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SPATIAL - MATHEMATIC METHODS FOR ANALYSIS OF
INDICATORS OF MORTALITY
Author’s name: Georgia Pistolla
Address: Platonos 5 Kounavi, B.O: 70100, Iraklion of Crete, Greece
E-mail: [email protected]
Mobile phone: 6949987655
Georgia Pistolla+*1, Poulikos Prastakos*2, Maria Vassilaki*3, Anastas Philalithis*4
Address: 1MSc, PhD student, Department of Social Medicine, Faculty of Medicine,
University of Crete, 2Research Director, Institute of Applied and Computational
Mathematics, Foundation for Research and Technology-Hellas (FORTH), Herakleion,
Greece, 3MSc, PhD, Research Associate, Department of Social Medicine, Faculty of
Medicine, University of Crete, 4Associate Professor of Social Medicine, Faculty of
Medicine, University of Crete.
E-mail: [email protected] , [email protected] , [email protected] ,
+Corresponding Author * Equal Contributors
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INTRODUCTION
The analysis of mortality through Standardised Death Rates (SDR)1 in different
geographic areas provides information that is useful for the understanding of health
needs and for the planning of health services raises interesting scientific questions and
may contribute to the administrative services
2
. Modelling is also a useful tool thatmay provide additional information and improve the quality of the analysis.
The usefulness of this methodology, which is based on mathematic significances and
techniques of non linear dynamics, has to do with the fact that a lot of systems cannot
be analyzed with probabilistic methods and techniques. They have to do with
deterministic dynamics of low dimensions. These methods find application in natural,
biological and economic systems e.g in the area of education (curve learning and the
threshold of chaos), in the area of health (fractals, chaos and heart rate collapse
cascade), in the area of art (chaotic music), in the area of economy (Stock Exchange),
of meteorology (forecast of time-phenomenon of fly of the butterfly), etc. 3
These methods are able to detect and take advantage of mathematic determinism, so
that the results of classic analysis and forecasting are improved. They may even
recode algorithms for equivalent natural, biological, economic and other systems.
The indicators of mortality are usually analyzed using the methods of classic
statistics, mainly simple comparison between the different indicators and their
corresponding limits of confidence, without checking their dynamics and their
characteristics.
The main goal of the present study is to examine the characteristics of indicators of
mortality for the years 2001 and 2006 in each prefecture of Greece and to find their
dimension, that is to say which factors can interpret completely the particular
indicators. Such an analysis should be useful for providing advice for the
epidemiologic interpretation of mortality for and decision-making in public health.
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MATERIAL AND METHODS
All the data that were used for the analysis of this particular project were provided
by the Greek Statistical Authority (EL.STAT.), previously known as the National
Statistical Service of Greece (ESYE). The data concern deaths per sex, age-relatedteams and causes of mortality per prefecture of Greece for the years 2001 and 2006.
The coding of causes of death is according to the ICD 10 classification and then these
causes of mortality were grouped into the 65 groups that are used by the Eurostat of
the European Union4 (G27). Generally, the methods that were used are Kriging of
optimized parameters, the methods of SPATIAL STRUCTURE FUNCTION, the
method of ANALYSIS OF GENERAL COMPONENTS and the connected
PROJECTION TECHNIQUES with the use of MATLAB.
EXPERIMENTAL
The methods of SPATIAL STRUCTURE FUNCTION are proportional and, hence,
conceived from corresponding her for time series of Provenzale.
THEORY/CALCULATION
In order to eliminate the difference between the demographic pyramid of the
population of each prefecture, direct standardization was carried out, using the G27
population as the standard. This was applied to the SDR’s of each prefecture.
For the underlying distribution of this phenomenon, the interpolating heuristic
method was used (usual Kriging of optimized parameters) 5 in environment ArcGIS
9.2, as shown in picture 1.
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Quantitative and qualitative study of data was carried out, so that results of classic
analysis and forecasting of corresponding biological system are improved, in order to
study the behavior of indicators of mortality in each prefecture. The methods of
SPATIAL STRUCTURE FUNCTION were used to answer the issue above.
Be it, a 2D (two Dimensioned) phenomenon, where for each pair of coordinates
(x,y) R R the compact space Ω, we set one and only price z R . For each axis of
coordinates we take N samples of semi-straight lines, and in each semi- straight line
prices z with step of sampling Γs. We set as interrelation of structure for each semi-
straight line the ordered set of numbers that is given by the relation:
R y x z
v
1i
2),(Δs νy)z(x,ÓÄ(í)
, where n is the total amount of points in
each semi-straight line N1, N2, ……. Nκ.
The graphic representation of Log (SD (n)) as for Log (n) shows the nature of
distribution of phenomenon.
If the phenomenon is completely randomly distributed, then the graphic
representation will by definition have an exponential form (in an ordered set of
accidental phenomena, each value that follows adds as much information, as exists in
this number series). If the phenomenon is about a colored noisy phenomenon, then the
graphic representation is approached satisfactorily by one increased straight line. If
periodicity appears, it is presented as a small scale oscillation on this straight line.
However, for a deterministic phenomenon, for small prices of an escalation of
exponential form and then an intense oscillation (valley effect) are presented – thenext values are predicted from the previous numbers series6.
Picture 1: The distribution of amenable dynamic mortality with spatial analytic methods. Right, for
2001, left for 2006
Picture 1: The distribution of underlying dynamic mortality with spatial analytic methods. Right, for
2001, left for 2006
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From the spatial structure function ,it is possible that controls of randomly or
deterministic natures of phenomenon are exported, as well as existence of periodicity
and generalized linearity, as shown in picture 2.
Because of the obvious underlying deterministic non – linear dynamic, self-
analysis7 was done, which attributed dimensionality of about 2.04 to 2.70 for these
years, with interpretation of data 87% to 95% with reverse equivalence, so that the
dimensionality of the phenomenon is checked and the data are arranged in the space
that they produce.
The change of vector space of data for these two years was studied with the method
of ANALYSIS OF GENERAL COMPONENTS and the connected PROJECTION
TECHNIQUES with the use of MATLAB.
Picture 2: Graph of spatial Structure function with random sample semi- straight lines and then with Ds = 7000
m., left for 2001 and right for 2006. It is obvious in both cases, the morphology implying deterministic spatial
phenomenon.
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Of course, WAVELET ANALYSIS 9 of their change shows that only very local linear
admissions are possible here. Fifth and higher frequencies’ level attributes, describes
almost completely, all the vector change, as shown in picture 5.
The phenomenon under study, therefore, while presenting characteristically
stochastic behavior (Possibilities’ theory), is deterministic, of low dimensionality, nonlinear and of powerful spatial memory (although it is not periodical). Such a
phenomenon is sensitive enough, which means that in certain regions of parameters of
the dynamic system that it is described, it leads to chaotic behavior. The fact that
their second order Laplasian of difference does not perform dominant volumes of
change strengthens the above assumption 10 , although it is a qualitative, presentative,
indicative control, as shown in pictures 6, 7.
Picture 4: Left, the difference of dynamic fields 2001-2006, as it is shown at absolute prices. Right, the same
variable as regularized percentage difference.
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Picture 7: Profile of second class of Laplasian of difference of data
2001 2006
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DISCUSSION
All the previously mentioned methods of analysis are important because they help
in the ascertainment of any usefulness of qualitative characteristics of standardisedindicators of mortality (in this respect for the years 2001 and 2006 in the 51
prefectures of Greece). Among various studies of mortality carried out in Greece,
these methods have not been used before. The results we report here aim at knowing
if our data emanate from meditative processes, in which case, if the distribution and
their development are connected with concrete distributions of probabilities, the usual
methods of statistical analysis are sufficient. If, however, they emanate from
deterministic dynamics, the study owes to be supplemented with special mathematic
methods and to calculate, even if only approximately, the minimal dimension of space
of immersion. Thus, the forecasting of the development of biological systems is
improved, and the particular study provides an application of the analysis of standard
indicators of mortality per prefecture.
With methods of classic analysis, modeling of data is not satisfactory, if these
emanate from deterministic systems that mainly have their origin in the data in the
space of health. The formulation of health policy is not satisfactory if the
phenomenon and problems that it is called to face, has powerful spatial memory,
random – like behavior and only local assumptions could be fulfilled with classic
methods of analysis. Placing, as objective, the qualitative study with techniques of
quantification (mathematic or statistical), in the analysis of territorial data, raises the
question whether the phenomenon under examination is able to be approached
meditatively. Then, the results of such an analysis of data (which immediately answer
the functional definitions) are able to create an explanatory frame for the findings, or,
at least, a sort of modeling, which will give specific algorithms as a result,
On the other hand, the mathematic methods used in the present study can be
applied to biological systems and, as has been shown, the given data can be used to
predict the behavior of these biological systems, without involving other factors in
first phase.
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REFERENCES
1. Marcello Pagano, Kimberlee Gauvreau, Harvard School of Public Health,
Principles of Biostatistics, 1996 by Buhbury Press, Απσέρ Βιοζηαηιζηικήρ Ίων, Έλλην, 2000®
2. Hakulinen T, Hakama M: Predictions of epidemiology and the evaluation of cancer
control measures and the setting of policy priorities. Soc Sci Med 1991, 33(12):1379-
1383.
3. Sytrogatz. S.H, Non linear Dynamics and Chaos, Addison- Wesley, 1994
4. http://epp.eurostat.ec.europa.eu/portal/page/portal/eurostat/home/
5. Koutsopoulos Konstantinos, «Ανάλςζη Χώπος: Θεωπία Μεθοδολογία και
Τεσνικέρ», Γιηνεκέρ, Αθήνα, 2006, Τομορ 1, 280-286 ®
6. Η Μέθοδορ αςηή είναι ανάλογη και , άπα, εμπνεςζμέν η με ηην ανηίζηοισή ηηρ για
ηιρ σπονοζειπέρ ηων Provenzale κ.α. 1992 (Papaioanou Aggelos, «Χαοηικέρ
Χπονοζειπέρ: Θεωπία και Ππάξη», Leader Books Α.Δ., Αθήνα, 2000, 199-200 ®
7.Koutsopoulos Konstantinos, «Ανάλςζη Χώπος: Θεωπία Μεθοδολογία και
Τεσνικέρ», Γιηνεκέρ, Αθήνα, 2006, Τομορ 2, 130-139μ ®
8. Πεπαιηέπω Μελέηη: Papaioanou Aggelos, «Ανύζμαηα και Τανςζηέρ», Κοπάλλι,
Αθήνα, 2003 ®
9. Πεπαιηέπω Μελέηη: Napler Addison «The Illustrated Wavelet Transform
Handbook», IOP Publishing Ltd., Μππίζ ηολ, 2002 ®
10. Mertikas Stilianos: «Τηλεπιζκό πιζη και Ψηθιακή Ανάλςζη Δικόναρ», Ίων,
Αθήνα, 1999, 307-310 ®
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® References in English
1. Marcello Pagano, Kimberlee Gauvreau, Harvard School of Public Health,
Principles of Biostatistics, 1996 by Buhbury Press, Ion, Ellin, 2000
5. Koutsopoulos Konstantinos, Spatial Analysis: Theory Methodology and
Techniques, Diinikes, Αthens, 2006, Volum 1, 280-286.
6. This Method is proportional and, hence, inspired with corresponding her for time
series of Provenzale etc. 1992 (Papaioanou Aggelos, «Chaotic time series: Theory
Methodology and Techniques», Leader Books Α.Δ., Αthens, 2000, 199-200.
7. Koutsopoulos Konstantinos, «Spatial Analysis: Theory Methodology and
Techniques», Diinikes, Αthens, 2006, Volum 2, 130-139μ.
8. Further Study: Papaioanou Aggelos, «Vectors and Tensors», Korali, Athens, 2003.
9. Further Study: Napler Addison «The Illustrated Wavelet Transform Handbook»,
IOP Publishing Ltd., Bristol,2002.
10. Mertikas Stilianos: «Remote Sensing and Digital Image Analysis», Ion, Athens,
1999, 307-310.
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