A Space-Time Permutation Scan Statistic For Measles Disease Hotspots Detection In West Java

ABSTRACT
DANI ARDIYANTO. A Space-time Permutation Scan Statistic for Measles Disease Hotspots
Detection in West Java. Under the advisory of ASEP SAEFUDDIN and BAGUS SARTONO.
In this research, scan statistic was implemented to detect clusters in a point process. The scan
statistic can be applied on wide area of interest, one of them are on disease area clustering. The
ability in performing disease surveillance without population-at-risk data is important in
developing countries, where these data may be hard to be obtained.
This paper presents the application of the scan statistic in order to detect measles disease
hotspots in West Java Province. Unlike the spatial scan statistic, space-time permutation scan
statistic not only detects the location of the significant hotspot cluster but also identifies its
occurrence. Further, the space-time permutation scan statistic can be implemented when the
population-at-risk is unavailable. This method creates a large number of permutations of the
spatial and temporal attributes of each dataset to get the expected number of cases, with the
underlying assumption that the probability of a case being in an area z, given the observed d, is
equal. The test statistic was based on likelihood ratio test and evaluated using Monte Carlo
hypothesis testing.
The research used aggregated measles disease case in West Java districts obtained from
Statistics Indonesia Potensi Desa (Podes) year 2003 and 2006. They were twelve detected
measles hotspots in West Java during year 2003 and 2006, which only four of them were
significant. The highest log-likelihood ratio values, the most likely cluster (MLC), happened in
Cirebon in 2006 time frame.

Keywords: space-time permutation scan statistic, measles, hotspot.

A SPACE-TIME PERMUTATION SCAN STATISTIC
FOR MEASLES DISEASE HOTSPOTS DETECTION IN WEST JAVA

DANI ARDIYANTO

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
2008

This thesis is dedicated to my father and my mother.
You’ll always have a place within my heart.
I Love You.
Bogor, January 2008

ABSTRACT
DANI ARDIYANTO. A Space-time Permutation Scan Statistic for Measles Disease Hotspots
Detection in West Java. Under the advisory of ASEP SAEFUDDIN and BAGUS SARTONO.

In this research, scan statistic was implemented to detect clusters in a point process. The scan
statistic can be applied on wide area of interest, one of them are on disease area clustering. The
ability in performing disease surveillance without population-at-risk data is important in
developing countries, where these data may be hard to be obtained.
This paper presents the application of the scan statistic in order to detect measles disease
hotspots in West Java Province. Unlike the spatial scan statistic, space-time permutation scan
statistic not only detects the location of the significant hotspot cluster but also identifies its
occurrence. Further, the space-time permutation scan statistic can be implemented when the
population-at-risk is unavailable. This method creates a large number of permutations of the
spatial and temporal attributes of each dataset to get the expected number of cases, with the
underlying assumption that the probability of a case being in an area z, given the observed d, is
equal. The test statistic was based on likelihood ratio test and evaluated using Monte Carlo
hypothesis testing.
The research used aggregated measles disease case in West Java districts obtained from
Statistics Indonesia Potensi Desa (Podes) year 2003 and 2006. They were twelve detected
measles hotspots in West Java during year 2003 and 2006, which only four of them were
significant. The highest log-likelihood ratio values, the most likely cluster (MLC), happened in
Cirebon in 2006 time frame.
Keywords: space-time permutation scan statistic, measles, hotspot.

A SPACE-TIME PERMUTATION SCAN STATISTIC
FOR MEASLES DISEASE HOTSPOTS DETECTION IN WEST JAVA

BY:
DANI ARDIYANTO
G14103029

Thesis
For the Degree Bachelor of Science
Department of Statistics

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
2008

Title

: A SPACE-TIME PERMUTATION SCAN STATISTIC FOR
MEASLES DISEASE HOTSPOTS DETECTION IN WEST JAVA

Name : Dani Ardiyanto
NRP : G14103029

Approved by:
Advisor I,

Advisor II,

Dr. Ir. Asep Saefuddin, M.Sc
NIP. 130938261

Bagus Sartono, M.Si
NIP. 132311923

Acknowledged by:
Dean of Faculty of Mathematics and Natural Sciences
Bogor Agricultural University

Dr. Drh.Hasim, DEA
NIP 131578806

Passed examination date:

BIOGRAPHY
Author was born in Bogor, July 17th, 1985, as the first of two children of Arief Murdiman and
Siti Rodiyah.
In 1997, author graduated from SD Negeri Cibuluh 1 Bogor, and then continued his study at
SLTP Negeri 1 Bogor and graduated in 2000. Author finished his study at SMU Negeri 1 Bogor in
2003, and then was accepted as a student at Department of Statistics, Faculty of Mathematics and
Natural Sciences, Bogor Agricultural University, in the same year through USMI (Undangan
Seleksi Masuk IPB).
During his study, author joined Himpunan Keprofesian Gamma Sigma Beta as a staff of
Departemen Olahraga dan Seni in 2004/2005. Author also became the lecturer assistant of
Matematika Dasar, Kalkulus, and Metode Statistika subjects. On February-April 2007, author
went to Malang, East Java, to fulfill his field practice at Indonesian Legume and Tuber Crops
Research.

PREFACE
All praise and gratitude for Allah SWT, God of the Universe, for all the blessing and kindness
that made me able to finished my thesis, with the title “A Space-Time Permutation Scan Statistic

for Measles Disease Hotspots Detection in West Java”. There are a lot of knowledge, lessons,
experiences, advices and valuable critics during the process of my research, so hereby I would like
to express my grateful to:
1. Dr. Ir. Asep Saefuddin, M.Sc and Bagus Sartono, M.Si for the early motivation,
discussions, advices, supports, and their great enthusiasm.
2. Lecturers and staffs at Department of Statistics, for the sharing their knowledge and
technical supports.
3. Martin Kulldorff and Ganapati Pawan Patil for their correspondence and supports.
4. My beloved family for the eternal pure loves.
5. Pramesti Puspitasari, untiringly shower me with lots of love and care.
6. The people of Palladium (Rio, Edo, Arif, Yudi, Ipunk, Daus, Bayu), Puri 9 (Meinalisa,
Indri, Dina), and Batosai (Deni, Adit, Agus) who always make me feel welcome.
7. The big family of Department of Statistics.
8. And everyone that helps me in this study, which can not be named personally.
This thesis is not perfect, to make this thesis useful to everybody, I am expecting the critics,
advises, and recommendations to people who read my thesis. Thank You.

Bogor, January 2008

Dani Ardiyanto

CONTENTS
Page
LIST OF TABLES .......................................................................................................................v
LIST OF APPENDICES ..............................................................................................................vi
INTRODUCTION
Background ............................................................................................................................1
Objective ................................................................................................................................1
DEFINITIONS
Measles...................................................................................................................................1
Hotspot ...................................................................................................................................1
Scan Statistic ..........................................................................................................................1
Space-time Permutation Scan Statistic ...................................................................................2
Relative Risk ..........................................................................................................................2
Likelihood Ratio Test .............................................................................................................2
Monte Carlo Hypothesis Testing ............................................................................................3
MATERIALS AND METHODS
Data Sources...........................................................................................................................3
Methods ..................................................................................................................................3
RESULTS AND DISCUSSION

West Java................................................................................................................................4
Detected Hotspots...................................................................................................................4
Significant Hotspots ...............................................................................................................5
CONCLUSION ............................................................................................................................6
SUGGESTIONS ..........................................................................................................................6
REFERENCES.............................................................................................................................7
APPENDICES .............................................................................................................................8

LIST OF TABLES
1.
2.
3.
4.
5.
6.
7.

Page
Top Ten Districts of Measles Case .......................................................................................4
Pearson Correlation of Measles Case 2003 and 2006 ...........................................................4

Description of the Detected Hotspots....................................................................................4
Summary of the First Significant Hotspots ...........................................................................5
Summary of the Second Significant Hotspots.......................................................................5
Summary of the Third Significant Hotspots .........................................................................5
Summary of the Fourth Significant Hotspots........................................................................6

LIST OF APPENDICES
1.
2.
3.
4.
5.

Page
2003 Measles Case Thematic Map .......................................................................................9
2006 Measles Case Thematic Map .......................................................................................9
SaTScan Software Output.....................................................................................................10
Summary of the Detected Clusters........................................................................................15
Map of the Significant Clusters.............................................................................................15

INTRODUCTION

DEFINITIONS

Background

Measles

There is a long history of geographical
surveillance of disease by publishing disease
atlases. If there are areas with exceptionally
high rates, they may give the clues to the
etiology of the disease, indicating areas where
health care needs to be improved, or to be
targeted
for
preventive
measures.
Implementing scan statistic, we can do the
surveillance of particular disease on particular

area. This study applied retrospective spacetime permutation scan statistic to construct
measles disease surveillance in West Java.
According
to
the
World
Health
Organization (WHO), vaccination rate has been
high enough to make measles relatively
uncommon in developed countries, but in
developing countries it is still common.
Globally, measles deaths went down 60
percent, from an estimated 873,000 deaths in
1999 to 345,000 in 2005. Africa has been the
most success area, with annual measles deaths
falling by 75 percent in just 5 years, from an
estimated 506,000 to 126,000 (UNICEF World
Press Release in Wikipedia, 2007).
The ability in detecting measles outbreaks
early is important in order to minimize
morbidity and mortality through timely
implementation of measles prevention and
control measures. A scan statistic can be used
widely in any field to recognize any significant
hotspot in terms to find any spatial areas that
have elevated risk than their surroundings.
In space-time, the scan statistic can provide
early warning of disease outbreaks and can
monitor their spatial spread. This study using a
retrospective space-time permutation scan
statistic for detecting measles disease hotspot
in West Java that utilized only case numbers,
with no need for population-at-risk data, where
these data are very difficult or irrelevant to be
obtained.
This method was applied on annual data of
measles disease cases in West Java in 2003 and
2006 periods.

Measles, also called rubeola, is a highly
contagious - but rare - respiratory infection that
is caused by a virus. It causes a total-body skin
rash and flu-like symptoms, including a fever,
cough, and runny nose.
Measles is spread through respiration
(contact with fluids from an infected person's
nose and mouth, either directly or through
aerosol transmission). About 90% of people
without immunity sharing a house with an
infected person will catch it. Airborne
precautions should be taken for all suspected
cases of measles. The incubation period usually
lasts for 4–12 days (during which there are no
symptoms). Infected people remain contagious
from the appearance of the first symptoms until
3–5 days after the rash appears (Wikipedia,
2007).

Objective
The objective of this study is to detect
measles disease hotspots in West Java in order
to reveal its outbreaks using historical data of
Podes 2003 and 2006, where the detected
hotspots indicated to be taken care due to the
condition of health care and preventive
measures action must be conducted.

Hotspot
Hotspot is defined as something unusual,
anomaly, aberration, outbreak, elevated cluster,
critical area, etc (Patil and Taillie, 2004).
Hotspot clusters were generated by setting
the relative risk in some counties to be larger
than one (Song and Kulldorff, 2003).
Hotspots are locations or regions that have
consistently high levels of disease and may
have
characteristics
unlike
those
of
surrounding areas (Haran, Molineros, & Patil,
2006 in Septiani, 2006).
Scan Statistic
First studied by Naus in 1965, the scan
statistic is an elegant way to solve problems of
multiple testing when there are closely
overlapping spatial areas and/or time intervals
being evaluated. Temporal, spatial, and space–
time scan statistic are now commonly used for
disease cluster detection and evaluation, for a
wide variety of diseases.
The basic idea is that there is a scanning
window that moves across space and/or time.
For each location and size of the window, the
number of observed and expected cases is
counted. Among these, the most “unusual”
excess of observed cases is noted. The
statistical significance of this cluster is then
evaluated taking into account the multiple
testing stemming from the many potential
cluster locations and sizes evaluated (Kulldorff
et al, 2005).

Space-Time Permutation Scan Statistic
The space–time permutation scan statistic
utilizes thousands or millions of overlapping
cylinders to define the scanning window, each
being a possible candidate for an outbreak. The
circular base represents the geographical area
of the potential outbreak.
A typical approach is to first iterate over a
finite number geographical grid points and then
gradually increase the circle radius from zero to
some maximum value defined by the user,
iterating over the areas in the order in which
they enter the circle. In this way, both small
and large circles are considered, all of which
overlap with many other circles.
The height of the cylinder represents the
times. For each center and radius of the circular
cylinder base, the method iterates over all
possible temporal cylinder lengths. This means
that we will evaluate cylinders that are
geographically large and temporally short,
forming a flat disk, those that are
geographically small and temporally long,
forming a pole, and every other combination in
between.
What is new with the space–time
permutation scan statistic is the probability
model. Since we do not have population-at-risk
data, the expected must be calculated using
only the cases. Suppose we have annually case
counts for z areas, where czd is the observed
number of cases in area z during time d. The
total number of observed cases (C) is

C = ∑∑ c zd …(1)
z

d

For each area and time, we calculate the
expected number of cases μzd conditioning on
the observed marginals:

μ zd =

1⎛
⎞
⎞⎛
⎜ ∑ c zd ⎟⎜ ∑ c zd ⎟ …(2)
C⎝ z
⎠⎝ d
⎠

In words, this is the proportion of all cases
that occurred in area z times the total number
of cases during time d. The expected number of
cases μA in a particular cylinder A is the
summation of these expectations over all the
area-time within that cylinder:
μA =
μ zd …(3)

∑

( z , d )∈ A

The
underlying
assumption
when
calculating these expected numbers is that the
probability of a case being in area z, given that
it was observed on time d, is the same for all
times d.
Let cA be the observed number of cases in
the cylinder. Conditioned on the marginals, and

when there is no space–time interaction, cA is
distributed according to the hypergeometric
distribution with mean μA and probability
function (Kulldorff, 2005):

⎛ ∑ c zd ⎞⎛⎜ C − ∑ C zd ⎞⎟
z∈ A
⎜ z∈A ⎟
⎜ c ⎟⎜⎜ ∑ c zd − c A ⎟⎟
⎝ A ⎠⎝ d∈A
⎠ …(4)
P (C A ) =
⎛ C ⎞
⎜
⎟
⎜ ∑ c zd ⎟
⎝ d∈A ⎠

The space-time scan statistic may be used
for either a single retrospective analysis or for
time-periodic prospective surveillance. In a
retrospective analysis, the analysis is done only
once for a fixed geographical region and a
fixed study period, evaluating both ‘alive’
clusters, lasting until the study period and date,
as well as ‘historic clusters’ that ceased to exist
before the study period end date. The
prospective option is used for the early
detection of disease outbreaks, when analyses
are repeated every day, week, month or year.
Only alive clusters, clusters that reach all the
way to current time as defined by the study
period end date, are then searched for.
This study using the retrospective spacetime scan statistic since the research only done
once in West Java Province in 2003 and 2006.
Relative Risk
The relative risk, any non-negative
number, representing how much more common
event (case) is in this location compared to the
baseline. Setting a value of one is equivalent of
not doing any adjustments. A value of greater
than one is used to adjust for an increased risk
and a value of less than one to adjust for lower
risk. A relative risk of zero is used to adjust for
missing data for that particular location.
Relative risk is calculated simply by dividing
observed number to its expected (Kulldorff,
2006).
Likelihood Ratio Test
For each location and size of the scanning
window, the alternative hypothesis is that there
is an elevated risk within the window as
compared to outside. When both

∑c

d∈A

∑c
z∈ A

zd

zd

and

are small compared to C, cA is

approximately Poisson distributed with mean
μA. Based on this approximation, we use the

Poisson generalized likelihood ratio (GLR) as a
measure of the evidence that cylinder A
contains an outbreak:

⎛ cA ⎞
⎟⎟
⎜⎜
⎝ μA ⎠

cA

⎛ C − cA ⎞
⎜⎜
⎟⎟
⎝ C − μA ⎠

(C − c A )

I ( ) …(5)

In words, this is the observed divided by the
expected to the power of the observed inside
the cylinder, multiplied by the observed
divided by the expected to the power of the
observed outside the cylinder. I() is an
indicator function. When the objective of this
study is set to scan only for clusters with high
rates, I() is equal to 1 when the window has
more cases than expected under the nullhypothesis, and 0 otherwise. The opposite is
true when the objective of the study is set to
scan only for clusters with low rates. When the
study scans for clusters with either high or low
rates, then I()=1 for all windows.
The likelihood function is maximized over
all window locations and sizes, and the one
with the maximum likelihood constitutes the
most likely cluster. This is the cluster that is
least likely to have occurred by chance. The
likelihood ratio for this window constitutes the
maximum likelihood ratio test statistic
(Kulldorff, 2006).
Monte Carlo Hypothesis Testing
Once the value of test statistic calculated,
it is easy to do the inference. We cannot expect
to find the distribution of test statistic in closed
analytical form. Instead we rely on Monte
Carlo hypothesis testing.
With Monte Carlo hypothesis test, the
statistical significance of an observed test
statistic calculated from a set of data that
assessed by comparing it with a distribution
obtained by generating alternative set of data
from some assumed model. If the assumed
model implies that all data orderings are
equally likely then this amounts to a
randomization test with random sampling of
the randomization distribution.
Monte Carlo hypothesis testing using in
scan statistic consist of four steps procedure:
1. Calculate the value of the test statistic for
the real data.
2. Create a large number of random data sets
under the null hypothesis.
3. Calculate the value of test statistic for each
random replication.
4. Sort the value of test statistic in step 3
(simulation data), then compare it with the
value of test statistic in step 1 (real data). If

value of test statistic for real data ranked in
the highest α percent of value of test
statistic for simulation data, then reject the
null hypothesis at α percent significance
level.
On the other hand, p-value can be denoted
by p-value = rank /(1 + number of simulation
generated) (Kulldorff, 1999).

MATERIALS AND METHODS
Data Sources
This study used secondary data of measles
disease cases in West Java obtained from 2003
and 2006 of Potensi Desa (Podes) surveys by
Statistics Indonesia.
Methods
During the completion of this study,
several steps were done as mentioned below:
1. Merging the 2003 and 2006 measles case
in West Java districts using SAS 9.1.
2. Generating any possible scan windows
with the maximum spatial cluster size was
10% of population and maximum temporal
cluster size was 1 year.
3. Calculating the relative risk of each
scanned window mentioned on step 2, and
then discarding the window with relative
risk less than 1.
4. Calculating the likelihood function value
of each scanned window obtained at step
3.
5. Obtaining the statistical significant value
for each hotspot candidate using Monte
Carlo simulation with 9999 replications.
6. Interpreting the results and presenting the
hotspot area on West Java map using
MapInfo Professional 7.8 SCP.
This study use SaTScan 7.0 to perform step 2
to 5.
The size of spatial and temporal window
can vary up to 50% of the total study area or
time. Subjectively, the value of the spatial
window was set up to 10% of the total West
Java area and the value of temporal window
was set up to 50% of the total two-year period
of study, 2003 and 2006. Before the value of
the spatial window was set to 10%, this
research had tried the different maximum
spatial windows, of 5%, 15%, 25%, and 50%.
The value of maximum temporal window
cannot be changed, because this research only
involved two points of time.
The maximum spatial and temporal
windows could not exceed 50% of the total

area study, because when it was allowed to
expand more, the likelihood no longer reflects
a cluster of increased disease risk inside, but a
decreased risk outside.

RESULTS AND DISCUSSION
West Java
According to Podes data from Statistic
Indonesia, West Java Province consists of 18
regencies/municipalities, divided into 507
districts in 2003 and 547 districts in 2006. The
observed measles cases in this study period
was 349 and 231 in 2003 and 2006
respectively, thus the total cases is 580 cases. It
means that the case was decreasing between
2003 and 2006, perhaps could be considered as
an indicator that West Java Province carried
out some improvement on public health
service.
The top ten districts on measles case
number could be seen on the Table 1. The
number in parentheses reflects the case of the
corresponding districts. More simultaneously
information about the spread of the measles
case can be reviewed by thematic map at the
Appendix 1 and 2.
Table 1. Top Ten Districts on Measles Case.
No
2003
2006
1 Ciawi Bogor (13)
Cikarang (11)
2
Talaga (11)
Mundu (11)
3 Megamendung(10)
Beber (7)
4
Garutkota (7)
Cisurupan (6)
5
Situraja (7)
Jatitujuh (6)
6
Cibarusah (6)
Bekasi Selatan (5)
7
Cidaun (6)
Cidaun (5)
8
Juntinyuat (6)
Kadungora (5)
9
Krangkeng (6)
Banjarwangi (4)
10
Waled (6)
Cibuaya (4)
The relationship degree of measles case
during two year period in each region of West
Java is shown on the Table 2. This table was
obtained after dividing West Java region into 4
non-overlapping areas and calculating the
Pearson correlation between 2003 and 2006
measles case in each area.
The correlation values were all significant
although the relationship between the 2003 and
2006 measles case data seems too weak,
because the Pearson correlation values tend
close to zero. This means that if there is an
excess measles case in certain area, the chance

of the excess still remains in that area is very
small because the tendency is weak.
Table 2. Pearson Correlation of Measles Case
2003 and 2006.
Area
Correlation P-value
North
0.13
0.050
South
0.17
0.014
West
0.14
0.042
East
0.15
0.028
Overall
0.14
0.003
After doing some adjustment conditioned
on the West Java digital map limitation, the
number of district in the area of study decrease
to only 442 districts. Hence, this study only
search cluster within districts registered on
existing digital map. Using SaTScan software,
the calculations for the retrospective spacetime permutation scan statistic on 800 MHz PC
with 384 MB of RAM took 11 minutes and 15
seconds. The output of the software can be
reviewed at Appendix 3.
Hotspot Candidates
After applying the retrospective space-time
permutation scan statistic with ten percent of
maximum spatial size window and 9999 Monte
Carlo replications, there are twelve measles
disease hotspots detected. All of them have the
relative risk value greater than one since the
objective of the study is to search clusters with
the high rates of measles case. Only four of
them were significant at five percent
significance level. Appendix 4 shows the
summary of these hotspot candidates.
Table 3. Description of Detected Hotspots.
No Time
LLR
P-value
RR
1 2006 5.858477
0.0003 1.98
2 2006 5.102465
0.0017 1.75
3 2006 4.569782
0.0056 1.88
4 2003 3.598986
0.0446 1.55
5 2006 3.308802
0.0788 1.72
6 2003 2.814259
0.2165 1.44
7 2003 2.436417
0.448 1.44
8 2003 1.528149
0.9865 1.57
9 2006 1.434325
0.992 1.79
10 2006 1.395643
0.9964 2.15
11 2006
1.28056
0.9993 2.51
12 2006
1.28056
0.9993 2.51

Significant Hotspots
From twelve detected hotspots with high
rates of measles case, only four of them were
significant at five percent significance level.
Three of them happened in 2006 time frame.
The first significant hotspot located in
Cirebon with radius 11.77 kilometers, and
contains 15 districts. The number of observed
case in this cluster was 1.98 times higher than
the expected. It means that the risk of a case
within this cluster is 1.98 times higher than the
risk the outside. The cases increase from 8 in
2003 to 30 in 2006, and the correlation was
0.36. The correlation p-value indicates that
there was no correlation between 2003 and
2006 measles data within this cluster, on the
other words there was no linear relationship
between them.
Having highest value of log likelihood
ratio among all, this cluster made itself to be
the most significant, so called the most likely
cluster. This cluster always has the highest test
statistic and hence, the smallest p-value. All
clusters excluding the most likely cluster
considered as the secondary clusters. The
summary of the Hotspot 1 can be reviewed on
Table 4.
Table 4. Summary of the first significant
hotspot.
6.7195 S, 108.4952 E
Coordinates
11.77 km
Radius
15
# district
2006/1/1 - 2006/12/31
Time frame
30
Number of cases
15.13
Expected cases
1.982
Observed/expected
5.858477
Test statistic
3/10000
Monte Carlo rank
0.0003
P-value
8
Case 2003
30
Case 2006
0.365962527
Correlation
0.18
Correlation p-value
The second significant hotspot located in
Bekasi. The observed measles case in 2006 was
37, meanwhile the expected was 21.11. This
number shows that in this cluster has the
observed case 1.75 times higher than expected.
The number of district in this cluster was 28,
spread across 34.76 kilometers from the cluster
centroid. The relationship between 2003 and
2006 measles case data within this cluster
seems to be strong. It can be seen from the

correlation value, this value was significant,
rejects the null hypothesis of no correlation. It
means the districts inside this cluster might
have constant increase or growth of measles
case from year to year, since the correlation
value was positive. The relationship showed by
the correlation value might be interest to be
examined in further study. The simple review
of hotspot 2 can be found on the Table 5.
Table 5. Summary of the second significant
hotspot.
6.1215 S, 107.0348 E
Coordinates
34.76 km
Radius
28
# district
2006/1/1 - 2006/12/31
Time frame
37
Number of cases
21.11
Expected cases
1.753
Observed/expected
5.102465
Test statistic
17/10000
Monte Carlo rank
0.0017
P-value
16
Case 2003
37
Case 2006
0.616517601
Correlation
0.000
Correlation p-value
The third significant hotspot located in
Western Bandung, The observed case higher
1.88 times than its expected, constitutes the
relative risk of the cluster. This cluster paced in
the top 56 from 9999 Monte Carlo replications,
make it significant with p-value 56/(9999+1) or
0.0056. In 2006, the case was 27, higher than
the case in 2003. It made this cluster occurs in
2006 time frame. The summary of this cluster
depicted on the Table 6.
Table 6. Summary of the third significant
hotspot.
6.8404 S, 107.2244 E
Coordinates
31.13 km
Radius
30
# district
2006/1/1 - 2006/12/31
Time frame
27
Number of cases
14.34
Expected cases
1.883
Observed/expected
4.569782
Test statistic
56/10000
Monte Carlo rank
0.0056
P-value
9
Case 2003
27
Case 2006
0.162724749
Correlation
0.39
Correlation p-value

The only 2003 significant hotspot detected
was located in Bogor, with radius 18.91
kilometers from the centroid and there are 17
districts inside this cluster. The observed
measles case was 41 meanwhile the expected
was 26.48. It means the risk of measles cases
being in this cluster higher 1.55 times
compared to the outside. The test statistic
obtained from the log value of equation (5),
assumed Poisson distributed. The higher the
value, the stronger he evidence that the data
gives clue of rejecting the null hypothesis that
are no elevated risk within the cluster. The
statistics of this cluster showed on the Table 7.
Table 7. Summary of the fourth significant
hotspot.
6.7697 S, 106.7848 E
Coordinates
18.91 km
Radius
17
# district
2003/1/1 - 2003/12/31
Time frame
41
Number of cases
26.48
Expected cases
1.549
Observed/expected
3.598986
Test statistic
446/10000
Monte Carlo rank
0.0446
P-value
41
Case 2003
3
Case 2006
-0.102210004
Correlation
0.696
Correlation p-value
That’s all significant hotspot obtained by
the retrospective space-time permutation scan
statistic. The hotspot always happens in the
frame time when the cluster has the higher
case. This is because the concern of this study
is to find hotspot with high rates of measles
disease case. And hence, the value of indicator
function in equation (5) sets to 1 only if the
relative risk value greater than 1. In other
words, the observed value is higher than its
expected, indicates the excess of case within
the cluster.
The map of the significant clusters
depicted on Appendix 5. Note that the
significant clusters are not perfect circles even
though we used a circular window. This is
because the data are aggregated to the district
level, so that all of a district is considered to be
within the window when the centroid is, and
vice versa. The only way to obtain perfect
circles is to have non-aggregated data.
Besides the circular windows used in scan
statistic, there is also an ellipses scan windows,
depends on the aim of the study. The

permutation scan statistic did not require the
population data, so it is an advantage if this
method applied in developing countries where
the population data may be difficult to obtain
or the quality is poor. If the population data is
available, the common scan statistic might be
applied, because the added information of the
population data could made the hotspot results
more reliable.

CONCLUSION
The space-time permutation scan statistic
is a method to detects aberration, anomaly, or
something unusual in some area comparing
with it surroundings. This method not only
detects where the cluster occurs, but also when
it happens. Since cylinders used as the window
scan, the hotspot obtained from this method
also approximately circular.
The space-time scan statistic is defined
trough a huge number of overlapping cylinders.
For each cylinder, a log likelihood ratio (LLR)
is calculated, and the test statistic is defined as
the maximum LLR over all cylinders. Once the
test statistic has been calculated, the next step
is to evaluate its statistical significance by
generating a large number of random data sets
under the null hypothesis of no clustering, and
then calculating the value of the test statistic
for each of those data sets as well.
After applying space-time permutation
scan statistic on West Java measles case data,
there are twelve detected hotspot using this
method which only four of them were
significant at five percent significance level.
Three of them happen in 2006, located in
Cirebon, Bekasi, and Western Bandung. The
fourth hotspot that still significant happens in
2003, located in Bogor.

SUGGESTIONS
In order to make the space-time
permutation scan statistic as an important tool
for local and national health departments that
are need a disease detection surveillance
system, the study times and the locations must
be widened.

REFERENCES
Kulldorff, M., and Nagarwalla, N. (1995).
Spatial Disease Clusters: Detection and
Inference. Statistic in Medicine 14, 799810.
Kulldorff, M. (1997). A spatial scan statistic.
Communications in Statistic: A Theory
Methods 26, 1481–1496.
Kulldorff, M. (1998). Evaluating Cluster
Alarms: A Space-Time Scan Statistic and
Brain Cancer in Los Alamos, New
Mexico. American Journal of Public
Health 88, 1377-1380.
Kulldorff, M. (1999). Spatial Scan Statistic:
Models, Calculations, and Applications.
p.303-322. Birkhauser.
Kulldorff, M. (2006). SaTScanTM User Guide
for version 7.0. http://www.satscan.org/
Kulldorff, M., Heffernan, R., Hartman,
J., Assunção, R., and Mostashari, F.

(2005). A Space–Time Permutation Scan
Statistic for Disease Outbreak Detection.
PLoS Medicine 2, 216-224.
Patil, G.P., and Taillie, C. (2004). Upper
Level Set Scan Statistic for Detecting
Arbitrarily
Shaped
Hotspots.
Environmental and Ecological Statistic 11,
183-197.
Septiani, D. (2006). A Flexibly Shaped Spatial
Scan Statistic for Detecting Poverty
Hotspots. Department of Statistics,
Mathematics and Natural Science Faculty,
Bogor Agricultural University. [Thesis]
Song, C., and Kulldorff, M. (2003). Power
Evaluation of Disease Clustering Tests.
International
Journal
of
Health
Geographics 2, 9.
Measles.
Wikipedia.
(2007).
http://en.wikipedia.org/wiki/Measles.
[June 24th, 2007]

APPENDICES

Appendix 1. A thematic map of West Java measles disease case in 2003

Appendix 2. A thematic map of West Java measles disease case in 2006

Appendix 3. The output from SaTScan software
_____________________________
SaTScan v7.0.3
_____________________________

Program run on: Thu Oct 04 00:27:46 2007
Retrospective Space-Time analysis
scanning for clusters with high rates
using the Space-Time Permutation model.
________________________________________________________________
SUMMARY OF DATA
Study period.............: 2003/1/1 - 2006/12/31
Number of locations......: 442
Total number of cases....: 580
________________________________________________________________
MOST LIKELY CLUSTER
1.Location IDs included.: weru, plumbon, cirebonselatan,
klangenan, cirebonutara, kesambi,
harjamukti, kejaksan, sumber,
pekalipan, lemahwungkuk, palimanan,
mundu, arjawinangun, beber
Coordinates / radius..: (6.719500 S, 108.495200 E) / 11.77 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 30
Expected cases........: 15.13
Observed / expected...: 1.982
Test statistic........: 5.858477
Monte Carlo rank......: 3/10000
P-value...............: 0.0003
SECONDARY CLUSTERS
2.Location IDs included.: babelan, tarumajaya, tembelang,
bekasiutara, cabangbungin,
bekasibarat, tambun, muaragembong,
bekasiselatan, bekasitimur,
sukatanibekasi, cibitung, pakisjaya,
cikarang, batujaya, jatiasih,
bantargebang, pebayuran, tirtajaya,
pondokgede, kedungwaringin, setu,
rengasdengklok, serang, gunungputri,
kutawaluya, cibuaya, telukjambe
Coordinates / radius..: (6.121500 S, 107.034800 E) / 34.76 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 37
Expected cases........: 21.11
Observed / expected...: 1.753
Test statistic........: 5.102465
Monte Carlo rank......: 17/10000
P-value...............: 0.0017

3.Location IDs included.: sukaluyu, karangtengah, ciranjang,
bojongpicung, cilaku, mande, cianjur,
cibeber, cipeundeuybandung,
cikalongkulon, cugenang,
warungkondang, sukaresmi, cipatat,
cipongkor, gununghalu, maniis,
campakamulya, pacetcianjur,
sukarajasukabumi, batujajar,
tegalwaru, plered, cikalongwetan,
padalarang, gegerbitung, cililin,
sukabumi, darangdan, sindangkerta
Coordinates / radius..: (6.840400 S, 107.224400 E) / 31.13 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 27
Expected cases........: 14.34
Observed / expected...: 1.883
Test statistic........: 4.569782
Monte Carlo rank......: 56/10000
P-value...............: 0.0056
4.Location IDs included.: cicurug, cidahusukabumi, cijeruk,
caringin, nagrak, parungkuda,
parakansalak, ciawibogor, cibadak,
ciomas, kalapanunggal, pamijahan,
bogorselatan, kadudampit, megamendung,
bogortimur, cisaruabogor
Coordinates / radius..: (6.769700 S, 106.784800 E) / 18.91 km
Time frame............: 2003/1/1 - 2003/12/31
Number of cases.......: 41
Expected cases........: 26.48
Observed / expected...: 1.549
Test statistic........: 3.598986
Monte Carlo rank......: 446/10000
P-value...............: 0.0446
5.Location IDs included.: ibun, pasehbandung, samarang,
pacetbandung, majalaya, leles,
cikancung, ciparay, kadungora,
tarogong, arjasari, rancaekek,
kertasari, banyuresmi, cicalengka,
bojongsoang, cisurupan, leuwigoong,
baleendah, cibiuk
Coordinates / radius..: (7.118200 S, 107.765200 E) / 19.49 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 26
Expected cases........: 15.13
Observed / expected...: 1.718
Test statistic........: 3.308802
Monte Carlo rank......: 788/10000
P-value...............: 0.0788
6.Location IDs included.: cikatomas, pancatengah, salopa,
cigugurciamis, cikalong,
cibalongtasik, karangnunggal, cimerak,
cijulang, sukarajatasikmalaya,
bantarkalong, langkaplancar, cineam,
manonjaya, cidologciamis, parigi,
cibeureum, kawalu, tanjungjaya,

cipatujah, tawang, cimaragas,
singaparna, cihideung, bojonggambir,
pamarican, cipedes, sidanulih, ciamis,
taraju, banjar, cijeungjing,
banjarsari, cikoneng, indihiang,
salawu, leuwisari, sadananya,
peundeuy, pataruman, pangandaran
Coordinates / radius..: (7.621300 S, 108.273200 E) / 41.84 km
Time frame............: 2003/1/1 - 2003/12/31
Number of cases.......: 45
Expected cases........: 31.29
Observed / expected...: 1.438
Test statistic........: 2.814259
Monte Carlo rank......: 2165/10000
P-value...............: 0.2165
7.Location IDs included.: bantarujeg, lemahsugih, talaga, maja,
cikijing, wado, argapura, panjalu,
panumbangan, darma, majalengka,
pagerageung, panawangan, cigasong,
kadugede, kawali, sukahaji,
cigugurkuningan, malangbong,
rajagaluh, panyingkiran, ciawitasik,
pasawahankuningan, ciniru, selajambe,
kramatmulya, kuningan, sindangwangi,
darmaraja, cibugel, tomo, jamanis,
jatinagara, cihaurbeuti, mandirancan,
jatiwangi, dawuhan, rajapolah,
kadipaten, jalaksana, situraja,
garawangi, palasah, cilimus, rajadesa,
leuwimunding
Coordinates / radius..: (6.990800 S, 108.266500 E) / 29.76 km
Time frame............: 2003/1/1 - 2003/12/31
Number of cases.......: 39
Expected cases........: 27.08
Observed / expected...: 1.440
Test statistic........: 2.436417
Monte Carlo rank......: 4480/10000
P-value...............: 0.4480
8.Location IDs included.: tirtamulya, lemahabangkarawang,
cikampek, klari, talagasari, jatisari,
karawang, rawamerta, ciampel,
cilamaya, tempuran
Coordinates / radius..: (6.318100 S, 107.443700 E) / 17.47 km
Time frame............: 2003/1/1 - 2003/12/31
Number of cases.......: 17
Expected cases........: 10.83
Observed / expected...: 1.570
Test statistic........: 1.528149
Monte Carlo rank......: 9865/10000
P-value...............: 0.9865
9.Location IDs included.: kertajati, ujungjaya, cikedung,
jatitujuh, conggeang
Coordinates / radius..: (6.646300 S, 108.127100 E) / 12.61 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 10

Expected cases........: 5.58
Observed / expected...: 1.793
Test statistic........: 1.434325
Monte Carlo rank......: 9920/10000
P-value...............: 0.9920
10.Location IDs included.: nanggung, leuwiliang, cigudeg
Coordinates / radius..: (6.663600 S, 106.554800 E) / 10.30 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 6
Expected cases........: 2.79
Observed / expected...: 2.152
Test statistic........: 1.395643
Monte Carlo rank......: 9964/10000
P-value...............: 0.9964
11.Location IDs included.: banjarwangi
Coordinates / radius..: (7.411100 S, 107.875800 E) / 0.00 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 4
Expected cases........: 1.59
Observed / expected...: 2.511
Test statistic........: 1.280560
Monte Carlo rank......: 9993/10000
P-value...............: 0.9993
12.Location IDs included.: tanjungsari, rancakalong, cimanggu,
cileungkrang
Coordinates / radius..: (6.868400 S, 107.809800 E) / 10.29 km
Time frame............: 2006/1/1 - 2006/12/31
Number of cases.......: 4
Expected cases........: 1.59
Observed / expected...: 2.511
Test statistic........: 1.280560
Monte Carlo rank......: 9993/10000
P-value...............: 0.9993
________________________________________________________________
PARAMETER SETTINGS
Input
----Case File
: C:\Documents and Settings\dani\Desktop\RUN!!!\campak\kasuscampak.cas
Coordinates File : C:\Documents and
Settings\dani\Desktop\RUN!!!\campak\koordinatkecamatan.geo
Time Precision : Year
Start Date
: 2003/1/1
End Date
: 2006/12/31
Coordinates
: Latitude/Longitude
Analysis
-------Type of Analysis
Probability Model
Scan for Areas with

: Retrospective Space-Time
: Space-Time Permutation
: High Rates

Time Aggregation Units : Year

Time Aggregation Length : 1
Number of Replications : 9999
Output
-----Results File
: C:\Documents and Settings\dani\Desktop\RUN!!!\campak\retro10.txt
Cluster File
: C:\Documents and Settings\dani\Desktop\RUN!!!\campak\retro10.col.txt
Cluster Case File : C:\Documents and Settings\dani\Desktop\RUN!!!\campak\retro10.cci.txt
Location File
: C:\Documents and Settings\dani\Desktop\RUN!!!\campak\retro10.gis.txt
Simulated LLRs File : C:\Documents and Settings\dani\Desktop\RUN!!!\campak\retro10.llr.txt
Data Checking
------------Study Period Check
: Check to ensure that cases and controls are within the Study Period.
Geographical Coordinates Check : Check to ensure that all locations in the case, control
and population files are present in the coordinates file.
Neighbors File
-------------Use Neighbors File : No
Spatial Window
-------------Maximum Spatial Cluster Size
: 10% of population at risk
Window Shape
: Circular
Temporal Window
--------------Maximum Temporal Cluster Size

: 50% of study period

Inference
--------Early Termination
: No
Report Critical Values
: No
Iterative Scan
: No
Clusters Reported
----------------Criteria for Reporting Secondary Clusters : No Geographical Overlap
Run Options
----------Processer Usage : All Available Proccessors
Logging Analysis : Yes
Suppress Warnings : No
________________________________________________________________
Program completed : Thu Oct 04 00:39:01 2007
Total Running Time : 11 minutes 15 seconds

Appendix 4. Summary of the clusters detected by using space-time permutation scan statistic
No
Location
Diameter Time Members LLR
P-Value Obs Exp
1 Weru
11.77 2006
15 5.85848
0.0003
30 15.13
2 Babelan
34.76 2006
28 5.10247
0.0017
37 21.11
3 Sukaluyu
31.13 2006
30 4.56978
0.0056
27 14.34
4 Cicurug
18.91 2003
17 3.59899
0.0446
41 26.48
5 Ibun
19.49 2006
20 3.30880
0.0788
26 15.13
6 Cikatomas
41.84 2003
41 2.81426
0.2165
45 31.29
7 Bantarujeg
29.76 2003
46 2.43642
0.4480
39 27.08
8 Tirtamulya
17.47 2003
11 1.52815
0.9865
17 10.83
9 Kertajati
12.61 2006
5 1.43433
0.9920
10
5.58
10 Nanggung
10.30 2006
3 1.39564
0.9964
6
2.79
11 Banjarwangi
0.00 2006
1 1.28056
0.9993
4
1.59
12 Tanjungsari
10.29 2006
4 1.28056
0.9993
4
1.59
Appendix 5. The significant clusters of measles disease in 2003 (blue) and 2006 (red)

RR
1.98
1.75
1.88
1.55
1.72
1.44
1.44
1.57
1.79
2.15
2.51
2.51

A SPACE-TIME PERMUTATION SCAN STATISTIC
FOR MEASLES DISEASE HOTSPOTS DETECTION IN WEST JAVA

DANI ARDIYANTO

DEPARTMENT OF STATISTICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCES
BOGOR AGRICULTURAL UNIVERSITY
2008

INTRODUCTION

DEFINITIONS

Background

Measles

There is a long history of geographical
surveillance of disease by publishing disease
atlases. If there are areas with exceptionally
high rates, they may give the clues to the
etiology of the disease, indicating areas where
health care needs to be improved, or to be
targeted
for
preventive
measures.
Implementing scan statistic, we can do the
surveillance of particular disease on particular
area. This study applied retrospective spacetime permutation scan statistic to construct
measles disease surveillance in West Java.
According
to
the
World
Health
Organization (WHO), vaccination rate has been
high enough to make measles relatively
uncommon in developed countries, but in
developing countries it is still common.
Globally, measles deaths went down 60
percent, from an estimated 873,000 deaths in
1999 to 345,000 in 2005. Africa has been the
most success area, with annual measles deaths
falling by 75 percent in just 5 years, from an
estimated 506,000 to 126,000 (UNICEF World
Press Release in Wikipedia, 2007).
The ability in detecting measles outbreaks
early is important in order to minimize
morbidity and mortality through timely
implementation of measles prevention and
control measures. A scan statistic can be used
widely in any field to recognize any significant
hotspot in terms to find any spatial areas that
have elevated risk than their surroundings.
In space-time, the scan statistic can provide
early warning of disease outbreaks and can
monitor their spatial spread. This study using a
retrospective space-time permutation scan
statistic for detecting measles disease hotspot
in West Java that utilized only case numbers,
with no need for population-at-risk data, where
these data are very difficult or irrelevant to be
obtained.
This method was applied on annual data of
measles disease cases in West Java in 2003 and
2006 periods.

Measles, also called rubeola, is a highly
contagious - but rare - respiratory infection that
is caused by a virus. It causes a total-body skin
rash and flu-like symptoms, including a fever,
cough, and runny nose.
Measles is spread through respiration
(contact with fluids from an infected person's
nose and mouth, either directly or through
aerosol transmission). About 90% of people
without immunity sharing a house with an
infected person will catch it. Airborne
precautions should be taken for all suspected
cases of measles. The incubation period usually
lasts for 4–12 days (during which there are no
symptoms). Infected people remain contagious
from the appearance of the first symptoms until
3–5 days after the rash appears (Wikipedia,
2007).

Objective
The objective of this study is to detect
measles disease hotspots in West Java in order
to reveal its outbreaks using historical data of
Podes 2003 and 2006, where the detected
hotspots indicated to be taken care due to the
condition of health care and preventive
measures action must be conducted.

Hotspot
Hotspot is defined as something unusual,
anomaly, aberration, outbreak, elevated cluster,
critical area, etc (Patil and Taillie, 2004).
Hotspot clusters were generated by setting
the relative risk in some counties to be larger
than one (Song and Kulldorff, 2003).
Hotspots are locations or regions that have
consistently high levels of disease and may
have
characteristics
unlike
those
of
surrounding areas (Haran, Molineros, & Patil,
2006 in Septiani, 2006).
Scan Statistic
First studied by Naus in 1965, the scan
statistic is an elegant way to solve problems of
multiple testing when there are closely
overlapping spatial areas and/or time intervals
being evaluated. Temporal, spatial, and space–
time scan statistic are now c