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STS580 Ross Sparks et. al
discovery rate is taken as one in 400 days. Note that the correlation between
these symptoms considered are very low, less than 0.079.
The result are as follows. All plans monitored the Pearson residuals of the
models (whether Weibull or negative binomial distributed) and these Pearson
residuals for a particular symptom are smoothed over time using the EWMA
statistic. The univariate TBE monitoring plans did not flag an unusual trend in
the TBE in either direction. The univariate daily counts indicate lower than
expected counts from 14 January 2015 to 11 February 2015. Any event that
was not flagged by more than two consecutive days were ignored in the
multivariate plans. The multivariate plan used the Weibull regression models
for each symptom separately. Hotellings robust version of the T-squared
statistic of Sparks (2015) was used to flag unusual events in terms of how large
their Pearson smoothed residuals are. Note that if the TBE increases, then there
is no outbreak. The TBE values need to significantly reduce to flag an outbreak.
Multivariate plans flagged several events that are listed in the table below:

Dates Reason
2015-02-24 to 2015-05-01 Larger waiting times between events for
diarrhoea and headaches
2015-07-19 to 2015-07-29 Larger waiting times between events for all
symptoms
2015-11-24 to 2015-12-24 Larger waiting times between events for
vomiting, diarrhoea and headaches
2017-03-22 to 2017-03-31 Larger waiting times between events for
vomiting and headaches
2017-08-17 to 2018-02-06 Larger waiting times between events for
diarrhoea and unwell. At times there are larger
waiting times between events for headaches

4. Multivariate charts are useful for diagnosing the nature of outbreaks
We use the dynamic biplot of Sparks et al (1997) to explore the nature of
outbreaks using unsmoothed version of Pearson residuals from the respective
Weibull regression models. Information on how to interpret this biplot can be
found in Sparks et al. (2017). We are looking for periods of TBE values that are
lower than expected, i.e., those in the biplot that are in the opposite quadrant
to the most recent points in the observation plot. For this we only use the days
with all symptoms occurring on the same day, i.e., only considering days where
there is at least one of the four symptoms on the day. This was by far the most
common situation – occurring in 86% of the days in the dataset.
The first 40 days are used as training data for setting up the multivariate
plans. The days without an event for a symptom were excluded from the
dataset being considered in this section because it resulted in missing data for
the day. Thereafter we explore the average TBE event daily, when they occur

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