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ScanZID: Spatial Scan Statistics with Zero Inflation and Dispersion

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Abstract

The spatial scan statistic is one of the most important methods to detect and monitor spatial disease clusters. Usually it is assumed that disease cases follow a Poisson, Binomial, Bernoulli, or negative binomial distribution. In practice, however, case count datasets frequently present zero inflation and/or dispersion (underdispersion or overdispersion), resulting in the violation of those commonly used models, thus increasing type I error occurrence. This paper describes the spatial scan statistic with the zero inflation and dispersion (ScanZID) to accommodate simultaneously the excess of zeroes and dispersion. The null and alternative model parameters are estimated by the expectation-maximization (EM) algorithm, and the p-value is obtained through the fast double bootstrap test. An application is presented for Hanseniasis data in the Brazilian Amazon.

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Acknowledgements

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

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Authors and Affiliations

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

    Max S. de Lima, José C. Neto, Márcio A. C. Ferreira & Vanessa A. de Lima

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

    Luiz H. Duczmal

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

    Letícia P. Pinto

  4. Computer Science Department, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Letícia P. Pinto

Authors
  1. Max S. de Lima
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  2. Luiz H. Duczmal
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  3. José C. Neto
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  4. Letícia P. Pinto
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  5. Márcio A. C. Ferreira
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  6. Vanessa A. de Lima
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Corresponding author

Correspondence to Max S. de Lima .

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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de Lima, M.S., Duczmal, L.H., Neto, J.C., Pinto, L.P., Ferreira, M.A.C., de Lima, V.A. (2017). ScanZID: Spatial Scan Statistics with Zero Inflation and Dispersion. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_41-1

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  • DOI: https://doi.org/10.1007/978-1-4614-8414-1_41-1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8414-1

  • Online ISBN: 978-1-4614-8414-1

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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