44 10. Repeating steps 4 to 9 for SS and ULS with the same data simulation.
11. Repeating steps 1 to 10 for other true hotspots. 12. Repeating steps 1 to 11 for other data sets.
13. Showing the summary in a table and graphs. 14. Analyze the results.
This simulation has four data sets, i.e.: Central Java, Java Island, Map X and Map Y. Two designs of true hotspot are given for each data set.
3.3.2 The Fourteen Criteria
Fourteen criteria for comparing circle based scan statistic SS hotspot detection and upper level set scan statistic ULS hotspot detection are the
following, 1. Cardinality is number of districts cells in zone area. Cardinality is
expected equal to the number of cells in the true hotspot. 2. LLR is Loglikelihood ratio of the hotspot, computed as follows,
Null hypothesis tends to be rejected for the large which means hotspot
is occurred. 3. RR-zone RR-MLE is maximum likelihood estimation of relative risk
, computed as follows,
Null hypothesis will be rejected for larger than 1, which means
proportion of occurrences upon population in the zone is greater than proportion occurrences upon population outside the zone.
4. RR-true hotspot is relative risk of true hotspot for every simulation.
Null hypothesis will be rejected for larger than 1 with the same
explanation of RR-zone.
45 5. MissCell is number of miss-out cells number of cells in the true hotspot
that are missing from MLE zone. A better detection has smaller number of miss-out cells
. 6. ExtrCel is number of extraneous cells number of cells in MLE zone that
are not in the true hotspot. A better detection has smaller extraneous cells count.
7. OverlpCell is number of cells that occur in the true hotspot and also in MLE zone overlap with hotspot. A better detection has equal number
with cardinality. 8. MissCell is percentage of miss-out cells upon the number of cells in
the true hotspot. A better detection has smaller percentage of miss-out cells
. 9. ExtrCell is percentage of extraneous cells upon the number of cells in
the true hotspot. A better detection has smaller extraneous cells percentage. 10. OverlpCell is percentage of OverlpCells cells that occur in the true
hotspot and also in the MLE zone upon the number of cells in the true hotspot. A better detection has greater overlap cells percentage
100. 11. SensCell is degree of sensitivity to detect hotspot cells, calculated as
follows, sensitivity cell = OverlpCellsCT 100. Larger sensitivity cell
means better detection, that is greater percentage of cells in the true hotspot are detected as hotspot.
12. SensPop is the same as number 11, based on population, calculated as follows, sensitivity population = OverlpPopCT_Pop
100. Larger sensitivity population means better detection, due to greater percentage of
population in the true hotspot are detected as population of hotspot cells. 13. SpecCell is degree of specificity cells, calculated as follows,
specificity cell = . A
better detection has larger specificity, i.e. smaller extraneous cells is expected.
14. SpecPop is degree of specificity population, calculated as follows,
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
