38 3
z z
1 Note:
z z
=
1
z z
r r
and
z z
r r
Hypothesis test of Circular based scan setup H
: No clusterhotspot:
a
, i.e. RR
a
= r
a
=1, for a M.
1 :
z IA
A
r H
and
1
z
r
, IA: Inside
z
is compared with average .
The following shows that H
A
implies :
H
A
: but
z z
z z
N N
N
i.e
z z
z z
. because
z z
and
z z
,
0 i.e and
,
The following shows that implies H
A
:
IA A
H
implies H
A
component involving RR, but not the component of inside and outside homogeneities.
and
3.2.3 Circle-based Scan Statistic SS Hotspot Detection
Circle based scan statistic hotspot detection is a method to detect hotspots on a study area based on circle zones with the center is in the coordinates of a cell.
The method works as follows: circles of different sizes from zero to 50 of the population size are placed at every cell in the study area. For each circle, a
likelihood ratio statistic is computed based on the number of observed and expected cases inside and outside the circle and compared with the likelihood L
under the null hypothesis. The likelihood function under the alternative hypothesis assuming Poisson distributed cases is proportional to:
where the symbols y and EY represent the observed and expected number of cases in a circle and N-y and N-EY the observed and expected number of
cases outside the circle. N is the total number of cases. The indicator function I is equal to 1 if the observed number of cases within the circle is larger than the
39 expected number of cases given the null hypothesis and 0 otherwise Kulldorff
2010. The process of scan statistics hotspot detection is shown by Figure 13. The radius of a circle becomes larger if a center of a closest district combines to that
circle, then a new circle revealed. In each district combining, the radius of circle, the number of cases, and the population size are bigger. A circle with the highest
likelihood ratio value is identified as a potential hotspot. An associated p-value based on Monte Carlo simulations is computed. For each simulation under null
hypothesis, the likelihood ratio statistic is computed and the actual value is compared with the set of simulated values to find significance probability. P-value
is determined as follows, say the simulation under null hypothesis is built for x = 9999 times. If the rank of likelihood ratio value of a circle from actual data is 400
then its p-value is 400x+1 = 0.04. The method produces a set of hotspot, the relative risk of event for the different hotspot, and a corresponding p-value for
each hotspot based on the Monte-Carlo simulations. Districts or cells are identified as cluster hotspot if they are associated with a cluster with p-value less than 0.05
Aamodt, Samuelsen, Skrondal 2006.
Figure 13 A part of circle based hotspot detection process
3.2.4 ULS Scan Statistic
