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Generalized Seasonal Autoregressive Integrated Moving Average Models for Count Data with Application to Malaria Time Series with Low Case Numbers

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  • Olivier J T Briët
  • Priyanie H Amerasinghe
  • Penelope Vounatsou

Abstract

Introduction: With the renewed drive towards malaria elimination, there is a need for improved surveillance tools. While time series analysis is an important tool for surveillance, prediction and for measuring interventions’ impact, approximations by commonly used Gaussian methods are prone to inaccuracies when case counts are low. Therefore, statistical methods appropriate for count data are required, especially during “consolidation” and “pre-elimination” phases. Methods: Generalized autoregressive moving average (GARMA) models were extended to generalized seasonal autoregressive integrated moving average (GSARIMA) models for parsimonious observation-driven modelling of non Gaussian, non stationary and/or seasonal time series of count data. The models were applied to monthly malaria case time series in a district in Sri Lanka, where malaria has decreased dramatically in recent years. Results: The malaria series showed long-term changes in the mean, unstable variance and seasonality. After fitting negative-binomial Bayesian models, both a GSARIMA and a GARIMA deterministic seasonality model were selected based on different criteria. Posterior predictive distributions indicated that negative-binomial models provided better predictions than Gaussian models, especially when counts were low. The G(S)ARIMA models were able to capture the autocorrelation in the series. Conclusions: G(S)ARIMA models may be particularly useful in the drive towards malaria elimination, since episode count series are often seasonal and non-stationary, especially when control is increased. Although building and fitting GSARIMA models is laborious, they may provide more realistic prediction distributions than do Gaussian methods and may be more suitable when counts are low.

Suggested Citation

  • Olivier J T Briët & Priyanie H Amerasinghe & Penelope Vounatsou, 2013. "Generalized Seasonal Autoregressive Integrated Moving Average Models for Count Data with Application to Malaria Time Series with Low Case Numbers," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-9, June.
  • Handle: RePEc:plo:pone00:0065761
    DOI: 10.1371/journal.pone.0065761
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    References listed on IDEAS

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    1. Konradsen, F. & Amerasinghe, F. P. & van der Hoek, W. & Amerasinghe, P. H., 2000. "Malaria in Sri Lanka: Current knowledge on transmission and control," IWMI Books, Reports H027692, International Water Management Institute.
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    Cited by:

    1. Ollech, Daniel & Webel, Karsten, 2020. "A random forest-based approach to identifying the most informative seasonality tests," Discussion Papers 55/2020, Deutsche Bundesbank.
    2. Vurukonda Sathish & Siuli Mukhopadhyay & Rashmi Tiwari, 2022. "Autoregressive and moving average models for zero‐inflated count time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 190-218, May.
    3. Gbenga J. Abiodun & Olusola S. Makinde & Abiodun M. Adeola & Kevin Y. Njabo & Peter J. Witbooi & Ramses Djidjou-Demasse & Joel O. Botai, 2019. "A Dynamical and Zero-Inflated Negative Binomial Regression Modelling of Malaria Incidence in Limpopo Province, South Africa," IJERPH, MDPI, vol. 16(11), pages 1-19, June.

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