=Paper=
{{Paper
|id=None
|storemode=property
|title=On Estimation of the Spatial Clustering: Case Study of Epidemiological Data In Olomouc Region, Czech Republic
|pdfUrl=https://ceur-ws.org/Vol-971/paper10.pdf
|volume=Vol-971
|dblpUrl=https://dblp.org/rec/conf/dateso/MarekPDT13
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==On Estimation of the Spatial Clustering: Case Study of Epidemiological Data In Olomouc Region, Czech Republic==
https://ceur-ws.org/Vol-971/paper10.pdf
On Estimation
On Estimation of of
thethe
Spatial Clustering:
Spatial Case Study
Clustering: Caseof
Epidemiological
Study Data In Olomouc
of Epidemiological DataRegion, Czech
In Olomouc
Region, Republic
Czech Republic
Lukáš Marek1, Vít Pászto1, Jiří Dvorský1, Pavel Tuček1
Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
1
Department of Geoinformatics, Faculty of Science, Palacky University in Olomouc, 17.
Department of Geoinformatics, Faculty of771
listopadu 50, Olomouc, Science, Palacky
46, Czech University in Olomouc
Republic
17. listopadu
{lukas.marek, 50, Olomouc, 771 46, Czech
pavel.tucek}@upol.cz, Republic
vit.paszto@gmail.com,
{lukas.marek, pavel.tucek}@upol.cz,
jiri.dvorsky@vsb.cz vit.paszto@gmail.com,
http://www.geoinformatics.upol.cz/
jiri.dvorsky@vsb.cz
Abstract. An evaluation of spatial patterns and a clustering play an important
role among methods of spatial statistics. However, traditional clustering
techniques are seldom suitable for analyses of spatial data and patterns because
they usually do not count on spatial relations and qualities of objects. This
paper aims to introduce usage of methods of spatial clustering estimation,
which are based mainly on the position of events and not only on the events
attribute space. Firstly, the methods of the spatial clustering or randomness
estimation are introduced and applied on a real dataset, then spatial clusters are
identified and the intensity of processes is quantified. Non-spatial properties
and a time are considered together with the location data. Also methods of the
multivariate statistics are used for the purpose of the classification of regions
with similar properties. Particularly, occurrence data of selected infectious
diseases in Olomouc Region in period 2004 – 2010 provided by Regional
Public Health Service in Olomouc are used for the case study.
1 Introduction
An application of the geographical information system, as well as a spatial statistics,
for the exploration of the spatial pattern of health data has been highly discussed in
the literature [2, 14, 18] and it is one of top topics in geosciences nowadays [5]. The
literature also often uses phrases geographical epidemiology, spatial epidemiology,
medical geography or even geomedicine that describe dynamic body of the theory
and analytic methods concerned with the study of spatial patterns of the disease
incidence and mortality [22]. Since John Snow’s famous geographical study of the
cholera in London in 1854 century, the interconnection of health data and analyses of
spatial patterns became a standard procedure. Possibilities of current geographical
information systems together with properties of databases, where health and
epidemiological data are stored, make spatial evaluation easier than anytime before
[13].
This contribution presents the usage of methods of spatial statistics applied on the
epidemiological data from Olomouc region – one of administrative units of Czech
V. Snášel, K. Richta, J. Pokorný (Eds.): Dateso 2013, pp. 1–12, ISBN 978-80-248-2968-5.
2 Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
Republic corresponding with NUTS3. Cases of one particular infectious disease –
parotitis - are assessed within the period 2004-2010. Records about infection come
from the database of infectious diseases, which is called EPIDAT. This database
contains information about every single case of the infection which is reported by
local doctors. EPIDAT also contains data about infected patients as the place of
residence, the place of infecting, the time of treatment, the way of isolation etc.
Although exact addresses of patients are reported, due to the necessity of preserving
anonymity only approximate addresses are provided. That is why the exact geocoding
is unfeasible and all records are aggregated into the regular fishnet or randomized
within it.
2 Case study and Data
This section intents to describe data and their adjustment for the usage within
techniques of Exploratory Spatial Data Analysis (ESDA) and Local Indicators of
Spatial Association. Epidemiological data comes from the EPIDAT (EPIdemiological
DATabase), which stores mandatory records about all infectious diseases in the
Czechia. The case study is dealing mainly with spatial attributes of one selected
disease – parotitis (i.e. mumps). Firstly, geocoded data are visualized in the form of
(false) choropleth maps. Choropleth maps [12] allows to the researcher first, so
called, “visual” analysis of spatial structure. Then quantitative analyses of
possibilities of spatial clustering are proceeding – a kernel density estimation and G-
function [3]. At last, data are aggregated and randomized into the regular hexagonal
fishnet and spatial autocorrelation in local scale is explored using Moran’s I, Getis
Ord General G and LISA, which are comprehensively described in [1, 10]. Software
tools used for the realization of case study was ArcGIS (choropleth maps, LISA) and
R-project with packages for the spatial statistics, manipulating with spatial data and
the visualization (spatstat, maptools, spdep, etc.).
The analyzed disease is a parotitis. Parotitis is an inflammation of one or both
parotid glands, the major salivary glands located on either side of the face, in humans.
The parotid gland is the salivary gland most commonly affected by an inflammation.
The Mumps is an airborne virus and can be spread by an infected person coughing or
sneezing and releasing tiny droplets of contaminated saliva, an infected person
touching their nose or mouth, then transferring the virus onto an object, or sharing
utensils [17]. Routine vaccinations have dropped the incidence of mumps to a very
low level [15].
2.1 Data
The EPIDAT database is used to ensure the mandatory reporting, recording and
analysis of infectious diseases in the Czech Republic. The database is used nation-
widely by Public Health Service of the Czech Republic from 1st January 1993. The
reporting of infectious diseases is the legal basis for local, regional, national and
international control of infectious diseases (EU, WHO). The data storage is used to
On Estimation of the Spatial Clustering 3
secure exchange of actual data sets on the prevalence of infections among the
departments of Public Health Service of CR, Ministry of Health of CR and Public
Health Institute in Prague.
Total of 53 diagnoses of infectious diseases are monitored into the EPIDAT
database. Each record contains 50 attributes. In terms of spatial analyses, the most
important properties are information about the patient's residence as well as the place
of infection and the place of sicken (the place where the patient became ill, often
place of clinic or doctor's office).
The data set for this study was provided by the Regional Public Health Service in
Olomouc. The original provided dataset contains 32 698 records of 11 selected
infections from 53 diagnoses and covers the period 2004-2010, but only 958 records
of one selected disease – parotitis. Because it is treated with sensitive personal data,
the name, surname, identity number and full address is not included. Furthermore,
geocoded data were randomized and anonymized using aggregation from the street
network and municipality membership into the regular hexagonal fishnet, which is
usual procedure in spatial epidemiology and econometrics [10]. The problem of
aggregating the point based spatial phenomena into the district is well known as
MAUP – Modifiable Area Unit Problem.
EPIDAT database is filled with data manually and it is a transcription of medical
records. That situation guarantees the occurrence of errors, mistyped characters and
different kinds of used abbreviations. A manual control and subsequent correction of
mistakes could be time consuming and almost impossible because of the amount of
records in database. That is why a tool for semi-automatic control, repairing and
geocoding was developed as the result of collaboration between Department of
Geoinformatics and Regional Public Health Service in Olomouc. Owing to this tool,
whole process of repairing wrong records is time acceptable. Besides using our
developed tool, the Google Geocoding API is used for geocoding addresses. Google
Geocoding API substitutes the physical ownership of complete street data and the
database of addresses and allows to geolocate with a suitable precision [23]. The
process of geocoding of 32 698 addresses took 49 469 seconds (13.75 hours).
Several requisite steps have been done before any global or local analyses were
executed. Firstly the data of selected infection diseases, as well as complete data,
were randomized and aggregated into the regular hexagonal fishnet. Each hexagon
has the area of 6.25 km2, which is similar to the area of the cell established by
Morishita index [16] and coincidentally, it is corresponding to the area of the average
cadastral unit in the region. A number of inhabitants in hexagons was estimated from
cadastral units and municipalities with usage of the areal weighting. Both, absolute
and relative (prevalence on 1000 population) aggregation units were created but only
the absolute occurrence entered the analysis. Secondly, spatial weight matrices were
generated for each input of the disease. K-nearest neighbors method, with K = 12,
was selected as the way of the spatial conceptualization, the other way is an
assessment of the maximum threshold (distance) of possible connections among
cases. The example of the spatial weight matrix is shown in the Figure 1.
4 Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
Fig. 1. The example of the generated spatial weight matrix. Points represent pseudo-
randomized cases of the disease. Lines symbolize links among points, each case is connected
to 12 other points / neighbors without taking into consideration of the distance
3 Methods
Analyses of spatial pattern of diseases occurrence, as well as their relations to
potentially risk factors of the environment, are important parts of health studies.
According to [7] three main broad areas of spatial epidemiology can be identified:
- disease mapping,
- geographic correlation studies,
- clustering, disease clusters, and surveillance.
The presented study is mainly focused on methods of the estimation and
assessment of a spatial clustering as well as a multivariate clustering. Firstly,
choropleth maps were constructed. Subsequently, the methods of the spatial
clustering or randomness estimation were applied on the dataset and then spatial
clusters are identified and the intensity of processes is quantified. Finally, the
multivariate statistical clustering is executed, which extends the previously proceeded
analyses.
Methods, which are introduced and described later in this chapter, are often
covered by a common name Exploratory Data Analysis (EDA). This label
On Estimation of the Spatial Clustering 5
incorporates a wide group of statistical techniques that are very useful for both, an
initial and deeper exploration of patterns and relations within the given data structure.
In case of involving spatial metrics, the group of methods is called Exploratory
Spatial Data Analysis (ESDA). The list of methods presented below in the text is not
a complete enumeration, but only a brief overview of elementary techniques
applicable to the problems and questions connected to the geographical space. It is
worth to note, that most of E(S)DA methods are traditional techniques with basis in
last century, but the progress in the (geographical) information science allows their
wider usage.
3.1 Choropleth maps
Choropleth maps are probably the most common type of map for the display of areal
data. These maps use different color and pattern combinations to depict different
values of the attribute variable associated with each area, which is colored according
to the category to which its corresponding attribute value belongs [22]. Although
choropleth maps do not show continuously distributed values, they often portray
densities [19]. Viewed in this way, one can consider them as a primitive visual tool
for the analysis of spatial distribution of phenomenon.
3.2 Identification of Spatial Processes
A huge amount of methods for the estimation of the prevalent type of processes in the
area are based on the testing of Complete Spatial Randomness (CSR) [6], the visual
comparison of the plotted function with CSR or quadrat counts. E.g. quadrat test, G-
function, K-function or Morishita index and Fry plot belong among these methods.
Other suitable method is then a density kernel. It is appropriate to mention that the
identification of spatial processes with the usage of previously presented methods is
based mainly on the location of disease cases.
The evaluation of the spatial pattern of parotitis in this paper is realized by the plot
of Morishita index and assesment of G-function. Morishita defined an index of spatial
aggregation for a spatial point pattern based on quadrat counts. The spatial domain of
the point pattern is first divided into Q subsets (quadrats) of equal size and shape
[16]. The number of points falling in each quadrat is counted. If the pattern is
completely random, index should be approximately equal to 1; values greater than 1
suggest clustering. Morishita plot is also helpful with an assessment of distances
within clusters and also with the estimation of the pixel size or aggregating units in
case of anonymization, for which the method of searching for the break point of the
biggest change, so-called “elbow” method, is used.
G-function is the nearest neighbour distance distribution function (i.e. empirical
cumulative distribution function of nearest neighbours). The shape of plotted G
function is usually compared with the simulated envelope of random processes. This
comparison allows unhiding the type of the possible spatial pattern. If the curve of G
function takes place above the CSR envelope, then clustering is assumed. Its position
6 Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
below the envelope means regular patterns and the position within the envelope refers
to the random pattern [3].
3.3 Global and Local Spatial Clustering
Spatial autocorrelation is the correlation among values of a single variable strictly
attributable to their relatively close locations on a two-dimensional (2-D) surface,
introducing a deviation from the independent observations assumption of classical
statistics [9]. Tobler’s first law of geography encapsulates this situation, “everything
is related to everything else, but near things are more related than distant things”.
The positive spatial autocorrelation refers to patterns where nearby or neighboring
values are more alike; while the negative spatial autocorrelation refers to the patterns
where nearby or neighboring values are dissimilar. One can distinguish two main
types of spatial autocorrelation, which are global and local autocorrelation.
These techniques are collectively denoted as Exploratory Spatial Data Analysis
(ESDA) and Local Indicators of Spatial Association (LISA), which are widely spread
in geosciences and GIS software. Comprehensive description of theory, as well as
detail examples of usage, can provide e.g. [1] or [10].
3.4 Multivariate Clustering
While the spatial clustering creates groups, which are based mainly on the similar
location or the location and one common characteristic, methods of the multivariate
statistics deals with an inverse situation. Thus, an aim of multivariate clustering is to
categorize set of object with the emphasis on their quantitative and/or qualitative
characteristics but mostly without implementing spatial dependencies [20], albeit
several attempts for the combination of both approaches have appeared in recent
years [4, 11].
For the purpose of this study, several methods of multivariate clustering, which
were evaluated as the most suitable by simulations, were performed. Firstly, the
similarity among all cases of parotitis through time is evaluated using the hierarchical
clustering method with average linkage based on the Sokal-Michener dissimilarity
distance measure for nominal variables [21]. Then similarity among hexagonal areas
with aggregated values is calculated using Partitioning Around Medoids (pam)
clustering algorithm based on the squared Euclidean dissimilarity distance measure.
Moreover, DBSCAN algorithm - A Density-Based Algorithm for Discovering
Clusters in Large Spatial Databases with Noise [8] – enables a different approach to
the estimation of clusters, which is based on the internal density of clusters and is
highly suitable for the usage with spatial database. The algorithm provides results,
which are visually similar to the density kernel in case of incorporating simple
locations. But it is more efficient in minimal requirements of domain knowledge to
determine the input parameters, discovery of clusters with arbitrary shape and good
efficiency on large databases [8].
On Estimation of the Spatial Clustering 7
4 Results
Two choropleth maps are constructed for the purpose of case study (Fig. 2). The first
map (left part) expresses occurrences (i.e. absolute number) of parotitis in the
municipalities of Olomouc region between January 2004 and December 2010. Darker
areas mean that higher absolute number of cases was reported from the area. The
second map expresses relative measure – prevalence, i.e. the number of cases of
parotitis in the population of municipality. Both maps show that the more populated
southern part of region is more affected by the parotitis than the northern part because
the darkest areas in the first map match the biggest towns in the region. But second
map is more particular and allows specifying of several centres.
Fig. 2. Visualization of absolute (occurence - left) and relative (prevalence - right) values.
Ellipses indicate places with high probability of misinterpretation
Results of Morishita index plot and the comparison between G-function and a
simulated CSR process (Fig. 3) prove previously predicted fact that a possibility of
clustering exists in several scales in the area. With the knowledge introduced before,
it is evident that according to MI plot (Fig. 3 left part) clustering processes dominate
in the area because the progress of function descends rapidly in the first part and after
the “elbow point” it starts to converge to 1. G function (Fig. 3 right part) is compared
with the envelope of CSR after 1000 simulations. The full line expresses observed
value of function G for data pattern, dotted line stands for simulated CSR and light
grey regions is 96% envelope of CSR. The curve of G function appears above the
CSR line up to the value 0.05, which points out to clustering processes again.
8 Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
Fig. 3. Morishita index plot (left) and the curve G-function (right)
Density map is the method for quick visualization of significant clusters similar to
choropleth maps or quadrat maps. The most important aspect in the estimation of
kernel is not the type of kernel but its size, called bandwidth. In this study the quartic
kernel with fixed bandwidth of size 0.01° (≈ 1 km) is used. This distance comes from
the cross validated bandwidth selection for kernel density of point processes. Density
map (Fig. 4 – left) then reveals primary spatial clusters, which are similar to those
previously mentioned.
Fig. 4. Estimation of the number of cases by Kernel density (left) enables visual estimation of
areas with dense occurrence of infection. The result of clustering by DBSCAN algorithm
(right) –several clusters are identifiable in the southern part of study area or even in body of
individual towns
On Estimation of the Spatial Clustering 9
Results of Moran’s I, as well as Getis Ord G, prove to the presence of clustering
processes. A neighbourhood for the analysis of local clustering and the size of
aggregated units is based on the previous calculation of Morishita index. The global
existence of clusters in the study area is proven by several methods, but their location
is still not known. That is why it is proceeded to LISA.
Particular localizations of significant clusters, as well as their type, are then shown in
the Figure 5. Main intensive clusters (grey areas) of high values (netted areas) with
similar size of the area are identified near biggest towns in the southern and central
part of the study area, while municipalities in the northern part of the region do not
show any significant clusters or outliers. Clusters of high values are dominant in the
area but also one outlier with low values appears.
Fig. 5. Localization of disease clusters based on places of occurence of parotitis with usage of
Local Indicators of Spatial Association (LISA)
For the purpose of this study, three methods of multivariate clustering, which were
evaluated as the most suitable, were performed. Firstly, the similarity among all cases
of parotitis through time is evaluated using the hierarchical clustering method with
average linkage based on the Sokal-Michener dissimilarity distance measure for
nominal variables (Fig. 6 left part). Then similarity among hexagonal areas with
aggregated values is calculated using Partitioning Around Medoids (pam) clustering
algorithm based on the squared Euclidean dissimilarity distance measure (Fig. 6 right
part). Especially second case is useful, because it found 3 categories with a similar
attribute space (categories 2-4), which corresponds with main towns in the study area
and furthermore it divides these towns in separate classes.
10 Lukáš Marek, Vı́t Pászto, Jiřı́ Dvorský, Pavel Tuček
Result of the third method is shown in the Figure 4 (right part). DBSCAN
algorithm is highly effective for the estimation of spatial clusters even in the noise
data. Fourteen clusters are found in the health data in the case study. These clusters
not only correspond with settlements in the area of interest but also express inner
differences in clusters and divide town into separate zones.
Fig. 6. Spatial visualization of multivariate clustering - similar cases (left), similar locations
(right)
5 Discussion and Conclusion
One can easily explore spatial pattern and spatial relations with usage of spatial
statistics and especially methods of spatial clustering estimation. But results of spatial
statistics and mainly their interpretation are usually experience-dependent, i.e.
subjective. Plenty of spatial techniques are also scale-dependent, thus their results are
very sensitive on the precise adjustment of parameters and one small change can
cause important differences in results. At least one example is given in this paper,
which is an estimation of the kernel for density maps. Both, global and local indices
of spatial autocorrelation are sensitive on the selection of parameters as well. The
evaluation of spatial patterns is influenced also by others environmental factors,
which some of them may be primarily hidden. Demographic factors are mostly the
most influential element in case of health datasets.
Earlier presented procedures and techniques are only sample of suitable tools for
spatial statistics, their further development and implementation lead not only to
On Estimation of the Spatial Clustering 11
spatial but to space-time and space-time-attribute analyses. Which are very complex
and I believe they will be the predominate type of analyses in near future.
This paper presented techniques of the exploration of the spatial pattern. The
usability of methods has been proved on the case study. An exploration of spatial
patterns of the occurrence of parotitis (mumps) in the Olomouc Region was chosen as
the model situation. Methods of EDA and ESDA confirmed the hypothesis that
clustering processes exist in the area. Firstly the randomness of occurrence was tested
and then the predominant type of the process was searched with a help of visualizing
methods (choropleth maps and density maps) and tested (Morishita index plot). The
spatial autocorrelation was explored on the aggregated data in the form of regular
hexagons. Several clusters have been identified using methods of LISA. This clusters
and their description are depicted on the map (Fig. 4). Clusters of high values with
intensive processes are prevailing in around the towns Olomouc, Hranice, Přerov,
Prostějov, Šternberk a Konice. Spatial statistics allows outstanding possibilities of
exploration of spatial and space-time patterns, although some of methods have their
strict limits and their interpretation can be subjective and experience dependent.
At last, data were evaluated by methods of multivariate statistics, which served to
the searching of similar cases and regions with similar characteristics of disease
occurrence.
Acknowledgement
The authors gratefully acknowledge the support by the Operational Program
Education for Competitiveness - European Social Fund (project
CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth and Sports of the Czech
Republic).
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