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8414-1

  • Online ISBN: 978-1-4614-8414-1

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