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Count data regression charts for the monitoring of surveillance time series

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  • Höhle, Michael
  • Paul, Michaela

Abstract

Control charts based on the Poisson and negative binomial distribution for monitoring time series of counts typically arising in the surveillance of infectious diseases are presented. The in-control mean is assumed to be time-varying and linear on the log-scale with intercept and seasonal components. If a shift in the intercept occurs the system goes out-of-control. Using the generalized likelihood ratio (GLR) statistic a monitoring scheme is formulated to detect on-line whether a shift in the intercept occurred. In the case of Poisson the necessary quantities of the GLR detector can be efficiently computed by recursive formulas. Extensions to more general alternatives e.g. containing an auto-regressive epidemic component are discussed. Using Monte Carlo simulations run-length properties of the proposed schemes are investigated and the Poisson scheme is compared to existing methods. The practicability of the charts is demonstrated by applying them to the observed number of salmonella hadar cases in Germany 2001-2006.

Suggested Citation

  • Höhle, Michael & Paul, Michaela, 2008. "Count data regression charts for the monitoring of surveillance time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4357-4368, May.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4357-4368
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    References listed on IDEAS

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    1. Harvey, Andrew & Koopman, Siem Jan & Riani, Marco, 1997. "The Modeling and Seasonal Adjustment of Weekly Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 354-368, July.
    2. C. P. Farrington & N. J. Andrews & A. D. Beale & M. A. Catchpole, 1996. "A Statistical Algorithm for the Early Detection of Outbreaks of Infectious Disease," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 547-563, May.
    3. Xie, M. & He, B. & Goh, T. N., 2001. "Zero-inflated Poisson model in statistical process control," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 191-201, December.
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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. Liu, Yafen & He, Zhen & Shu, Lianjie & Wu, Zhang, 2009. "Statistical computation and analyses for attribute events," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3412-3425, July.
    3. Linus Schiöler & Marianne Fris�n, 2012. "Multivariate outbreak detection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 223-242, April.
    4. Bekiros, Stelios & Kouloumpou, Dimitra, 2020. "SBDiEM: A new mathematical model of infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    5. Ben Omrane, Walid & Heinen, Andréas, 2010. "Public news announcements and quoting activity in the Euro/Dollar foreign exchange market," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2419-2431, November.
    6. Manuel Oviedo de la Fuente & Manuel Febrero-Bande & María Pilar Muñoz & Àngela Domínguez, 2018. "Predicting seasonal influenza transmission using functional regression models with temporal dependence," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-18, April.
    7. Salmon, Maëlle & Schumacher, Dirk & Höhle, Michael, 2016. "Monitoring Count Time Series in R: Aberration Detection in Public Health Surveillance," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i10).
    8. Assuno, Renato & Correa, Thais, 2009. "Surveillance to detect emerging space-time clusters," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2817-2830, June.

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