today today a today
The term Stoday in Eq. 10 refers to the number of people who are sick on the current day while the term Ctoday refers to the number of people who visited the ED on the current day. Atoday is the probability that a patient will visit the ED for the day of week specified by today. Figure 14.18 shows the availability estimated in the period leading up to the synthetic ramp outbreak: it shows a consistent picture that we usually see far more patients on Mondays than Sundays, and then the visits taper off during the rest of the week. Figure 14.19 shows both the original count and the estimated sickness (count/availability). Sickness is much more stable than the original count because day of week effects have been greatly reduced. It is now possible to run a time series algorithm on the sickness values. In this case, we chose to use moving average with a window of seven days. The resulting alarms show something that was not achieved in any m
HON HON MON HON HON HON
AUG-16-2004 AUG-23-2004 AJG-30-2004 SEP-OS-2004 SEP-13-2004 SEP-20-2004
figure 14.19 The black "count" line shows the raw data.The gray "sickness" line shows the sickness after the count has been divided by the corresponding availability value from Figure 14.18. Note how the sickness time series is now smoother than the original data and decorrelated with day of week. The alarm levels are derived from moving average applied to the sickness time series.
of the previous illustrations: a strong alarm resulting from the higher-than-expected counts for the Sunday.
We would like to emphasize that the sickness availability method only smoothes the time series. It is not a detection algorithm by itself. Instead, a detection algorithm, such as the control chart, moving average, or CUSUM algorithms should be used on the smoothed data.
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