Page 206 - Special Topic Session (STS) - Volume 4

STS580 Ross Sparks et. al
model in real-time when engaging in prospective surveillance plans. We
explored the option of aggregating the time between events within a day in
this paper. This does reduce the problem to daily monitoring but still has the
advantage of treating it as a multivariate problem and hence can have greater
power when these are reasonably highly correlated. The next section will
explore this option in more detail.

2. Multivariate TBE
The multivariate TBE considers the average daily TBE values for all events
that occurred on a particular day. This means that the dimension of the
multivariate monitoring plan changes with each day. If only one of the
symptoms diarhoea, vomiting, headache and generally feeling unwell occurs
in a day then we apply the univariate TBE monitoring as outlined in Sparks
et.al. (2019a, b) for that one symptom. Otherwise the monitoring plan is
multivariate with the potentially changing the dimensions of the multivariate
monitoring plan each day. Treating the monitoring plan as multivariate on
some days hopefully offers it greater power for such monitoring plans.
We will assume that the in-control distribution is Weibull, and this can be
fitted using gamlss library in R (Stasinopoulos et al., 2006, Stasinopoulos and
Rigby, 2007) for each symptom separately. This model is used to define the
in-control non-homogeneous expected (parameter) values for TBE. These are
predicted at the time of each event using the respective Weibull regression
models. Since we don’t have enough data to deliver a Phase I and Phase II,
for developing our plan, we only use a retrospective surveillance approach.
The model includes the following adjustments (explanatory variables):
seasonal harmonics, day of the week, and within day harmonics.
Since there can be more than one event in the day, the statistic used the
average time between events that occurred on that day. Since this average has
a smaller standard error to those with only one event in the day, we multiply
the average by the square root of the number of events within a day, so each
average has the same standard error.

3. Assessment process
We assess the performance of the plans using the number of days to an
alarm and train all plans to have the same false discovery rate, so they can be
fairly compared. The daily counts where fitted using a negative binomial
regression model as in Sparks et. al. (2010, 2011) and the EWMA is applied to
the Pearson residuals of this model. If an “event” is not signalled within 7 days
as unusual then it will be regarded as having been missed. The assessment
process looks at univariate counting process monitoring, univariate time
between events and the multivariate approach outlined above. The out-of-
control false discovery rate is taken as one in 100 days for the multivariate
process, whereas the univariate charts examined an out-of-control false

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