10 Ijaest Volume No 1 Issue No 2 Spatial Ma Thematic Methods for Analysis of Indicators of Mortality

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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] ,

[email protected] ,

+Corresponding Author * Equal Contributors

Georgia Pistolla et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIESVol No. 1, Issue No. 2, 135 - 146

ISSN: 2230-7818 @ 2010 http://www.ijaest.iserp.org. All rights Reserved. 35

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http://freemail.services.in.gr/[email protected]



http://freemail.services.in.gr/Members/[email protected]











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.


ISSN: 2230-7818 @ 2010 http://www.ijaest.iserp.org. All rights Reserved. Page 136



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.





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





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.





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.





Picture 7: Profile of second class of Laplasian of difference of data

2001 2006





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.





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 ®



http://epp.eurostat.ec.europa.eu/portal/page/portal/eurostat/home/



http://www.amazon.com/s/ref=ntt_athr_dp_sr_1?_encoding=UTF8&sort=relevancerank&search-alias=books&field-author=Napler%20Addison





® 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.





10 Ijaest Volume No 1 Issue No 2 Spatial Ma Thematic Methods for Analysis of Indicators of Mortality

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