Biology Reference
In-Depth Information
R> plot(s.far, ylab = "No. of deaths", xlab = "time (weeks)",
main = "")
The figure is interpreted as follows: Starting in ISO week 40 of 2007, we use
only values from the past to construct a prediction interval for the observed
number of counts for week 40. When comparing the actually observed num-
ber 15 with the upper limit
u
t
0
=.
, we have no reason to believe in an
excess number of deaths and hence no alarm is generated. The upper limit
would have been 30.3 or 29.4 cases for the two other transformations. The
same procedure is now repeated for ISO week 41, etc. In week 02 of 2008,
the observed number of counts exceeds the threshold of the
“
none
”
line for
the first time, and hence an alarm is generated for that week. No further
alarms are generated during the 65 weeks of surveillance. Once an alarm is
sounded, the alarm must be verified and the public health significance inves-
tigated. In this instance, investigation of available epidemic intelligence did
not reveal any specific explanation for the mortality peak that would indicate
a significant public health event.
Note also the prospective behavior of the detection: At each time point,
we are only allowed to look back in time, never ahead in time. Thus, detec-
tion mimics the arrival of new data each week, which would be the case in
practical applications. Choosing a specific value for α is particularly depen-
dent on the application and mode of operation. A value of, for example,
α
=
0.01 means that for a particular week the probability of observing a value
yu
t
28 1
>
by pure chance under the estimated model is α/2 = 0.5
%
. If these
probabilities are assumed independent for the individual weeks, the prob-
ability of observing a false alarm during the 65 epochs of the monitoring is
thus 1-(1-0.005)
65
= 0.28. In Section 12.1, the actual run-length distribution of
the algorithm is studied in further detail.
A call to an aberration detection algorithm fills the
alarm
slot of the
sts
object. This is an
n
′ ×
m
matrix of Booleans stating for each time point (aka.
epoch
) and series whether the time point was classified as aberration. Here,
n
′ corresponds to the number of elements in the
range
argument of the call.
Furthermore, the
upper-bound
slot contains an
n
′ ×
m
matrix of values cor-
responding to the minimum number of cases each week that would have
resulted in an alarm. Finally, the slot
control
contains the list of control
arguments that was used to invoke the aberration detection algorithm.
For the EuroMOMO project, an important aspect besides the detection of
aberrations is the quantification of excess mortality. A first measure of this
excess could be based on the predictive distribution. For example, Figure 12.3
shows the predicted expected number
t
0
0
ˆ
µ
of cases in-control, allowing for a
t
−
ˆ
µ
. By computing confidence inter-
definition of excess as, for example,
y
t
t
ˆ
µ
, one would also be able to assess the uncertainty of such an excess.
As a further tool in this direction, Figure 12.4 shows the quantiles of the
predictive distribution. The Farrington procedure sounds an alarm once the
1-α/2 quantile is exceeded.
vals for
t
