Estimation and Evaluation of Some Interdependencies of Environmental Conditions, Welfare Standards, Health Services, and Health Status

Bojanczyk, M. and Krawczyk, J.

IIASA Collaborative PaperOctober 1981

Bojanczyk, M. and Krawczyk, J. (1981) Estimation and Evaluation of Some Interdependencies of Environmental

Conditions, Welfare Standards, Health Services, and Health Status. IIASA Collaborative Paper. Copyright ©

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ESTIMATION AND EVALUATION OF SOME INTER- DEPENDENCIES OF ENVIRONMENTAL CONDITIONS, WELFARE STANDARDS, HEALTH SERVICES, AND HEALTH STATUS

M. ~ojahczyk J. Krawczyk

October 1981 CP-81-29

CoZZaborative Papers report work which has not been performed solely at the International Institute for Applied Systems Analysis and which has received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organi- zations supporting the work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria

FOREWORD

The principal aim of health care research at IIASA has been to develop a family of submodels of national health care systems for use by health service planners. The modeling work is pro- ceeding along the lines proposed in the Institute's current Research Plan. It involves the construction of linked submodels dealing with population, disease prevalence, resource need, resource allocation, and resource supply.

A national health care system is closely connected to the nationaleconomy and its environment. It is therefore necessary to consider the important links and interactions involved. This paper briefly summarizes research recently carried out in Poland thatanalyzessome of the interdependencies relating health status to welfare standards.

Recent publications in the Health Care Systems Task are listed at the end of this report.

Andrei Rogers Chairman Human Settlements and Services Area

ABSTRACT

The building of complex models of socio-economic development especially on the regional level, requires the knowledge of important relations and feedbacks between the health status of a population and the indices describing welfare standards such as environmental conditions, income level, and public services. In developing a family of submodels of national health care systems for use by health service planners, it is important to consider the environmental impact on health status as well, since the environment forms one of the most significant external sub- systems influencing health care. Needless to say, more effort is needed in modeling the links between health care systems and the national economy.

In this paper, a set of basic health standard relationships are postulated. Through this the consequences of resource allo- cation policies can be determined, thus aiding the decision- making process. Proposed formulae are estimated on Polish statistical data using cross-sectional analysis, and a critical evaluation of the significance of these relationships is given.

CONTENTS

1 . INTRODUCTION

2. IND ICES DESCRIBING WELFARE STANDARDS

3 . I N D I C E S OF HEALTH STATUS

4. VERIF ICAT ION OF THE S IGNIF ICANCE OF THE HYPOTHESES

4.1 G e n e r a l R e m a r k s on the R e g r e s s i o n A n a l y s i s 4.2 V e r i f i c a t i o n R e s u l t s

5. CONCLUDING REMARKS

REFERENCES

RECENT PUBLICATIONS I N THE HEALTH CARE TASK

This paper was o r i g i n a l l y prepared under t h e t i t l e "Modell ing f o r Management" f o r p r e s e n t a t i o n a t a Nater Research Centre (U.K. ) Conference on "River P o l l u t i o n Cont ro l " , Oxford, 9 - 1 1 A s r i l , 1979.

ESTIMATION AND EVALUATION OF SOME INTER- DEPENDENCIES OF ENVIRONMENTAL CONDITIONS, WELFARE STANDARDS, HEALTH SERVICES, AND HEALTH STATUS

1. INTRODUCTION

Recent developments in industry, modifications in the welfare

of populations, and changes of environmental conditions have

contributed to alterations in health status. Generally, it is

rather difficult to define these transfomations, not to mention

their quantification. The aim of this paper is to estimate some

simple, econometric relationships that describe aspects of the

health of a population as a function of the indices that charac-

terize these changes. The authors believe that such an approach

may contribute to a better evaluation of the present day situa-

tion in the health care domain, may show the potential dangers

in this sphere of activity, and finally, may induce some positive

changes in trends. It is worth noting that some hypotheses about

the significance of the relationships could have had more practical

meaning if the statistical data had been more comprehensive at

the time of the study.

The major motivation of the study is simply to provide a

regional development model (RDM) (e.g., Krug et al. 1980) with

a tool that predicts the average health of the population as a

function of production, consumption (including health care

s e r v i c e s ) , t h e emiss ion o f p o l l u t a n t s , and o t h e r f a c t o r s t h a t

cor respond t o a p a r t i c u l a r development s c e n a r i o . Thus t h e method

i s based on a model t h a t h a s as i n p u t v a r i a b l e s t h e q u a n t i t i e s

gene ra ted by t h e RDM t h a t i n some agg rega te s e n s e d e s c r i b e

c o n d i t i o n s o f l i f e i n a r eg ion . Development models ( e .g . ,

Krug e t a l . 1980) u s u a l l y o p e r a t e w i t h some agg rega te v a r i a b l e s .

However, i n t u i t i v e models r e l a t i n g t h e h e a l t h s t a t u s t o t h e

envi ronment a r e based on d e t a i l e d measures o f t h e c o n c e n t r a t i o n

o f p o l l u t a n t s (e .g . , SO2 [q] , t h e we igh t o f su lphu r d i o x i d e [SO2] m

p e r cubic meter o f a i r ) t h a t d i r e c t l y a f f e c t t h e human organism.

Thus t h e v a r i a b l e s d e s c r i b i n g t h e envi ronment env isaged by WM and t h e i n t u i t i v e model do n o t co r respond e x a c t l y w i t h one

ano the r . T h i s can be overcome by

a) b u i l d i n g a s imp le and e f f i c i e n t model d e s c r i b i n g t h e

d i f f u s i o n o f p o l l u t a n t s

b ) b u i l d i n g a model t h a t e v a l u a t e s h e a l t h s t a t u s , based

on p o l l u t i o n c o n c e n t r a t i o n data

Unfo r t una te l y , none o f t h e l i n k s i n t h e h y p o t h e t i c a l c h a i n

shown i n F i g u r e 1 can be made i n Poland a t p r e s e n t . T h i s i s

because t h e e x i s t i n g d i f f u s i o n models a r e h i g h l y complex and

s t i l l need more d i s a g g r e g a t e d i n p u t data t h a n t h e RDM can

p rov ide (Pudykiewicz 1980) . Fur thermore, t h e d a t a a v a i l a b l e

t o t h e a u t h o r s d e s c r i b i n g p o l l u t i o n c o n c e n t r a t i o n are c o l l e c t e d

o n l y i n c e r t a i n g e o g r a p h i c a l l o c a t i o n s and n o t i n a l l areas

(see Borkowska 1979, and Atmospheric P o l l u t i o n Yearbook 1974) .

These d a t a i n c l u d e two groups o f p o l l u t i o n : water ( b i o l o g i c a l

oxygen demand and con tamina t ion by f e c e s ) and a i r (SO2 concen-

t r a t i o n , d u s t c o n c e n t r a t i o n and d u s t f a l l ) . They cou ld n o t b e

used i n o u r s t u d y , however, because t h e y were n o t comprehensive

enough. Hence, t h e ass ignment o f ave rage h e a l t h i n d i c e s [ s e e

Yearbook o f Hea l t h Care i n Poland i n 1978 (1979) l t o such

env i ronmenta l d a t a i s a lmos t imposs ib le . Taking t h e above i n t o

accoun t , t h e a u t h o r s dec ided t o i n v e s t i g a t e t h e s i g n i f i c a n c e

of hypotheses concern ing t h e impact o f emiss ion a g g r e g a t e data

on t h e h e a l t h o f a p o p u l a t i o n s i n c e t h e models o b t a i n e d can be

used as tools only if the hypotheses have been tested.* The

place of the proposed model and its connection with the RDM is

shown in Figure 1.

However, it has to be emphasized that the structure proposed,

which is based on emission data, obviously has drawbacks, because

it does not take into account the effects of pollutants imported

from outside the region.** Thus the approach presented is a

compromise between the availability of statistical data and what

is ideally required. Its practical outputs should be viewed,

therefore, as an examination of the broad impact of development

scenarios on a population's health status and the relative degree

of influence the various pollutants have on health.

Taking into account the above-mentioned compromise,

Bojaiiczyk and Krawczyk (1 980) set forth a number of indices

describing standards of life by means of emission data (considered

the explanatory variables) and indices of the health status

(explained variables). The hypotheses were then tested for

their significance through a multiple regression analysis. The

relationships were obtained, by a cross-sectional analysis,

using statistical data provided by 49 Polish voivodships

(administrative areas) for the year 1978.

In this paper, only those groups of indices are presented

for which the respective relations proved to be statistically

significant in ~ojaiiczyk and Krawczyk (1980). The complete set

of indices is broader, containing more measures of welfare

standards.

It should be borne in mind that according to the standard

rules of regression analysis, the hypothesis concerning the

significance of a relationship is accepted only when the null

hypothesis is statistically rejected. The conclusions obtained

by this method, which is based on a cross-sectional analysis,

*A similar approach was presented in North and Merkhofer (1975) and Buehring et al. (1976).

**Unfortunately in some regions, imported pollutants contribute to 30% of the total pollution (measured in terms of concentra- tion) (Juda 1980).

do not consider the dynamics of the processes under consideration.

Thus their use in prediction is restricted to systems that are

not supposed to change very much--at least in the short run

(say, 2-4 years) .

2. INDICES DESCRIBING WELFARE STANDARDS

According to the analysis carried out in Bojaficzyk and

Krawczyk (1980), the description of welfare standards is given

by a series of indices of natural units.*

The first are indices describing the natural environment

quality

x - various gas emissions in tons per hectar 1 x2 - water purification coefficient (amount of non-

purified industrial wastes and municipal sewage related to water consumption in tons per ton)

+ x3 - population density (number of inhabitants per kmL

--a measure of social environment)

The choice of these indices assumes an obvious correlation

between the emission and concentration of pollutants as well

as the somewhat unreliable functioning of the water purification

system.

The second is an index describing the welfare standard

x - energy consumption in kilowatt hours per person 4

This characterizes the level of wellbeing which is at present

more important and significant in Poland, rather than the income

level. **

*Some other methods of describing welfare standards are considered in the publications of Hellwig, 1968; e.g., a certain kind of multi-criteria1 approach aimed at comparisons of different regions or systems.

**Some measures of income have been considered in Bojaficzyk and Krawczyk (1980), but have been omitted in the further analysis due to the fairly weak explanatory features.

The t h i r d a r e i nd i ces descr ib ing t h e hea l th c a r e se r v i ces

l e v e l x - number of phys ic ians per l o4 populat ion 5 x6 - number of beds i n genera l h o s p i t a l s per l o4 populat ion

The chosen i nd i ces desc r ibe the a c c e s s i b i l i t y t o hea l t h c a r e ser-

v ices . Hence, they a l s o descr ibe t he l e v e l s of t h e se r v i ces i n

each a rea . The authors a r e convinced t h a t t h e above series of i nd i ces

do no t exhaust t h e sub jec t of we l fa re s tandards . I t i s poss ib le

t o make each group r i c h e r o r t o add new ones. Kostrzewski e t

a l . (1973) , among o t h e r s , have worked on t h i s t op i c . However,

t h e au thors f e e l t h a t es t imat ion and eva lua t ion of t h e r e l a t i on -

sh ips desc r ib ing t h e impact of t hese i nd i ces on hea l t h s t a t u s

may become a use fu l and i n t e r e s t i n g t o o l f o r p lanners and dec is ion

makers.

INDICES OF HEALTH STATUS

I n t h i s paper, a s i n Bojaficzyk and Krawczyk (1980) , t h e

hea l th s t a t u s of t h e soc i e t y i s descr ibed by a set of i nd i ces

( i n na tu ra l u n i t s ) t h a t cha rac te r i ze t o some ex ten t , t h e two

s t a t e s of "bad hea l th " : d i sease and death. Thus t h e two

phenomena, morbidi ty and mor ta l i t y , have been considered.

Morbidity and mor ta l i t y f i g u r e s a r e those most o f t e n m e t i n

World Health Organizat ion pub l ica t ions : e.g. , O f f i c i a l Record

WHO (1973) , and o t h e r s such a s Kostrzewski e t a l . ( 1 973) and

Shigan (1978). These papers g ive comparative s t u d i e s of t h e

hea l t h s t a t u s f o r d i f f e r e n t coun t r i es .

A na tu ra l and broadly app l ied method of t ack l i ng t h e hea l th

s t a t u s problem i s by analyz ing t h e da ta of d i sease frequency,

d i sease s t a g e ( e a r l i e r , advanced, o r te rmina l ) and death r a t e s .

Unfortunately, in format ion on morbidi ty (new cases of d i sease

i n a t i m e u n i t adopted f o r an ana l ys i s ) and prevalence ( a l l

cases of d i sease ) a r e q u i t e i n s u f f i c i e n t .

Basically, the routine statistical data in Poland consist

of registered patient cases only, which is a rather typical

situation for most countries. The data for latent patients

(ill persons unaware of being ill) and unregistered patients

(ill persons aware of being ill but staying away from health

care services) are unavailable. However, it is possible to

calculate morbidity, mortality, and prevalence rates using

programs elaborated at the International Institute for Applied

Systems Analysis in Laxenburg, Austria (see Shigan 1978;

Fujimasa et al. 1978; Kitsul 1980; Klementiev 1977). Unfortu-

nately, some of these programs require, as a prerequisite, very

expensive screening analyses for the representative subpopula-

tions. This drawback cannot be overemphasized, since it limits

the applicability of such modeling procedures.

Finally, the statistical data give the number of health

services rather than the demand for health services, which would

better characterize the health status of the society (Shigan

1978). (That is, they describe the realized demand, which is

usually equal to the supply level.)

In this paper, three groups of indices have been proposed.

The data are taken from routine statistical yearbooks [Yearbook

of Health Care in Poland in 1978 (1979) and Yearbook of Voivod-

ships in 1978 (1979)1, which implies the acceptance of their

well-known limitations:

a) indices describing the process of health care services

delivery (treated as some measures of morbidity*)

y1 - number of consultations with physicians (or dentists) per inhabitant

y2 - number of patients in general hospitals per 10 4

population**

*The indices of both a) and b) describe the approximate size of population afflicted with a disease.

**It would be more interesting to disaggregate this number according to disease group specification in c), but the data are not available.

b) morbidity indices - morbidity (new cases) in chosen

disease groups per 1 o5 population* :

y j - influenza

5 c) mortality indices - number of deaths per 10 population

caused by diseases from the following disease groups:**

y4 - cancer

y5 - cardiovascular diseases

y6 - respiratory diseases

4. VERIFICATION OF THE SIGNIFICANCE OF THE HYPOTHESES

4.1 General Remarks on the Regression Analysis

The set of programs for multiple regression analysis

developed in the Systems Research Institute (Identification

Programs for Mathematical Models 1977) has been used to test

the significance of postulated linear relationships (linear

type y = ax + e) between the welfare standards and health status

indices. The indices describing welfare standards x = [xl. ... x61

may be grouped in three classes:

(1) x ~ ~ x ~ ~ x ~ - describes the quality of the environment

(2) x4 - denotes the level of welfare

( 3 ) X51X6 - measures the supply of health services

The index describing the health status is y = [y 1...y6]

For a given type of regression model (linear or nonlinear),

the above-mentioned package calculates and performs

- regression coefficients (matrix)

- regression model significance tests

- regression coefficients significance tests

*Data for morbidity rates for disease groups given in c) is required.

**The postulated impact of the natural environment quality on morbidity was the main motivation of this choice.

The run begins with the full model (including all the input

variables) and eliminates automatically non-significant

coefficients until the final version of the model is obtained.

This version has all the coefficients significant and/or minimal

residual variance.

Note that once a regression model has been obtained, it

must be analyzed carefully. A regression analysis is a useful

tool in the early stage of determining the probability (postulated)

relationships between inputs and outputs. However, one should

not use it as a decisive criterion for the evaluation of cause-

and-effect relationships.

4.2 Verification Results

The package of programs and procedures described in section

4.1 has been used to analyze the regression relationships between

the index of health status (y) and indices of welfare standards

(x). In the sequence proposed in section 3, the final forms of

linear regression models are now given.

The models obtained are characterized by three parameters

that define the significance of the regression relationships

(F) - value of standard F-Snedecor test (at 0.05 signi- ficance level)

(a) - estimator of the square root of residual variance

( p ) - multidimensional correlation coefficient

In Figure 2 and the remaining figures in this section,

the average values of input and output variables have been

denoted with broken lines. In several cases, the essentially

multidimensional models have been obtained, i.e., more than one

input variable is significant. In such cases, it is necessary

to project the received regression hyperplane on the two-dimensional

plane (parametrically dependent on average values of other

u 4J -4 E: 0 -4 h k A an ak

aJ rn U S a J 0 0 4 J

E: k W aJ a o r n .n aJ E a J k g m a , E: 3

4 m a J u E

A a J 4 cra LI - tn '44 4 0 .d

cr) a aJ aJ uuar G -4 A a J a u rn r: c.4 E: aJ -4 a r: a r o m a .d 3

4J d 3 d 4 d 4 G d + ' 0 0 0 -4 a, cr

input variables). Therefore, these figures are for illustrative

purposes only.*

The first regression model that will be presented here is

the one referring to the number of consultations given by

physicians (and dentists) per inhabitant (see Figure 2):

where Fcrit has been calculated for N=49 with the number of

degrees of freedom corresponding to the type of model.

Observe that the medical consultation rate (treated as a

certain measure of morbidity, see section 3) depends on the

environment quality, i.e., on gas emissions (x ) and on the 1 amount of non-purif ied water (x2) .

The second regression model refers to the number of patients

in general hospitals per l o 4 population (Figure 3) :

where the number of observations equals 49.

The results of the analysis show that the number of

patients is explained by the number of physicians per catchment

population. They confirm the general opinion that the number

*In the figures, Warsaw is the biggest urbanized area with a relatively high welfare standard and health services level, and Katowice is the heavy industrialized region with probably the poorest environmental standard.

no.of hospitalized patients 4 10 pop. I

I I I I no.of physicians I

! 10 pop. I

Figure 3. Regressional dependence between the hospitalized patients and the number of physicians.

of physicians is far from the satisfactory saturation level*.

It seems that at present and in the near future, every increase

in the number of physicians enables the admission of more

patients (and therefore decreases the number of patients on

waiting lists). In the health care systems of centrally

planned economies such as Poland, there is usually a connection

between the increase in the number of physicians and the increase

in the number of beds, a phenomenon referred to as a standard

or norm ratio. The concept of standards (or norms) is fundamental

in the planning practice of ministry and regional administrative

bodies.

The third model gives the number of people suffering from

influenza (y3) (new cases) per 1 o5 population (Figure 4) :

Thus the morbidity rate for influenza depends on:

-- population density with a positive coefficient (the

higher the population density, the closer the inter-

personal contacts that influence the morbidity rate

of infectious diseases)

-- the number of physicians per catchment population also

with a positive coefficient

The latter result can by no means by unexpected whereas

at present, the number of physicians per lo4 population is

fairly low [15.0 in Poland, 19.4 in FRG, 23.1 in Hungary, see

Yearbook of Health Care in Poland in 1978 (1979)l. An increase

in the number of physicians would, of course, result in better

health diagnoses and better detection of illnesses. As soon

*The saturation level is itself a controversial concept (Shigan 1980; Silver 1972).

I no.of influenza cases 7 * ,- I

X + Warsaw

no.of phys. = 14.5 4 10 pop.

population density

Figure 4. Regressional dependence between the number of new influenza cases and the population density.

a s t h e demand l e v e l i s reached, a f u r t h e r i n c r e a s e i n t h e number

o f phys i c ians would improve t h e s tanda rd o f h e a l t h s e r v i c e s and

lower t h e morb id i ty l e v e l .

The f o u r t h r e g r e s s i o n model measures t h e number o f dea ths 5

caused by cancer (y4) p e r 10 popula t ion* (F igure 5)

From t h e f o u r t h r e g r e s s i o n model (F igu re 51, it can be seen

t h a t t h e d e a t h r a t e f o r cancer d i s e a s e depends on:

-- w a t e r p u r i f i c a t i o n e f f i c i e n c y , popu la t ion d e n s i t y ,

and energy consumption w i th p o s i t i v e c o e f f i c i e n t s .

(These q u a n t i t i e s i n f l u e n c e t h e morb id i t y l e v e l . )

-- number of beds w i t h a n e g a t i v e c o e f f i c i e n t . (I t i s

necessary t o e n l a r g e f a c i l i t i e s o f i n - p a t i e n t h e a l t h

s e r v i c e t o improve t h e c o n d i t i a n s o f therapy . )

The f i f t h model d e s c r i b e s t h e number o f d e a t h s caused by 5 ca rd iovascu la r d i s e a s e s (y5) p e r 1 0 popu la t ion (F igure 6) :

*Here, it would be methodolog ica l ly more j u s t i f i e d t o t a k e t h e emiss ion d a t a o f po l l ukan ts from t h e p a s t ( le t us say 5-8 yea rs e a r l i e r ) because t h e d i s e a s e p rocess has i t s own dynamics. However, t h e s e d a t a were n o t a t o u r d i s p o s a l , and t h e r e g i o n a l s h a r e s o f p o l l u t i o n i n t h e t o t a l p o l l u t a n t emiss ion do n o t vary much w i t h i n t h i s t i m e i n t e r v a l .

a a, m c , U a , + E : m a u a m 5 0 0 c m z a, -4 a5 '4-4 a, 0 5 k

a h ddc, a 3.4 E: U d 0 m - 4 -4 a Q m 3.4 mom a, -4 m k 5 a, D k U a , a u t z u a

In this model as in the fourth model, the mortality rate

for cardiovascular diseases depends on:

-- population density with a positive coefficient (impact

on morbidity for "civilization disease")

-- number of beds with a negative coefficient (see explana-

tion for the fourth model)

The sixth model gives the number of deaths caused by

respiratory diseases per 10' population (Figure 7) :

The last model shows a regressional dependence of the

mortality rate for respiratory diseases on the number of

available beds with a negative coefficient. It is very similar

to the fourth and fifth models.

5. CONCLUDING REMARKS

The conclusions resulting from the above testing of the

hypotheses is summarized here:

-- In three models, a relatively significant dependence

of outputs (indices y) to the number of beds in hospitals

has been manifested, especially mortality indices

(from group c in section 3). This suggests that an

improvement of hospital conditions could effectively

contribute to the amelioration of the health status

in Poland.

-- The water purification process may have been responsible

for some mortality.

no-of deaths caused by respiratory diseases 5

10 POP*

X X

I

Figure 7. 'Regressional dependence between the number of deaths caused by respira- tory diseases to the accessibility of hospitals.

-- An a p p a r e n t l y unexpected l a c k o f dependence between

t h e proposed i n d i c e s d e s c r i b i n g t h e n a t u r a l environment

and some morb id i t y measures h a s been n o t i c e d (see more

d e t a i l e d a n a l y s i s i n ~ o j a f i c z y k and Krawczyk (1980) .

According t o t h e a u t h o r s , t h i s i s because: a ) t h e

i n d i c e s proposed d e s c r i b i n g t h e emiss ion o f p o l l u t a n t s

a r e i n f a c t an i n s u f f i c i e n t measure o f t h e d e t e r i o r a t i o n

o f t h e envi ronment (see Lave and Freeburg 1973, Werk

1977 and North and Merkhofer 1975 ) ; b ) a n ave rage l e v e l

o f t h e envi ronment p o l l u t i o n w i t h r e s p e c t t o t h e whole

coun t r y h a s n o t reached t h e c r i t i c a l p o i n t .

-- An a p p a r e n t l y unexpected i n c r e a s e i n t h e g iven morb id i t y

measure ( t h e number o f h o s p i t a l v i s i t s , etc . ) (group

a i n s e c t i o n 3 ) wi th an i n c r e a s e i n t h e number o f

phys i c i ans has po in ted t o t h e n o n s a t u r a t i o n demand

s i t u a t i o n f o r h e a l t h care, which s u p p o r t s t h e wide ly

accep ted op in ion o f t h e demand f o r h e a l t h care seeming

t o b e i n s a t i a b l e (Sh igan 1978; Kostrzewski 1973) . I t should also be borne i n mind t h a t t h i s s tudy has been

r e t r o s p e c t i v e , i .e . , t h e i n fo rma t i on abou t t h e w e l f a r e s t a n d a r d s

de f i ned i n s e c t i o n 2 w a s n o t e s p e c i a l l y adap ted t o t h e h e a l t h

s t a t u s i n d i c e s ( s e c t i o n 3)--nor w a s t h e r e v e r s e done.* Both

groups of i n d i c e s have been r e c e i v e d from r o u t i n e s t a t i s t i c a l

p u b l i c a t i o n s [Yearbook o f Hea l th Care i n Poland i n 1978 (1 979) , and Yearbook o f Voivodships i n 1978 ( 1 9 7 9 ) J . I n t h e f u t u r e

a p r o s p e c t i v e s tudy shou ld be made. Werk (1977) and Lave and

Freeburg (1973) p r e s e n t p o s s i b l e u s e o f some p r o s p e c t i v e methods

where t h e sets o f i n p u t and o u t p u t v a r i a b l e s are less numerous,

b u t t h e s t a t i s t i c a l d a t a a r e ve ry r i c h and e s p e c i a l l y chosen.

However, t h i s k i nd o f approach r e q u i r e s s u b s t a n t i a l l y l a r g e r

expend i t u res .

*Some subpopu la t ions cou ld be chosen and ana lyzed , e .g . , t h e groups exposed t o we l l -de f ined env i ronmenta l hazards .

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Borkowska, E. (1979) Practical Verification of Chosen Socio- Economic Methods in Evaluation of the Environment Preservation. Internal Report of the Institute of the Environment Formation. Warsaw (in Polish).

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S i l v e r , M. (1972) An Econometr ic Ana l ys i s o f S p a t i a l V a r i a t i o n s I n M o r t a l i t y R a t e s by Age and Sex; e d i t e d by V. Fuchs. Essays i n t h e Economics and HeaZth and Medical Care, NBER and Columbia U n i v e r s i t y P r e s s . New York.

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