Biology Reference
In-Depth Information
often used as a criterion when evaluating the performance of a detection
method. A more thorough discussion on such criteria can be found, for
example, in Frisén (2003).
12.4 The Farrington Algorithm
The aim of the Farrington et al. (1996) algorithm was to develop a robust
and fast method applicable for the routine monitoring of weekly reports
on infections for many different pathogens at the former Communicable
Disease Surveillance Centre (now Health Protection Agency) in the United
Kingdom. For the current time point
t
week
year
, that is, week,
t
0
week
, in
year,
t
year
; this is done by formulating a statistical algorithm for predict-
ing the observed number of counts
y
t
0
. This prediction is based on a subset
of the historic data: Centered around the current week,
t
0
week
, for example,
week 23, one includes
w
values to the left and right of that week together
with the week itself, for example, week 21-25, if
w
= 2. This is done for each
of the years
t
=
(
t
,
t
)
0
0
0
year yea− −
,,
. Thus, a total of
b
·(2
w
+ 1) reference values are
extracted. Now, an overdispersed Poisson generalized linear model (GLM)
with log-link is fitted to the reference values. The GLM has the following
mean structure:
1
b
…t
0
0
Ey
()
=,
µ
where
log(
µ αβ
)
=+,
t
(12.2)
t
t
t
a nd Va r(
y
t
) = φ
μ
t
with α, β, and φ>0 being coefficients to estimate. See, for
example, Fahrmeir and Tutz (2001) for further information about GLMs. One
can show that an approximate (1 - α) · 100% prediction interval for
y
t
0
based
on this GLM has an upper limit,
ˆ
ˆ
(
ˆ
φ
µ
+
Var
)
µ
t
t
ˆ
ˆ
ˆ
u
=+ ⋅
z
Var
(
y
− =⋅ +
)
1
z
,
µ
µ µ
0
0
t
12
−/
α
t
12
−/
α
t
t
t
0
0
ˆ
2
0
0
0
µ
t
0
where
z
1 − α/2
is the 1 - α/2 quantile of the standard normal distribution, while
t
0
ˆ
ˆ
µ
,
and
Var(
ˆ
µ
can be obtained from the GLM output. If the observed
value
y
t
0
is greater than
u
t
0
, then the time point
t
0
is flagged as an outbreak,
that is, in the notation of Section 12.3:
)
t
0
y
u
.
t
ˆ
()
xt
=
I
>
1
0
0
t
0
(12.3)
