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Detecting the start of an influenza outbreak using exponentially weighted moving average charts.

Steiner SH, Grant K, Coory M, Kelly HA - BMC Med Inform Decis Mak (2010)

Bottom Line: Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates.The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia.The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. of Statistics, University of Waterloo, Ontario, Canada. shsteine@math.uwaterloo.ca

ABSTRACT

Background: Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates. The severity and length of influenza outbreaks vary from year to year. Quick and reliable detection of the start of an outbreak is needed to promote public health measures.

Methods: We propose the use of an exponentially weighted moving average (EWMA) control chart of laboratory confirmed influenza counts to detect the start and end of influenza outbreaks.

Results: The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia.

Conclusions: The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks.

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Related in: MedlinePlus

Comparison of ARL for EWMA, MA(4) and Shewhart Methods Solid line: EWMA, dashed line: MA(4), dashed dot line: Shewhart.
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Figure 6: Comparison of ARL for EWMA, MA(4) and Shewhart Methods Solid line: EWMA, dashed line: MA(4), dashed dot line: Shewhart.

Mentions: Next we compare the proposed EWMA method using λ = 0.5 with the four period moving average, MA(4), an approach advocated by Muscaltello et al. [14] and the Shewhart approach where we simply compare the observed count each week with a threshold. In this comparison we assume the number of ILI cases out-of-season follows a Poisson distribution with mean 2 and model outbreaks of various sizes by increasing the Poisson mean. We do not use the empirical out-of-season Victoria data here because, due to the small amount of data, it is not possible to find a Shewhart chart with a reasonably large in-control (or out-of-season) ARL. By setting up a Markov chain model that takes into account all four values that make up the moving average and because each count is an integer we can determine exact results for the performance of the MA(4) method. The results for the Shewhart chart are also exact while for the EWMA we use the Markov chain approximation. Figure 6 gives the results on a log scale for the average run lengths of the three approaches. We were unable to exactly match the in-control performance of the three charts because of the inherent discreteness of the count data. With control limits of 4.4, 3.9 and 6.9 for the EWMA(λ = 0.5), MA(4) and Shewhart approaches respectively we have a steady state in-control ARL of 190 for the EWMA and MA(4) methods but 220 for the Shewhart approach. We see in Figure 6 that, as expected, the EWMA and MA(4) approaches are quicker to detect outbreaks than the Shewhart approach when the outbreak is relatively small. In addition for very large shifts the Shewhart chart is marginally better than the EWMA approach while the MA(4) approach takes longer to signal. This comparison is limited for our context because with influenza outbreaks we expect sudden but not instantaneous large shifts in the mean number of counts. Modeling a more realistic influenza outbreak would require additional assumptions about how quickly changes take place and require either simulation or a much more complicated analysis to generate results. We feel that because the EWMA approach works very well in comparison to the MA(4) and Shewhart approaches for shifts of any size it is the preferred approach. Note in particular the EWMA is substantially better than the MA(4) approach for the larger shifts we hope to be able to detect quickly.


Detecting the start of an influenza outbreak using exponentially weighted moving average charts.

Steiner SH, Grant K, Coory M, Kelly HA - BMC Med Inform Decis Mak (2010)

Comparison of ARL for EWMA, MA(4) and Shewhart Methods Solid line: EWMA, dashed line: MA(4), dashed dot line: Shewhart.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2909986&req=5

Figure 6: Comparison of ARL for EWMA, MA(4) and Shewhart Methods Solid line: EWMA, dashed line: MA(4), dashed dot line: Shewhart.
Mentions: Next we compare the proposed EWMA method using λ = 0.5 with the four period moving average, MA(4), an approach advocated by Muscaltello et al. [14] and the Shewhart approach where we simply compare the observed count each week with a threshold. In this comparison we assume the number of ILI cases out-of-season follows a Poisson distribution with mean 2 and model outbreaks of various sizes by increasing the Poisson mean. We do not use the empirical out-of-season Victoria data here because, due to the small amount of data, it is not possible to find a Shewhart chart with a reasonably large in-control (or out-of-season) ARL. By setting up a Markov chain model that takes into account all four values that make up the moving average and because each count is an integer we can determine exact results for the performance of the MA(4) method. The results for the Shewhart chart are also exact while for the EWMA we use the Markov chain approximation. Figure 6 gives the results on a log scale for the average run lengths of the three approaches. We were unable to exactly match the in-control performance of the three charts because of the inherent discreteness of the count data. With control limits of 4.4, 3.9 and 6.9 for the EWMA(λ = 0.5), MA(4) and Shewhart approaches respectively we have a steady state in-control ARL of 190 for the EWMA and MA(4) methods but 220 for the Shewhart approach. We see in Figure 6 that, as expected, the EWMA and MA(4) approaches are quicker to detect outbreaks than the Shewhart approach when the outbreak is relatively small. In addition for very large shifts the Shewhart chart is marginally better than the EWMA approach while the MA(4) approach takes longer to signal. This comparison is limited for our context because with influenza outbreaks we expect sudden but not instantaneous large shifts in the mean number of counts. Modeling a more realistic influenza outbreak would require additional assumptions about how quickly changes take place and require either simulation or a much more complicated analysis to generate results. We feel that because the EWMA approach works very well in comparison to the MA(4) and Shewhart approaches for shifts of any size it is the preferred approach. Note in particular the EWMA is substantially better than the MA(4) approach for the larger shifts we hope to be able to detect quickly.

Bottom Line: Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates.The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia.The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept. of Statistics, University of Waterloo, Ontario, Canada. shsteine@math.uwaterloo.ca

ABSTRACT

Background: Influenza viruses cause seasonal outbreaks in temperate climates, usually during winter and early spring, and are endemic in tropical climates. The severity and length of influenza outbreaks vary from year to year. Quick and reliable detection of the start of an outbreak is needed to promote public health measures.

Methods: We propose the use of an exponentially weighted moving average (EWMA) control chart of laboratory confirmed influenza counts to detect the start and end of influenza outbreaks.

Results: The chart is shown to provide timely signals in an example application with seven years of data from Victoria, Australia.

Conclusions: The EWMA control chart could be applied in other applications to quickly detect influenza outbreaks.

Show MeSH
Related in: MedlinePlus