AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

H. KITAAN EVALUATION MODEL OF THE LEVEL OF
EMERGENCY MEDICAL SERVICE IN SPARSELYPOPULATED AREAS
Hideyuki KITA
Professor
Department of Social Systems Engineering, Tottori University
Tottori, Japan(Received August 5, 2004)
In rural areas, services to support daily life are generally short and a large disparity exists from place to place. This study proposes an index tomeasure the level of emergency medical service, a minimum service to support daily life, at given locations. The required characteristics of the levelof service index are firstly discussed, and then an accessibility type index is proposed with holding the characteristics pointed out in the discussion.
By using this index, we develop a systematic method to find the sub-system of that improvement that contributes the most to raising the level ofservice. This method gives us the order of improvement over sub-systems under the restrictions of budget, time, and other resources. The usefulnessof the methodology is examined through a case study.
Key Words: Performance based design, Emergency medical service, Level-of-service, Rural areas, Network analysis

1. INTRODUCTION
Services to support daily life are generally few anda large disparity exists from place to place in rural areas.
Under the situation wih a high percentage of elderly
people in rural areas, emergency medical services are oneof the most important services for daily life. The role ofinfrastructure development is important in order to raise
the level of services and reduce the disparity.
Evaluation of infrastructure development has been
done mainly from the viewpoint of the supply side. However an evaluation from the user side, in other words “performance evaluation”, is more essential. For the supply
side evaluation, indices of output such as total distanceof road improvement and the number of community libraries are used, for example. For the user side evaluation, indices of outcome should be used, such as saved
travel time due to road improvement and the number ofvisitors or the number of books loaned.
This study proposes an index to measure the levelof emergency medical services, a minimum service tosupport daily life, at given places, and develops a systematic method to find a sub-system which can most efficiently raise the service level, or find the order of
improvement over sub-systems under the restrictions ofbudget, time, and other resources. In chapter 2, the re-quired characteristics of the level of service index are discussed firstly. Then, an accessibility type index is proposed whose characteristics are pointed out in the above
discussion. In chapter 3, following the clarification therelationship between the contents of improvement in the
sub-system level and the survival rate as an evaluation index of the total system, we develop a method to find thesub-system whose improvement contributes the most to
raising the level of service. The usefulness of the methodology is examined through a case study in chapter 4.
Chapter 5 concludes this study.

2. PROPOSED INDEX TO EXPRESS THE
LEVEL OF EMERGENCY MEDICAL SERVICE
2.1

Study review
The aim of emergency medical services is to save
lives. The survival rate on a point basis is therefore selected as the index to express the supply level of emergency medical services.
Currently used indices are divided into three groups.
The first one uses characteristics of a system component
to measure the level of service.
Emergency medical services have the following two
characteristics, (1) providing immediate medical care when
IATSS RESEARCH Vol.28 No.2, 2004 •13

TRANSPORT AND EMERGENCY MEDICAL RESPONSE SYSTEMS

needed, (2) the place for medical care is usually different from the scene. As a result of these characteristics,
accessibility to a hospital becomes an important factor
which influences the level of service. Accordingly, how
the accessibility relates to the survival rate is essential inevaluating an emergency medical system. This in turnimplies the necessity to quantify the accessibility. The
indices in the second group are to measure physical levelof accessibility expressed by distance or response time1, 2.
In the emergency medical service, however, thetime lag from time of the incident occurrence to the timeof arrival at a hospital is not linearly related to the survival rate. Eisenbelg et. al3 found a statistically significant relationship between these two by examining datafrom more than 600 cardiac arrests in the U.K. and arranging the data as a survival rate curve. These types ofindices are those in the third group. However, these indices are related to the supply side, so that the conditionsof medical facilities, which vary in time, are not be taken
into consideration. In addition, they assume only one levelof emergency medical care is given to a patient/injury before arriving at a hospital.
Swersey4 reviews a wide variety of past studies
about the deployment of emergency service units including emergency medical services.
2.2

Basic idea of this study
There exists three necessary conditions that thelevel-of-service index should hold. The first condition isthat the index can evaluate the level-of-service directly.
The supply level of emergency medical service has been
expressed by such indices as “the number of ambulances
deployed per km2” or “the number of doctors per ten thousand residents”5. The numbers of facilities and personnel for emergency medical services partly contribute to
the level of service, but are not a measure of the level ofservice itself.
There is a problem in comparing the situations under the different conditions by “unit area” or “unit number of population”. These problems originate fromlooking not to the essence of the service, but to a components of the supply system. Hence, such confusion could
be avoided if there is an index that expresses the level ofservice itself. From this point of view, an index of thelevel of service should be defined relating to the essenceof the service.
The second condition is that the index should bea point base index. Generally in mountainous areas, thedistance between hamlets is long because the hamlets arelocated linearly along valleys, so the level of emergency

14 • IATSS RESEARCH Vol.28 No.2, 2004

medical service differs greatly from hamlet to hamlet. The
arrival time of an ambulance to the scene varies from acouple of minutes to a couple of hours6. Clearly therefore,
the level of emergency medical service is highly dependent upon the location.
There is a question in using an average type index
for expressing the level of service with a big variance.
This is because the index must evaluate the level of service not on an area basis but on a point basis because of
the existence of locational disparity. A major interest ofa current or a future resident is placed on the disaggregate level of service at his/her residential location.
The third condition is that the index must be sensitive in improvement. The level of service at a reference
point is a function of both the accessibility from the reference point to the surrounding service points, and the quality of service at the service point. The level of service canbe raised by improving the transportation system foreasier access to/from the reference point to the service
point and/or upgrading the service facility to supply ahigher quality of service, for example. In addition, there
is an attempt that the supply side of the service also approaches the consumers. A mobile library, doctor’s house
call, and mail order with delivery service are good examples.
In the emergency medical service, faster conveyance of the patient by ambulance, upgrading the level of
medical care at medical facilities, and giving a higher
level of pre-hospital care during transportation to the hospital are effective improvements for raising the level ofservice. The level of service index must be sensitive
enough to the differentiate between alternative improvements and must reflect the change of “quality of life”
which is carried by the system improvements.
The index proposed in this study is formed of twoparts: estimated pre-hospital time after an incident occurrence taking the hospital choice into consideration, andestimated survival rate taking into account the existenceof some different levels of emergency medical care before arriving at a hospital. It means that this index evaluates an emergency medical system, as being acomprehensive system including both medical care andpatient conveying, from the view point of accessibility.
2.3

Estimation model of arrival and conveyance times
Patients/injuries who need emergency medical service are usually conveyed by ambulance. The arrival timeat the scene and conveyance time to a hospital dependon the running speed of the ambulance, the distance fromthe ambulance station to the scene, and the distance from

AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

the scene to the hospital. In spite of the expectation thatrunning speed depends on traffic and road conditions, forexample, road width, curvature, and traffic congestion
can be considered as constant regardless of these conditions, from the result of regression analysis using action
data. The running distance can be understood to be equal
to the road distance from the closest ambulance station
to the scene.
The conveyance distance varies depending on thelocation of the chosen hospital. Though many factors influence hospital choice, the dominant factors are the severity of the incident, the type of incident, and the timeof occurrence. Figure 1 shows a tree to estimate a chosen hospital by considering these influencing factors. In
this figure, “Severe Case” means an injury or disease thatneeds hospitalization for more than three weeks, “Minor
Case” means an injury or disease that does not need hospitalization, and “Intermediate Case” means those excluded from the above two types.
Based on this result, arrival time at a scene, ts, andconveying time, tc, can be estimated as,t s = d s / vo

(1)

tc = d c / vo + to(2)

where, ds is the road distance between a scene and theclosest ambulance station, dc is the road distance between
the scene and the hospital given by the hospital choice

H. KITA

tree in Figure 1, vo is the average speed of the ambulance,
and to is the average treatment time at the scene.
The estimated times show a good fit to those observed, and hence the proposed estimation model can betaken to have a good replication capability.
2.4

Estimation model of the beginning time of emergency medical care
Patients are usually conveyed to a hospital while receiving so called pre-hospital care from a basic life support unit (BLS), advanced life support unit (ALS), and/or doctor(s). The available treatment of care restricted bylaw varies in the above listed care levels, Figure 2 shows
an image of the relationship between the time length ofstages, time length under a certain care level, and the care
beginning time of each care level, “Care level” means astage at which a medical unit of a certain care level provides medical care to a patient, “Stage” means an action
component which composes a stage such as ambulancerunning from a scene to a hospital. In this example, timeshortening of any stage will contribute to the beginning
time of doctor’s care because the stages are connected inseries. The beginning time of care level, m, can be obtained by summing up the time length of preceding carelevels, 1, ..., m-1, as follows,
tk = tk − 2 + ∑m tk −1,m(3)

tk −1,m = max n [tk −1,m ,n ( s )]Surgery (Pm1)
Severe Case (Pk1)
Internal Medicine (Pm2 )Surgery (Pm1)

Daytime (Pn1 )D.H. (Pj1)(Pn2 )

D.H. (Pj1)

Night

Daytime (Pn1 )D.H. (Pj1)

Night(Pn2 )

D.H. (Pj1)

Daytime (Pn1 )D.H. (Pj1)
I.H. (Pj2)(Pn2 )

D.H. (Pj1)

NightIntermediate Case (Pk2)
Internal Medicine (Pm2 )(Pn2 )

D.H. (Pj1)
I.H. (Pj2)
D.H. (Pj1)

Daytime (Pn1 )I.H. (Pj2)

Night

Daytime (Pn1 )Night

Surgery (Pm1)
Minor Case (Pk2)
Internal Medicine (Pm2 )(Pn2 )

D.H. (Pj1)

Daytime (Pn1 )I.H. (P j2)(Pn2 )

D.H. (Pj1)Night

D.H. : Designated Hospital
I.H. : Undesignated HospitalFig. 1 Tree of hospital choice
IATSS RESEARCH Vol.28 No.2, 2004 •15

TRANSPORT AND EMERGENCY MEDICAL RESPONSE SYSTEMS

where tk-1,m means the m th stage in care level k-1. tk-1,m,n(s)means the n th concerning action, which must be completed by the beginning of the next stage, and the length
can be controlled by an improvement of sub-system, S.
2.5

Survival rate corresponding with a certain incident typeThis curve relates the survival rate with the beginning time of medical care is called the “survival rate
curve”. The shape of the survival rate curve varies withincident type. The curves are characterized by the degreeof steepness of its middle part and the time delay whensurvival rate becomes 0. Based on Cara7, a logistic curveis selected to represent a set of survival rate curves.
f i ,k (tk ) = 1 −tient, Pi,k, involved in an incident of type i at the beginning time of care, tk, is given as,
 f i ,k (tk )Π kk −'=11 {1 − f i ,k ', (t k ' ){ ( k ≥ 2)
Pi ,k = 
( k = 1)
 f i ,1 (t1 )This probability, Pi,k, also depends on the time of
day of incident occurrence, h, and the place of occurrence.
x, so that rewriting the survival rate as Pi,h,x,,k, the resultant survival rate after receiving the highest medical careof level K, is expressed as,k

Pi total, x ,h = ∑ Pi , h , x , k

(6)

k =1

1
1 + exp[− ai ,k (tk − bi ,k )]

(5)

(4)

where fi,k(tk) is the survival rate of a patient with incidentof type i, the care beginning time (of care level k) is tk,
and ai,k and bi,k are parameters.
Some survival rate curves with different incident
types are shown in Figure 2. Attention should be focusedon the big difference that exists in the sensitivity of thesurvival rate to the care beginning time between the
curves.
A point base index of service level
While being conveyed from the scene of the incident to a hospital, patients receive pre-hospital care by
several life supporting units that provide different levelsof medical treatment. The level of medical treatment isgenerally higher at later stages. The probability that thelife support unit with medical treatment of level k firstly
succeeds to save a life, is the probability that the life support units at earlier stages could not succeed in doing so,
and that the unit of level k can. The survival rate of a pa-

The probability of the incident occurring varies withthe type of incident and the hospital choice depends on
the time of the occurrence. Taking this into account, thepoint basis index is then defined as,
S ( x) = ∑∑ Pi Ph Pi,total
h ,x
i

(7)

h

The index value of an area with more than two reference points, is given by taking the summation of S(x)weighted by the population ratio of the area.

2.6

Survival Rate

1

0.5

0
Beginning Time of Medical CareFig. 2 Survival rate curves

16 • IATSS RESEARCH Vol.28 No.2, 2004

3. NETWORK ANALYSIS FOR SYSTEMIMPROVEMENT
3.1

Stages as a job unit
Similar to other systems, an emergency medical
system also consists of sub-systems. Because of budget
restrictions or other conditions relating to the system improvement, it is important to find a sub-system to be improved whose improvement will be the most effective inraising the level of emergency medical service in an area.
For such a purpose, the relationship between an improvement plan of a sub-system and the effect, resultant changeof the level of service, should be made clear.
An emergency medical system, as a total system
including the conveyance and medical services, consistsof many components such as scene, ambulance stations,
hospitals, heliports, ambulances, etc. The service suppliedby the emergency medical system can be broken down
into several job units such as a request to the fire/police
department, dispatching an ambulance to the scene, con-

AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

veying the patient from the scene to a hospital, and giving appropriate medical treatment to the patient at the hospital. We will call each of the job units a “stage”,
hereafter. Each stage is supported by several sub-systems
to perform its function. The combination of these subsystems such as the location of ambulance deployment,
the type of conveyance means, the medical level of a hospital, and the location of the hospital, determine the duration of each stage. By using this time length of eachstage, called “stage length” hereafter, we can obtain the
cumulative time length before providing a certain levelof medical treatment to the patient after the time of incident occurrence.
3.2

Network of stages
What is important in the emergency medical system is how fast the patient can receive adequate medical
treatment. Let us focus on shortening the time length ofthe longer stage which is comparatively easy to shorten.
Here, attention should be paid to the fact that the improvement of a stage does not necessarily mean the improvement of the total system. In this case, several stages work
simultaneously and the following stage can be started
only if all the preceding stages have ended.
Figure 3 outlines a typical process of an emergency
medical service. An arrow represents a stage and the direction shows the direction of time passing. The symbolof node “ ” denotes the node where the following stage
can start if one of the preceding stages has ended. The
beginning time of the following stage is, therefore, given
as the ending time of the earliest ended preceding stage.
The other symbol of node “ ” represents the node atwhich the following stage cannot start if all the stages
concentrated at the node have not ended. At a node of thistype, the beginning time of the following stage is given
as the latest end time of the preceding stage. (In the above
mentioned case, several stages work simultaneously.) In
such a case, an improvement of a sub-system, which relates only the stages and has no bearing on the beginning
time of the following stage, does not carry any improvement to the total system.
3.3

Critical path
A path composed of several consecutive stages,
where total stage length directly affects the time lengthof the total system, is hereafter called the “critical path”
in this study. This is a similar concept to those used in
the context of PERT, a technique for system optimization. By identifying the critical path, we can find which
stage dominates the time length of the total system. The

H. KITA

Scene to HeliportTransfer

Scene toHospital

Loading

Heliportto HospitalHeli-station
to Heliport

DemandScene toHeliport

DispatchCommand
Heliport
to Scene

Ambulance Station
to SceneScene
to HospitalFirst-aid& LoadingFig. 3 A network of stages

total system can be improved by improving the sub-system which supports the stage on the critical path.
The critical path can be found systematically as follows. The first step is to represent the emergency medical service as a network of the component stages. The
nodes are numbered from left to right. A stage is specified by the node numbers at both ends. Denote a stage,
Sl,m and the stage length, dl,m where l and m are the node
numbers of the beginning node and ending node, respectively, and l<m. The second step is to calculate the earliest node time of node l, tlE , and the latest node time ofnode m, tmE .
The earliest node time of node m, tmE, is definedas,t 0E = 0max t lE + d l , m( for δ = 1) 
 E Sl , m ∈St m = 
E
δ
t
+
d
(
for
=
2
)
min l

l ,m

∈
S
S
 l ,m(m = 0,1, …, n) , l < m

[
[

]
]

( m = 0)(m ≥ 1)(8)

where Sl,m ∈S shows that the stage Sl,m is a member ofthe system S, and tlE is the starting time of the stage
which precedes the stage starting at tmE. δ = 1 corresponds
to the node “ ” and δ = 2 corresponds to the node “ ”.
The earliest node time at the last node n, tnE , becomesthe ending time of the last stage, λ. The latest node timeof node l is defined as,
t nL = λ(l = n)LLt =(l ≤ n − 1)
min t m + d l , m l
S l , m ∈S
(l = n, n − 1,…, 0) , l < m

[

]

(9)

where tmL is the starting time of the stage which follows
the stage starting at tlL.
IATSS RESEARCH Vol.28 No.2, 2004 •17

These two node times are equal for some nodes andare not equal for remaining nodes. A critical path can be
defined as the path formed by the consecutive stages
while having the following relationship between the beginning and the ending nodes,
tlE + d l , m = tmL(10)

The stage length of a stage on the critical path isdenoted as τl,m , hereafter.
3.4

The stage to be improved
What should be done next to the critical path identification is to select the stage to be improved among thestages which compose the critical path. For this purpose,some evaluation indices are introduced. As stated earlier
in this study, the index for selecting a stage to be improved must strongly reflect the level of emergency medical service as essential. The author proposed the survival
rate of a patient as the essential index of the level of service8. The survival rates will also be used in this study as
the index of the level of emergency medical service. Indices which measure the efficiency of system improvement will be formed by taking this index of survival rate
and relating factors into consideration. The efficiency indices will be based on the degree of influence resulting
from an improvement of a stage on the survival rate. We
shall look back at the estimation process of the survival
rate in the next section.
3.5

The survival rate of a patient
Usually, patients are conveyed to the closest hospital with a sufficient level of care while receiving the
pre-hospital care by medical staff. The medical care staff
are classified into several classes based on their care level,
e.g. basic life support unit (BLS), advanced life support
unit (ALS), and doctor(s). The level of available treatment is restricted by law to staff with the care levels mentioned above. Figure 4 illustrates an example of therelationship among the stage periods, beginning time ofcare of a certain care level. An emergency medical service consists of several stages from the occurrence of anincident to the beginning of medical care by doctors. On
Figure 4, reduction of stage length of any stage contributes to shortening the time before they receive care fromdoctors. This means that all the stages shown here exist
on the critical path, in this case.
The point base index at x, S(x), is given by taking
the survival rate of a patient, Pi,h,xtotal formulated by,

18 • IATSS RESEARCH Vol.28 No.2, 2004

level of medical care

TRANSPORT AND EMERGENCY MEDICAL RESPONSE SYSTEMS

DoctorBasic Life Support

t0

t1

t2

t3

t0 : incident occurrence
t1 : reportt2 : turning out of ambulancet3 : arrival at the scene

t4

t5

t6

time

t4 : beginning of pre-hospital caret5 : arrival at a hospitalt6 : beginning of doctor’s caseFig. 4 Stages and the care levels

S ( x ) = ∑∑ Pi Ph Pi total, h, x(11)

Kita8, while taking into account the type of incident,
i , and the time of incident occurrence, h, which affects
the hospital choice.
3.6

Efficiency indices for system improvement
For selecting a stage to be improved from the stages
composing the critical path, introducing some criteria will
be useful. There exists many factors which should betaken into consideration for system improvement, e.g. thereduced time of stage period, the increase of survival rate,
improvement cost, technology, environmental impact,
public acceptance, etc. For simplicity, we take only thefollowing three factors into consideration, i.e. (1) increaseof survival rate, (2) reduced time length before providing a medical treatment, and (3) improvement cost.
Two indices, SD and SC, are introduced which aredefined as,
SD =∆S ( x )∆τ l , m

(12)

SC =

∆S ( x )Cl , m(13)

SD measures the sensitivity of reduced time length
on the survival rate, and SC measures the sensitvity of
improvement cost on the survival time. ∆S(x) is the increase of the survival rate at point x, S(x), ∆τl,m is the reduced stage length of the stage, sl,m, on the critical path,and Cl,m is the improvement cost due to the improvement

AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

H. KITA

Select a level of service index of EMS

Evaluate the level of service of EMS

Search a critical path of EMS

SapporoTottori

Choose a stage on the critical pathTokyo

Choose a sub-system supporting the stage

Osaka
Fukuoka
Improvement costof the sub-system

Increase of the levelof service by improving
the sub-system

Fig. 6 Eastern Tottori region

Efficient
?

No

Yes
A selected improvement plan of EMS

Fig. 5 The planning processof the sub-system corresponding with the stage sl,m. The
purpose of this approach is to find the stage which contributes the most to raising the level of service index, S(x),and to make an improvement plan for the sub-system supporting the extracted stage. Figure 5 shows the processof this approach.

4. CASE STUDY
4.1

Study area and the setting conditions
The region selected for this case study is the southern part of Eastern Tottori region (Figure 6), which consists of eight towns and villages. Low mountains prevailon the most part. The major roads are Route 53, runningfrom the north to the south, and Route 29 from north tosoutheast. Five hospitals, one is in Chizu town and theremaining four are in Tottori City, are designated as
emergency hospitals. One hospital, with an emergency
medical center, located in Tottori city can provide ahigher level of emergency medical care for patients/injuries with more severe conditions than the others. The
Eastern Tottori Department of Fire Defence supplies theambulance service. Four ambulance stations exist in the
study area, and another ambulance station close to thearea, which covers a part of the area. The speed of anambulance is assumed to be 60 km/h.
For simplicity, three kinds of incidents, i=1, 2, and3, are taken into consideration which correspond to “cardiac arrest”, “cease breathing”, and “excessive bleeding”,
respectively, for simplicity. Three levels of emergency
medical care, k=1, 2, and 3 are also considered in this study,
which correspond to basic life support (BLS), advanced
life support (ALS), and doctor support, respectively.
Hence, nine types of survival rate curve are used in total.
The parameters of survival curves, ai,k and bi,k, arefixed based on Cara7 as shown in Table 1. The incident
occurrence probability for each kind of incident, P1, P2
and P3, are assumed to be equivalent to the occurrence
probability of these diseases, and estimated as 0.187,
0.187, and 0.088, respectively9. Estimation of system improvement cost is based on the cost data shown in Yano10
and Yonekura11.
IATSS RESEARCH Vol.28 No.2, 2004 •19

TRANSPORT AND EMERGENCY MEDICAL RESPONSE SYSTEMS

that these places are not safe for people with a high possibility of having ceased breathing such as an asthmatic.

Table 1 Parameters of survival curve
aj,k

bj,k

k =1

k =2

k =3

k =1

k =2

k =3

i =1

2.76

3.45

4.61

5.0

4.0

3.0

i =2

0.92

1.15

1.38

15.0

12.0

10.0

i =3

0.46

0.55

0.69

30.0

25.0

20.0

The data analysis is carried out on a hamlet basis
called “koaza”. The number of reference points is 220 intotal in this area. If needed, the value of the level-of-service index at each point can be aggregated by taking theiraverage on a municipality basis.
4.2

Point base level of emergency medical service
and its disparity
Figure 7 shows the spatial distribution of the service level for the incident of type, k =2. It can be foundthat a rather big disparity in the level of service exists between reference points even though they are in the samemunicipality. This stems from the geographical characteristics of mountainous sparsely populated areas where
hamlets are located linearly along the valley. The importance of a point basis measurement can be understoodfrom this fact. People who are involved in this kind ofincident, cease breathing, at a place of high service level
denoted by the symbol denoted by . It can be said

4.3

System improvement 1
The solid line on Figure 8 shows the present levelof emergency medical service in each municipality. In
finding a sub-system to be improved, the time length of
the stages, namely the arrival time at the scene, and theconveyance time to the hospital as estimated by the
choice tree, were retrieved. From the result of the comparison, it can be found that the conveyance time is longer
than the arrival time in most cases (Figure 9). To reducethe conveyance time, there exists several planning alternatives such as setting up new medical facilities, road
improvement, introduction of a helicopter, and so on. A
helicopter supported conveyance system is examined in thisstudy. The helicopter station is assumed to be located at
the emergency medical center in Tottori city. By changing the conveyance means from ambulance to helicopter,the conveyance time was reduced (Figure 9) and the valueof the index went up in every municipality (Figure 8).
For the improvement of this helicopter supported
conveying system in raising the value of index, a key is
to make the departure time from the closest heliport tothe scene earlier. This departure time from the heliport
depends on both the arrival time of the helicopter (to theheliport) as well as the arrival time of the patient (to the

0.00 – 0.25
0.25 – 0.50
0.50 – 0.75
0.75 – 1.00
ambulance sta.
hospitalFig. 7 Spatial distribution of the service level

20 • IATSS RESEARCH Vol.28 No.2, 2004

AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

4.4

1
Present
With Paramedies

0.9

Value of Index

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Ct.

Mt.

Sv.

kat.

Kot.

Ft.
Ht.
Wt.
Towns and Villages

Fig. 8 Supply level of emergency medical service
40
35

Heliport to Hospital
Station to Heliport (dep.)

Time (min.)

30
25
20
15
10
5
0

Ct.

Mt.

Sv.

kat.

Kot.

Ft.

Ht.

Wt.

kat.

Kot.

Ft.
Ht.
Wt.
Towns and villages

40
35

Sence to Hospital
Station to Sence

Time (min.)

30
25
20
15
10
5
0

H. KITA

Ct.

Mt.

Sv.

System improvement 2“Increase in the number of ambulance stations”,“Increase in the number of medical facilities”, “road improvement”, “introducing a helicopter”, etc. are listed ascountermeasures to shorten the stage period of thesestages. Among them, the following three alternatives are
selected for analysis,
S1 : road improvement between the closest ambulance station and the scene;
S2 : road improvement between the scene and the closest
hospital;
S3 : introducing a helicopter for emergency medical service.
Road improvement can increase the traveling speedof an ambulance. Introducing a helicopter can raise theconveyance speed. It can be expected to shorten the stage
period of the stage “conveyance from the scene to thehospital” which is a component of the critical path.
The values of point base index S(xa) and S(xb) at
the points A and B are evaluated as 0.148 and 0.110, respectively, shown in Figure 10. Among the stage periodof each stages, the stage period of the stages “from ambulance station to the scene” and “from the scene to thehospital”, which exist on the critical path, are longer thanthe others.
Table 2 shows the estimation value of indices under the condition of the sub-systems being improved. In
Table 2, the alternative S1 carries the biggest improvement on the level of service index S(xa) at point A, andthe alternative S3 carries the biggest one at point B. This
result shows that the same alternative does not necessarily carry the same effect. This difference showed that thedegree of effect varies at points since it highly depends
on the geographical conditions. In the Mountainous area

Fig. 9 The time of stages

30
Time (min.)heliport) from the scene. The result of examinations,which consider relocation of the helicopter station to theformer and road improvement for the latter, show that theroad improvement from the scene to the heliport can reduce the time more and carries higher level of service than
relocation of the helicopter station. This can be interpreted
because there are many reference points far from the closest heliport in this area, a fact which highly affects theresult. Even though it was not examined in this study, developing new heliports may therefore also be effective.

40
S0{A}=0.148

S0{B}=0.110

Ambulance Station
to Scene
Scene to Hospital

20

10

0
point A

point B

Fig. 10 Stage length

IATSS RESEARCH Vol.28 No.2, 2004 •21

TRANSPORT AND EMERGENCY MEDICAL RESPONSE SYSTEMS

Table 2 Estimating value of indices(point A)
SystemS1

S2∆S(x) (×10 )

3.65

0.06

2.27

∆τl,m

1.14

2.93

13.55

Cl,m (×102 yen)

1.83

4.72

2.22

SD (×10–2 /min)

3.20

0.02

0.17

SD (×10–10 /yen)

1.99

0.01

1.02

S1

S2

S3

∆S(x) (×10 )

3.11

0.09

5.72

∆τl,m

1.37

2.74

15.83

–2

S3

(point B)
System–2

Cl,m (×102 yen)

2.20

4.41

2.22

SD (×10–2 /min)

2.27

0.03

0.36

SD (×10–10 /yen)

1.41

0.02

2.58

dealt with in this case study, a rather big disparity in geographical conditions exists from point to point, e.g. thedistance to the central place of the area and the terrain
along the road connecting them. This is the reason why
the orders of alternatives in their effects are in reverse at
the points A and B.
∆τl,m in Table 2 shows the amount of time by which
the stage length has been reduced. Since these stages areon the critical path, the reduced time length directly affects the total reduced time. The values corresponding to
the alternatives differ from each other. The increase ofS(x) per unit reduced time SD, also shows the existenceof a difference. Attention should be given to the resultthat an alternative with a bigger value of ∆τl,m is not necessarily an alternative with a bigger value of SD. The reason why the value of SD for the alternative S1 is bigger
than those for S 2 is because of the existence of nonlinearlity in the survival rate curve. The shape of the survival rate curve varies according to the types of incident
and the level of medical care. The effect of an alternative is high if the range of reduced time is in the part ofthe survival rate curve with high sensitivity, and is low
if it is in the part with low sensitivity. The time reduced
by an alternative is in the highly sensitive part in one case,the time reduced by the same alternative is in the low sensitive part in another case, depending on the point andthe type of incident. The improvement effect increases
if the range of reduced time overlaps more into the highly
sensitive part of the survival rate curve. As seen from22 • IATSS RESEARCH Vol.28 No.2, 2004

Table 2, the improvement effects differ from each otherincluding the reverse order of alternatives in ∆τl,m and∆S(x).
Comparison of S1 and S3 shows an example. S3gives a bigger improvement than S1 in time reduction at
both points of A and B. However, the improvement effect by S3 measured in the increase of the level of service is smaller than that by S1 at point A, and bigger atpoint B. This is because the sensitive part of the survival
rate curve corresponding to the doctor level in the medical care and type 2 in the type of patient overlaps therange of reduced time by S1 at point A, while it does notoverlap the range at point B. Similarly, in the comparison of S1 and S, the reason, why the improvement effectof S1 is bigger than S, is because the time reduction by S
greatly overlaps the range where sensitivity of the time
before commencing medical care on the survival rate ishigh, while the sensitivity is low in the range of time reduction by S2 .
In comparison to the average of SD at each point,
over all the reference points in the case area, the biggest
ones are due to S1. The reason can be understood because
the contribution of S1 on the improvement of the earlier
stage is bigger than those of S2 and S3, and thus, the earlier medical care given to patients is effective. This result underlines the importance of medical care given at
the earlier stages.
From the view point of index S(x), S1 should be selected as the best plan for system improvement for hamlet A, and S3 for hamlet B. However these plans need an
improvement cost, Cl,m , so that the cost should be taken
into consideration in the selection of planning alternatives.
By focusing on the increase of the level of service
per unit cost, SC, the alternative S1 for hamlet A and S3for hamlet B show the biggest value, respectively. If thebudgets for hamlets A and B are restricted to a certain
amount, S1 should be selected for hamlet A and S3 forhamlet B, respectively. In this case, the selected plans forhamlets A and B from the view point of maximizationof the level of service, S(x), are the same as those fromthe view point of cost-effectiveness. This is, however, aresult under the assumption that the effects of the alternative plans are independent from each other. In actuality, there often exists an “economy of scale” and/or“economy of scope” in an alternative such as the introduction of a helicopter system for raising the level of service at hamlet B and hamlet A.

AN EVALUATION MODEL OF THE LEVEL OF EMERGENCY MEDICAL SERVICE IN SPARSELY POPULATED AREAS

H. KITA

5. CONCLUSIONSREFERENCES

This study discussed the measurement of a level of
emergency medical service as a basic service for supporting life, and then proposed an index based on the survival
rate. The usefulness of the proposed index, the ability toindicate the level of service on a point basis and the sensitivity enough to evaluate alternatives for system improvement, etc., are demonstrated through the case study.
This index may be useful for cost-effectiveness analysis
by taking the cost needed for improvement into consideration, and also be applicable in evaluating investment
for enlargement of the service area of a hospital, for example.
By using this index, a methodology was developed
for choosing an improvement plan to raise the level of
emergency medical service as a basic life support service.
To sustain a certain level of life support service is essential to establishing sustainable communities in sparsely
populated areas. Several alternative plans exist from different fields of administration, such as construction,
health, transport, etc., for raising the level of service. The
execution of these plans tends to be done by different sections of government in parallel without enough coordination. Given a restricted budget in infrastructuredevelopment, selection of a more effective alternative
should be considered not within one section but across
many sections.
A comprehensive evaluation of the emergency
medical system on a point basis has been made possible
by using the proposed index. An opportunity was given
to select the most effective plan for system improvement
under budget restrictions, by taking into consideration
both the increase of survival rate and the costs resulting
from the improvements of subsystems. Some useful results were found through the case study, e.g. shortening
the stage period of an earlier stage is effective for raising the level of service, and an effective improvement
plan differs from point to point. The usefulness of the proposed methodology based on the stage periods is demonstrated for a detailed investigation that considers thelocation-specific conditions.
However, this study does not touch on how to establish priority of improvement to each hamlet. A question of this sort, which cannot avoid the discussion about
efficiency and equity, is for further study. A minimum
level of service to be supplied should be discussed in discussing sustainability of peripheral areas. This issue will
also be left for further studies.

1. Savas, E. Simulation and Cost-effectiveness Analysis in New York’s
Emergency Ambulance Service. “Management Sci.” 15 (12 B). (1969).
2. Volts, R.A. Optimum Ambulance Location of Semi-rural Areas. “Transp.
Sci.” l.5 (2). (1971).
3. Eisenberg,M.S., L.Bergner and A.Hallstrom. Cardiac Resuscitation in
the Community. “JAMA”. 241 (18). (1979).
4. Swersey, A.J. The Deployment of Police, Fire, and Emergency Medical
Units. in Pollock, S.M. (ed.): Handbook in OR & MS. l.6. pp.151-200.
Elsevier Science B.V. (1994).
5. Association of Welfare Statistics. Fundamental Statistics of Regional
Medical Plan. (1990). (in Japanese).
6. Tottori Prefectural Government. Annual Report on Fire Defense andDisaster Government. (1991). (in Japanese).
7. Cara, M. The Emergency Medical Service of Paris. “Bull. Acad. Natl.
Med.” 165 (3). (1981).
8. Kita, H., N. Hirosaka, and T. Morita. A Point Base Evaluation of the
Supply Level of Emergency Medical Service. Proceedings of Infrastructure Planning. “JSCE” 17. (1995). (in Japanese).
9. Ministry of Welfare. An Emergency Medical in 21 Century. Daiichi
Houki Shuppan. pp.14. (1991). (in Japanese).
10. Yano, T. On the National Subsidy System for Helicopter Use. “FirePrevention Research” 49. (1991). (in Japanese).
11. Yonekura, R. Construction Worcs. Sankai-do. (1995). (in Japanese).

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