There are different approaches to modeling health care demand-supply interactions according to the management problems of the different types of health care systems and to the struc- ture of existing information and its availability to modelers.
For example, in highly developed countries with private health care systems such as the US and the Netherlands, the modeling approach must incorporate specific aspects of the system. Due to a relative resource saturation, an absence of a national HCS planning body, and confidentiality of individual medical in- formation, the main research attention must focus on the short- term behavior of health care service management in an equilibrium situation. The modeler must take into account the possibility of a changing equilibrium in accordance with a changing resource level or environmental condition.
In countries with national health care systems that depend on the level of centralization, the aim of health care modeling consists of the creation of tools that can be used in HC planning
*
See DHEW (1978:122).f a b l o 7
.
Health care coverage status. pccording to type of coverage: United States. 1976 (Data are based o n household interviews of a sample of the civilian noninstitutionalized population)Health care coverage status
-. - - -- - I I
Number Cumulative
of persons number of Percent Cumulative
in persons i n of percent of
thousands thousands population population
NOTE: In order to avoid multiple counting of individuals, these estimates were derived b y assigning each individual to one coverage category only. Persons w;lh both private insurance and Medicare, for example, were placed i n the private insurance category. As a result. Medicare and Medicaid estimates do not correspond t o counts available from those programs.
- . .
Privoto hospital insurance1 ---,,---
Medicare coverage only*
.,--,--,,,,,,,..~~---
-. . - - -k5;dicoid coverage onlyJ --,,,,_,,,,,,, ,,--- . . - - - - - . . 1
Other programs only ---,,--.---,---
private hospital irlsuranco, but kind of coverage 'nknawn --,,
unknown if covered - ----,,-,-,,,,--,,--- . . - . . . . - - . Nocoveraoe ---,,,,,,,,-..---,,,-,-,-,--- . . . . . . . . . -
- -
SOURCE: DHEW (1978:403)
a Includes all persons with private hospital insurance coverage whether or not they have other coverage (e.9. Medicare) rs well.
'Includes persons Qver 65 years of age who have Medicare with no private coverage and persons under 65 years of q e who havo Medicare with n o other public or private coverage.
alncludes persons w l ~ o did not have private insurance or Medicare. and reported either (a) receipt of Medicaid services i n the previous ycar, or ( b ) eligibility for Medicaid as a reason for n o t having other coverage, or ( c ) receipt of benefit paymen:s under Aid to Fam~lies with Depecdent Children or Supplemental Security Income in the past ycar.
41ncludes military (Civilian Health and Medical Program of the 'Jniformed Services), Veterans Administrat:on, private surgical coverage only. and professional courtesy as reasons for holding no other type of public or private coverage.
. -. - - . . . - -
on regional or national levels. This leads to the study of not only the static (or equilibrium) situation, but also the dynamic behavior of the health care system.
We do not pretend to make a comprehensive analysis of
existing HCS models here, and shall mention only (Culyer et al.
1977), a bibliography of work done in English on health economics and IIASA publications (Fleissner and Klementiev, 1977, and
Shigan et al. 1979) which allows us to propose a possible classification of health demand-supply models (Figure 5). We would like to consider several approaches of HCS modeling which
illustrates the differences as well as the common features of health care management problems in various health care systems.
As mentioned above, HC modeling is based mainly on diffe- rences in the possible influences on demand-supply interactions and on differences in the structure of available information.
The differences in demand-supply interactions lead to a variation in the length of the planning period:
a) Short-term planning or b) Long-term planning
The differences in available information are:
a) Routine statistics
b) Routine statistics and periodical comprehensive studies
C) Linkage record studies: collection of medical information on an individual during his lifetime
In the framework of this paper, we would like to outline the certain directions of health care systems modeling related to the
features mentioned above.
4.1. Econometric Approach
An econometric approach usually is used for short- or
long-term planning (a), (b) and is based on routine statistics (a).
This approach falls into broad categories relating the allocation of resources between health care facilities to health care faci- lities themselves. The first problem is mainly tackled with
economic theory, using econometric methods to qualify relations in behavioral type models. Problems of management and effi- ciency within health care institutions are usually solved by modelers with operations research methods, where some objective
functions are optimized under certain restrictions (Rutten,1979).
In econometric modeling the different curves of health
services demand (linear, loglinear, semilogarithmic, logarithmic, double-logarithmic, polinomial, etc.) which describe resource demand as a function of different social variables and avail- able resources are used. Several models of this type of ana- lysis of the use of health care facilities in the Netherlands and the analysis of physician fees and care can be found in the doctoral thesis of Rutten (19781, in the publications of the Urban Institute, Hadley and Lee (1978), and in the monograph of Yett et al. (1979). Of course the concrete models are very different in terms of exogenous and endogenous variables, but in general they focus on the determination of the relation
where y and xi, i = - 1,n, are some specific variables. For ex- ample, when describing the level of primary care the following relation is used in Rutten (1978:46,48):
where PF1 : the patient flow towards the first level of care (measured as the number o f first visits to the general practitioner per 1000 publicly insured)
PCHO : a vector o f characteristics o f the publicly insured
CP : the number o f general practitioners per 1000 population (a proxy for the capacity of first level care)
DENS: the population density
PINS: the perccntaqe publicly insured o f the population
For a description of the patient flow from the first to the second level of medical care, a similar relation is used:
where PF2 : t h e p a t i e n t f l o w from t h e f i r s t t o t h e second l e v e l o f c a r e (measured a s t h e number o f r e f e r r a l s t o t h e s p e c i a l i s t p e r 1000 p u b l i c l y i n s u r e d )
PF1 : t h e p a t i e n t f l o w t o w a r d s t h e f i r s t l e v e l o f c a r e PCHl : t h e p a t i e n t c h a r a c t e r i s t i c s o f t h e p a t i e n t f l o w t o t h e
f i r s t l e v e l o f c a r e ( c h a r a c t e r i s t i c s o f PF1)
CP : f i r s t l e v c l c a p a c i t y : t h e number of g e n e r a l p r a c t i t i o n e r s p e r 1000 p o p u l a t i o n
SPECO: second l e v e l c a p a c i t y : t h e number o f s p e c i a l i s t s p r o v i d i n g o u t p a t i e n t c a r e p e r 1000 p o p u l a t i o n
DENS : t h e p o p u l a t i o n d e n s i t y
PINS : t h e p e r c e n t a g e p u b l i c l y i n s u r e d of t h e p o p u l a t i o n
The problem is to determine the function which is usually con- sidered as given with unknown parameters. These parameters can be found with the help of' least-squares techniques.
The difference between this approach and the one proposed by Reinhardt (1975), is the consideration of some of the utility
functions as characteristics of physician behavior; but in gene- ral, the modeling approach is much the same. Such an analysis is usually static and often does not include any health indices as econometric variables. As mentioned in DHEW (1976:9) it is clear that such models "cannot mirror the complex changes that are taking place in the health care systems today. What is re- quired is a generalized model of the health care system". An econometric analysis should be considered as an important and necessary step in the construction of dynamic health care demand- supply models. "The model should be comprehensive; it should be sensitive to the interaction of the variety of economic, cultural and demographic variables which affect the demand for health ser- vices" (DHEW, 1976:9).
4.2. Deterministic Dynamic Modeling
Deterministic dynamic modeling is used for the same planning aim (a),(b) as the econometric approach and is based not only on the routine statistics but also on periodical comprehensive studies (b). Routine medical statistics are in some way an extension of demographic statistics. They include such indices as sex, age, place of residence and also medical indices which reflect the health status of individuals. This is the reason why existing dynamic HCS models either include demographic sub- models or are extensions of demographic models that include
health status elements (see for example, Fleissner and Klementiev, 1977 and Shigan et al., 1979).
The main feature of such models is the consideration of the fact that the population can be classified in different groups for receiving health services. These groups can be distinguished by age,sex, income,type of insurance, type of disease, stage of disease, etc. For the case of HCS in the US, physicians are viewed as treating four types of patients:
1. Medicaid
2. Medicare assigned 3. Medicare non-assigned
4. Non-medicare; non-medicaid
as shown in Hadley and Lee (1978:9). These four groups are then aggregated into subgroups according to demographic classifica- tions such as age and sex. When the results of comprehensive studies as well as routine statistics are available, some "un- observable" categories can be introduced to the model to des- cribe the dynamics of the individual's behavior in the HCS.
In this case, in addition to demographic categories, it is possible to consider the following health categories:
--
Healthy--
Latent--
Out-patient--
In-patientThese categories may then be divided into subcategories, accord- ing to the type of disease, stage of disease, or type of service required [see for example Petrovsky et al. (19781, and Lave et al. (1974)l.
From the mathematical point of view, the dynamics of the population group can be equally described by a system of partial differential equations or by the ordinary difference equation.
A further example of this type of modeling (Zemach, 1970) con- siders the cost of personnel, building space, technological equipment, and health requirements for the individual. We are not going to deal with the detailed description of these models.
For the purpose of this paper, it is more important to emphasize the main problems which arise at the evaluation stage of such models.
The first problem is the identification of the rate of change from one category to another using annual routine data available in most countries. Using these data, one can deter- mine relatively easily the exchange rates and which model is appropriate for the implementation of such rates in order to allow us to forecast the size and extent of these population groups. However, if we consider this problem from a resource need and allocation point of view, we will encounter at least two problems. First, it is very difficult to estimate the tran- sition rates (among the health categories) as the function of resources used in given categories, and hence it is difficult to use such tools for the direct modeling of resource allocation.
Second, the same transition rates between the population cate- gories can be obtained (from annual data) for completely diffe- rent "individualn transition rates. This may lead to an in- correct estimation of resource needs, because the particular resource need strongly depends on the number of individual transitions from one type of service to another.
The latter problem is closely related to problems in social demography [Taeuber et al. (1978)l especially in the study of morbidity and multiregional migration. To overcome these diffi- culties, it is necessary to consider the possibility of stochastic
modeling which can take into account the behavior of indivi- duals and from this find the natural combination of data and a logical aggregation of results from linkage record studies.
4.3. Stochastic Dynamic Modeling
Stochastic dynamic modeling is used for long-term planning based on routine statistics and linkage record studies. As mentioned above, in many cases it is necessary to take into consideration the fact that each individual can change "groups"
many times during his lifetime. A person moves from one age group to another, he can be affected by different diseases, or he can be covered by different types of health insurance. All causes of movements from one group to another could be divided into two types: subjective and objective. The subjective
type includes such causes as the desire of the person to change groups, i.e. the type of health care service that he has. The objective type reflects the development of the individual's health status depending on the aging process or the stage of disease.
In developing a pathological analysis, there are several stages: healthy, latent, diseaseland death. Each individual could be allocated to one of these stages with the help of different methods. These methods can be divided into two groups.
--
The first method is the use of international classi- fications of diseases in order to divide the popula- tion into several subcategories after a classification has been made by multiphase screening, medical exami- nation, and laboratory testing. The precise list of the ICD three-digit categories would be included in the modelland since the ICD code is internationally accepted, it is a feasible approach for an interna- tional comparison, model-building process.--
The second method includes the use of a set of diffe- rent socio-economic, biologicalland other risk-factors in order to estimate m.athematically the probabilityof having a disease or dying and to classify the popu- lation into risk groups. But unfortunately this
approach, which is more accurate for specific regions and time, strongly depends on how many and which fac- tors are selected for classification. These factors could be very important for one locality and not so important for another, or they could be important for the present but not for the future.
Depending on the aging process, the development of illness, the appearance of new diseases, or the different risk-factors, individuals could move from one group to another in either di- rection, excluding the terminal groups (Figure 6).
---
HealthyCompensated Stage
---
Temporal Decompensation---
Stable Decompensation (disease)---
Terminal Stage of Disease Death1
. .
. . .>
TIMEFigure 6. The profile of an individual's health history.
Linkage record studies allow one to obtain statistics about all persons being considered in the analysis. This information can then be used to estimate the classification of the whole population into different groups over time.
What type of mathematical model should be proposed for a formal description of the real process of an individual's
health history as shown in Figure 6?
Taking into account two main features of this process, i.e. random moment of group exchange and piecewise trajectory, we inevitably come to the conclusion that such processes should be described by a so-called step-wise process. In fact, in the theory of social demography [Taeuber et al. (1978)l and in the modeling of social processes [Bartholomew (1973)1, the Markovian step-wise processes are widely used for description of population mobility. The necessary condition required to apply Markovian models is knowledge of transition probabilities.
It is one of the main tasks of mathematical modeling to define the probability properties using available sampling data. Let us consider an example [see also Yashin and Shigan (197811.
Denote by
St
the history of the individual's transitions, among the m health categories and the set of transition-intensity matrices { A }
,
whose elements depend on the un.known parameter 8, and accept one of the n possible values, with cer- tain a p r i o r i probabilities Pi. This parameter is chosen just to distinguish the different possible intensity matrices {Aij}. 8The question is how can we estimate the intensity matrix (e.g. the transition probabilities) from the history (linkage record study of individual) for a given time interval [oft].
It is possible to show that under the Markovian assumption, a p o s t e r i o r probability distribution n (t) = P(e=Bj/SO) t
,
whereEt
is the observed realization, can be~found j as the solution of the following equation:J
( 0 1
Tr,
( t 1 =Tr, (oI+lt I j
( s - )1
ACs! # (s- -
X0 6,- # 5s
ids
where
here T is moment of transition from one group to another, and i
bitj
= E(Ai 0 ./EO) t is the conditional expectation of intensity1 3
A .O.
.
We then have1 3
A similar equation can be obtained in more general, even non-Markovian cases. Using this approach, we can select the correct transition matrix. The comparison of different tran- sition matrices,which can be obtained for different resources of treatment in various regions, will allow us to obtain the real measure of resource efficiency and the dependence of ex- change rates on the resource supply in different regions in an aggregative model.
The consideration of this approach is only an example of how data can be used in individual health care demand-supply modeling. We would like to emphasize that different methods can be used in the creation of a stochastic dynamic model which will forecast population health tendencies by region, and thereby supply information that will aid in the allocation of health resources.and test several planning alternatives.
Unfortunately, a linkage record study is very expensive and difficult from the managerial point of view. That is why even in developed countries, there are not many examples of such ongoing permanent investigations. Nevertheless, models of this type are still beneficial when routine data are used
(Figure 7). Comparison of these indices and their distributions leads to the estimation of the correction coefficient which can then be used not only for building dynamic models of health care systems in specific regions, but also for the estimation of
health demand-supply interaction for other regions.
The general scheme of health care demand-supply interaction as it is now being studied at IIASA is shown in Figure 8. In addition, such a model allows us to estimate health care systems in regions other than those having linkage studies.
V A R I A B L E S V A R I A B L E S
/
number of outpatient visits per capitaLinkage
t-
number of consultations per capitaaverage length of stay in hospital
record study
- 9-
number of outpatientvisits per capita
\
number of laboratory tests per capita
- ,
K2- number of consultationsper capita
-1
Routine,
K3- number of laboratory statistics tests per capita--, KO- average length of stay in hospital
\
age/sex distribution ---r c age / sex distribution/
K = Coefficient for correction
Figure 7. Comparison of variables taken from comprehensive studies with official reports.
5 . CONCLUSION
In spite of many differences in organizing health care systems, there are some features that create a basis for the development of a common approach which can be applied to the modeling of health care systems. The advantage of this approach
is that for all countries, populations are divided into groups according to their health care needs and resources.
REFERENCES
Bartholomew, D.J. (1973) S t o c h a s t i c M o d e l s f o r S o c i a l P r o c e s s e s . 2nd ed. New York: Wiley.
Boldy, D. (1975) Some C o m p a r a t i v e I n f o r m a t i v e o n H e a l t h Care S y s t e m s i n D i f f e r e n t C o u n t r i e s and t h e A p p l i c a t i o n o f O p e r a t i o n a l R e s e a r c h . Report on the first meeting of the EURO Working Group: Operational Research Applied to Health Services. Exeter, 1-2 September.
Culyer, A.J., Wiseman, J., and A. Walker (1977) An A n n o t a t e d B i b l i o g r a p h y o f H e a l t h E c o n o m i c s . Martin Robertson &
Co. Ltd. London.
Davis, K., and L.B. Russel (1972) The s u b s t i t u t i o n o f H o s p i t a l O u t p a t i e n t c a r e and I n p a t i e n t C a r e . Review of Economics and Statistics. May: 54(2), p.109-200.
Fleissner, P., and A.A. Klementiev (1977) H e a l t h Care S y s t e m M o d e l s : A R e v i e w . RM-77-49. Laxenburg, Austria:
International Institute for Applied Systems Analysis.
Fuchs, V.R., and M.J. Kramer (1972) D e t e r m i n a n t s o f E x p e n d i - t u r e s f o r P h y s i c i a n s ' S e r v i c e s i n t h e U n i t e d S t a t e s
1 9 4 8 - 6 8 . Washington D.C.: US Department of Health,
Education and Welfare, National Center for Health
Services, Research and Development. DHEW, Publication NO (HSM) : December, p .6 3.
Gibson, R., and C. Fisher (1978) N a t i o n a l H e a l t h E x p e n d i t u r e s , F i s c a l Y e a r 1 9 7 7 . Social Security Bulletin 41 (7) :3-20.
Hadley, J., and R. Lee (1978) P h y s i c i a n s t P r i c e and O u t p u t D e c i s i o n s : T h e o r y and E v i d e n c e . Working Paper 9-998-8.
Final Report, Vol.111. Washington, D.C.: The Urban Institute. (April)
.
Helms, L.J., Newhouse, J.P., and C.E. Phelps (1978) Copauments and Demand f o r M e d i c a l C a r e : The C a l i f o r n i a M e d i c a i d E x p e r i e n c e . R-2167, February. Rand Corporation Report.
Also published in The Bell Journal of Economics, Spring 1978.
Lave, J., Lave, L.B., and S. Leinha-rd. (1974) Mode Zing t h e D e l i v e r y o f M e d i c a l S e r u i c e s . ( I n M . P e r l m a n , a d . ) The Economics o f Health and Medical Care: 326-351(44).
Lee, K. (ED) (1978) Economics and H e a l t h P l a n n i n g . London: