46 A better detection method has larger specificity, i.e. smaller extraneous
population is expected.
Note: These abbreviations will be used at the Appendix 7 to 14
CT : cardinality number of cells of the true hotspot
OverlpPop : population in the overlap cells
CT_Pop = population in the cardinality cells
MissPop: population in miss out cells
ExtrPop: total population in extraneous cells
OverlpPop : total population in the overlap celsl
MissPop : percentage population in the miss out cells from the total population
in the true hotspot. ExtrPop
: percentage population in the extraneous cells from the total population in the true hotspot.
OverlpPop : percentage of population in the overlap cells from the total
population in the true hotspot. Significance index is percentage of null hypothesis rejection in simulations.
Power comparisons Every simulation gives the result of detection or no detection base on the given
significance level. Detection power is relative frequency of correct detection. Detection means declaration of the existence of a hotspot. In this simulation,
power is obtained from percentage of null hypothesis rejection.
3.4 The Results and Analysis
Table 9 shows performance comparisons between Upper Level Set ULS and Scan Statistic SS hotspot detection for 5 significance, while Table 10 for
1 significance. Number of cells in column 1 is the number of cells in true hotspot which determined in preparation step of simulation. Column 3 is the
cardinality mean of 10000 simulations. All means of criteria Appendix 7
– 14
47 are compared between ULS and SS. The dot sign in each column means a better
value between two rows, ULS and SS row. In last row, sign “” means “greater value means better performance”, sign
“” means “smaller value means better performance”, and sign “ 1” means “more different from 1 is better”. In general, better performance means the method able
to detect hotspot. The counts of dots at every row is at the last two columns, as a resume for ULS column 18 and SS column 19, whereas the total count of dots
is at the last row. Total dots of ULS and SS in Table 9 are 63 and 39, respectively. Furthermore in Table 10 are 57 and 38 for ULS and SS, respectively.
Appendix 7 – 14 are more detail output of the simulation results.
Table 9 Performance criteria comparison of ULS and SS for 5 significance
N u
mb er
o f
cel ls
M et
h o
d ca
rd ina
lity LLR
RR -Z
o n
e RR
-T ru
e M
issou t
Cells E
xtr a
n e
o u
s Ce lls
Ove rlap
Ce lls
M issou
t Cell
E xtr
a n
e o
u s Ce
ll
Ove rlap
Ce ll
S e
n sitiv
it y Ce
ll
S e
n sitivi
ty P
o p
S p
e cifici
ty Cell
S p
e cifici
ty P
o p
S ign
ifican ce
in d
e x
ULS SS
1 2
3 4
5 6
7 8
9
10 11
12 13
14 15
16 17
18 19
Central Java 5 ULS
11
7 SS
7
5 11 ULS
14
9
SS 6
4 Java
11 ULS 32
7
SS 16
5
13 ULS 34
7
SS 16
6 Map X
12 ULS 19
9 SS
10
11 ULS 18
9 SS
10
4
Map Y
103
ULS 89
8 SS
24
5 88 ULS
82
7 SS
26
6
better value if 1
1 63
39
Table 10 Performance criteria comparison of ULS and SS for 1 significance
48
N u
mb er
o f
cel ls
M et
h o
d ca
rd ina
lity LLR
RR -Z
o n
e RR
-T ru
e M
issou t
Cells E
xtr a
n e
o u
s Ce lls
Ove rlap
Ce lls
M issou
t Cell
E xtr
a n
e o
u s Ce
ll
Ove rlap
Ce ll
S e
n sitiv
it y Ce
ll
S e
n sitivi
ty P
o p
S p
e citivi
ty Cell
S p
e citivi
ty P
o p
S ign
if ican
ce in
d e
x
ULS SS
1 2
3 4
5 6
7 8
9
10 11
12 13
14 15
16 17
18 19
Central Java 5
ULS 10
8
SS 7
5
11 ULS
14
9
SS 6
4 Java
11 ULS
30
8 SS
16
5 13
ULS 33
7
SS 17
5
Map X 12
ULS 19
9 SS
11
4
11 ULS
18
9
SS 11
4 Map Y
103 ULS
91
8
SS 26
5
88 ULS
82
7 SS
27
6
better value if
1 1
57 38
According to the results of comparisons, it is believed ULS hotspot detection method is better than SS. The study is continued to obtain the hotspot of bad-
nutrition cases in 9 districts in Java Island that chosen randomly. The results of hotspot detection will be used as a covariate in modeling in
chapter 4.
49
3.5 ULS Hotspot Detection for Bad Nutrition Case in Some Districts in Java Island
