spatial - mathematic methods for analysis of indicators of mortality

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

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

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

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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 services2. Modelling is also a useful tool that may 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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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-related teams 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. IJA

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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) RR 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:

Ryxz

v

1i

2),(Δsνy)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 – the next 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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RESULTS

The result of analysis of the spatial structure function proves that the phenomenon

(the general indicator) is conditioned by a non linear spatial dynamic system. In any

direction, the information that is further away, was found to be without spatial

periodicity, as expected and decreases the entropy of the data (the analysis of wavelets

supplements the statement that only very local linear admissions are possible).

The discontinuities of models of Spatial Interpolation do not allow consideration

the underling low-frequency spatial generalizations or periodicity or even self-

similarity to exist.

Consequently, an analysis was fulfilled, which attributed dimensionality of about

2, 04 to 2, 7, interpretation of data 87% to 95% with reverse equivalence. The data,

therefore, were arranged, after their space in three dimensions was produced, as

shown in picture 3.

The dynamic fields of data in 2001 and 2006 present differences 8 , which are not

accidental, but present an inner non linear dynamic, (picture 4).

Scatterplot 3D

Final ConfigurationDimension 1 vs. Dimension 2 vs. Dimension 3

C _5C _3 C _1C _2C _4C _8C _9C _7C _6C _11C _12

C _10C _15C _16C _14

C _13

C _18C _20C _17C _19

C _21C _22C _23

C _25C _24C _26C _27

C _28C _30C _29C _31C _32C _33C _34

C _35C _36

C _38C _37

C _43C _39C _42C _40C _41

C _44C _45C _46C _48

C _47C _49C _51C _50

C _5C _3 C _1C _2C _4C _8C _9C _7C _6C _11C _12

C _10C _15C _16C _14

C _13

C _18C _20C _17C _19

C _21C _22C _23

C _25C _24C _26C _27

C _28C _30C _29C _31C _32C _33C _34

C _35C _36

C _38C _37

C _43C _39C _42C _40C _41

C _44C _45C _46C _48

C _47C _49C _51C _50

Scatterplot 3D

Final ConfigurationDimension 1 vs. Dimension 2 vs. Dimension 3

C _5

C _3

C _1C _2

C _4

C _8C _9C _7C _6C _11C _ 12

C _ 10

C _15C _ 16C _ 14

C _13

C _ 18C _20

C _17C _ 19

C _21C _22

C _23

C _25C _24C _26

C _27

C _28C _30

C _29

C _31

C _32

C _33C _34

C _35

C _36

C _38

C _37

C _43

C _39

C _42

C _40C _41

C _44C _45

C _46

C _48

C _47C _49

C _51

C _50

C _5

C _3

C _1C _2

C _4

C _8C _9C _7C _6C _11C _ 12

C _ 10

C _15C _ 16C _ 14

C _13

C _ 18C _20

C _17C _ 19

C _21C _22

C _23

C _25C _24C _26

C _27

C _28C _30

C _29

C _31

C _32

C _33C _34

C _35

C _36

C _38

C _37

C _43

C _39

C _42

C _40C _41

C _44C _45

C _46

C _48

C _47C _49

C _51

C _50

Picture 3: The classification of indicators in the 3D space, which suffices for their complete depiction. IJAEST



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, non

linear 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 6: The difference of dynamic fields 2001-2006

Picture 5: Wavelet analysis (Daubechie1 Wavelet)

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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 standardised

indicators 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., Μππίζηολ, 2002 ®

10. Mertikas Stilianos: «Τηλεπιζκό πιζη και Ψηθιακή Ανάλςζη Δικόναρ», Ίων,

Αθήνα, 1999, 307-310 ®

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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.

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

spatial - mathematic methods for analysis of indicators of mortality

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analysis of mortality

indicators of mortality

analysis of indicators

faculty of medicine

department of social

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different indicators

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