日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）

原著論文

Evaluation of the Medical Service Environment for a Second Medical
Area Using Data Envelopment Analysis
Shinya MIZUNO†1, Haruka OHBA†1, Atsuo KAKEHI†2, Yoshikazu FUJISAWA†3 4
Abstract: Low birth rates and an aging society indicate that the aging population will continue to grow. Thus, medical services areof increasing importance. Under these circumstances, the administration has formulated regional medical vision by introducing acomprehensive nursing care security promotion law. This regional medical care initiative is considered a unit of secondary medicine
where independent medical services are required. However, regional disparity exists. We focus on data envelopment analysis(DEA), which is an operational research method, and apply it to large-scale typing. Feature amount extraction is indispensable forthe analysis of big data. DEA is not an average evaluation; however, because it evaluates a characteristic quantity, it is suitable forextracting feature quantity. In this research, to evaluate the health care provision capacity of the area, we first make a database of
all areas using open data. We then conduct basic analysis using this information and statistically evaluate the second medical area.
Using DEA, we obtain a reference set including 32 DMUs that are further clarified by their dependent sets. We show the processof acquiring the index to improve the medical services provided by a second medical area. It is possible for all second medical
areas to improve medical services in the same way that shows how to aim for an effective second medical area.
Keywords: DEA, second medical area, open data

area has a large influence on medical treatment trends for the

1. INTRODUCTION

whole medical area and a portion of the second medical area, it is

Currently, the aging population is expected to continue to growdifficult to construct a medical service organization. In theconsidering the declining birthrate and aging society. Therefore,

Medical Planning Guidelines, we clarify the idea of instituting a

medical services are of increasing importance. Under thesesecond medical area based on a certain population size, constantcircumstances, the administration of each prefecture mustpatient inflow, and outflow ratio. The second medical area is notformulate a regional medical care initiative [1] according to theestablished as an integrated area that provides medical treatment

MedicalEncouragement

pertaining to hospitalization to prefectures [4]. Second medical

Promotion Act [2]. In Japan, medical areas can be categorizedareas are adjacent to constituent areas, and change affects all

into three types. First medical areas provide health care that isneighboring second medical areas. Regional disparities are also

closely related to daily life. They are basically units of aincreasing in medical care; thus, a comprehensive assessment ismunicipality. Second medical areas are composed of a plurality

needed. Although second medical area evaluation focuses on aof municipalities and provide general health care and complete

certain subject in preceding research, a comprehensive evaluation

medical services. Third medical areas are basically prefecturalreflecting the actual circumstances of each second medical area

units; they provide special medical care that requires advanced

in recent years has not been conducted [5-9]. Geographicaltechnology [3]. This regional medical care initiative is a unit of

information on second medical areas is also considered importantsecond medical areas, and future autonomous medical services in[10,11].

Nursing

Care

Comprehensive

the second medical area are required. However, there are regional

We focus on data envelopment analysis (DEA), which is andisparities in the second medical area. Here, the second medical

operations research method and apply it to large-scale typing.

area is defined as a unit in which the plurality of municipalities

Feature amount extraction is indispensable for the analysis of big

composes the unit, and it is defined as a range within which daily

data [12]. DEA is not an average evaluation, but because it

medical services can be completed. Therefore, considering theevaluates a characteristic quantity it is suitable for extracting

actual circumstances of current second medical areas, regionalfeature quantity. The analysis platform that we construct is usedevaluation of the second medical area is necessary because of

to classify second medical areas to investigate the type oflimited medical resources.

categories produced. There are several DEA models. Cost

Reviews of second medical areas have been conducted many

reduction is emphasized in the Industry 4.0 framework and it istimes. In the case where the population size of the second medical

very important for Japan where population declines. Thus, we†1 Shizuoka Institute of Science and Technology(Correspondence Author: mizuno.shinya@sist.ac.jp)†2 Kogakuin University†3 Miyagi University†4 Tokyo Medical University
Received 15/Nov./2018
Accepted 28/Feb./2019ⓒ2019 Japan Social Data Science Society

27日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）
Table 1 Open data list
Name

SourceContents

National Land Numeral Information Medical Area Data [29]MLIT

Second medical area information
Population
Rates of elderly and young people

Municipalities of municipalities by statistics 2016 [30]MIC
Number of hospitals
Number of doctors

2014 patient survey [31]adopt the input-oriented model. Additionally, when the dataamount is large, to calculate the solution within the actual use
time, the linear model is preferable from the perspective of thecalculation amount. Therefore, we use the CCR model.

MIC

Estimated number of hospitalized patients

2. BASIC ANALYSIS OF SECOND MEDICALAREA INFORMATIONIn this section, we conduct a basic analysis of the items used in

DEA was proposed as a method to measure relative efficiency

DEA. We use these open data in Table 1. In this study, we target

from entity information [13]. At the time, the CCR model was

344 second medical areas.

the main mode, but the BCC model [14], additive model [15], andFig. 1 shows the relationship between the population and themultiplicative model [16,17] were also proposed. In addition tonumber of hospitalized patients. Using the regression line as anevaluating the entity, research that also incorporates judgment ofindex, the number of hospitalized patients varies. Similarly, Fig.

the evaluator has been proposed [18-21]. Due to the development

2 shows the ratio of the number of doctors to the population. Weof such a theory, DEA has been widely applied and is recognized

see that there is variation in the doctor rate in each second medical

as one method of data analysis used to visualize data. There arearea.

also many algorithms of DEA [22-25]. Many of these perform
DEA calculations on a single computer. To solve these problems,a method performs distributed processing of DEA [26] andanother method uses network technology [27]. Now that cloudcomputing is widespread, a DEA computing environment
suitable for these environments is necessary. A general-purpose
platform to utilize the DEA theory is effective in the current big
data environment [28].
In this research, to evaluation the health care provision

Fig. 1 Relation for Population and Number of hospitalized

capacity of the area, we first make a database of all areas using

patients

open data. In the analysis of local second medical areas, we will
evaluate all such medical areas using open data. We next conduct
basic analysis using this information and statistically evaluate thesecond medical area. To evaluate health care provision using
DEA, we use inpatient rate, the rate of elderly people, and patient
outflow rate as input items. For output items, we use doctor rate,
the rate of young people, and patient inflow rate. We use these to
analyze with DEA and elect second medical areas as good models.
From the dual problem, we calculate the direction ratio for the

Fig. 2 Relation for Population and Number of doctors

reference set and use it as a future index. When using DEA, it
becomes clear how to supplement the functions in regions with

Next, we check the inflow and outflow rates of hospitalized

low evaluations, because such evaluations become an index thatpatients for the second medical area. From Fig. 3, the patient

can be used to complement the disparity in second medical areas.

inflow rate is biased towards a low rate, but the outflow rate is
wide. The figure shows that it cannot respond within the second
medical area, and there is a lack of medical service capability.
Fig. 4 shows the population rates for those aged zero to 15ⓒ2019 Japan Social Data Science Society

28日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）
years and the population rate of people aged 65 years and over in𝑚each second medical area. In Japan, the declining birthrate and

s. t.

𝑠

− ∑ 𝜈𝑖𝑘 𝑥𝑖𝑗 + ∑ 𝜇𝑟𝑘 𝑦𝑟𝑗 ≤ 0,
𝑖=1

aging population is progressing, the graph shows that the rate of

𝑗 = 1,2, … , 𝑛

𝑟=1

myoung people is low, and the elderly population rate is high.

∑ 𝜈𝑖𝑘 𝑥𝑖𝑘 = 1
i=1

𝜈𝑖𝑘 , 𝜇𝑟𝑘 ≥ 0,

𝑖 = 1,2, . . , 𝑚; 𝑟 = 1,2, … , 𝑠[Dual Problem for 𝐷𝑀𝑈𝑘 ]
min

𝜃𝑘

s. t.

− ∑ 𝑥𝑖𝑗 𝜆𝑗𝑘 + 𝜃𝑘 𝑥𝑖𝑘 ≥ 0 ,𝑛𝑖 = 1,2, … , 𝑚

𝑗=1n∑ 𝑦𝑟𝑗 𝜆𝑗𝑘 ≥ 𝑦𝑟𝑘 ,𝑘 = 1,2, … , 𝑛

j=1

Fig. 3 Inflow and outflow rate of hospitalized patients

λjk ≥ 0,

𝑗 = 1,2, … , 𝑛

The above DEA calculation for 𝐷𝑀𝑈𝑘 is performed for all
𝑘 = 1, 2, . . . , 𝑛. When the value of the objective function is 1, it isefficient, and when the value is lower than 1, the efficiency isworse. The primary problem in DEA is the constraint condition
for each DMU, but in a dual problem it becomes a constraint
condition of individual input and output items. From theviewpoint of efficiency improvement, we will show improvement
information based on the solution to the dual problem.
3.2 Calculating the Reference Groups and Classification for
Fig. 4 Population rates of zero to 15 years of age and population
rate of people 65 years old and over

DMUs
In classification analysis platform, we perform large-scaleclassifications. To clarify the features of the DMUs, we calculate

3. ANALYSIS OF SECOND MEDICAL AREA
INFORMATION USING DEA

reference groups using the following process:(1)

Calculate an objective function of the primary problem andselect DMUs for which the value of the objective function

Using the classification analysis platform and proposed

is 1 as reference sets. Insert the target DMUs into theimproving plan, we analyze multiple elements using DEA [31-reference set table.

33]. We use the object features to perform an evaluation. In
particular, we use the CCR model [34], which enables us to treat
the task as a linear programming problem.
3.1 Formularizing the DEA CCR Model
The object the decision-making units (DMU) are denoted as
𝐷𝑀𝑈𝑗 (𝑗 = 1, 2, . . . , 𝑛). The 𝑖th input data element is 𝑥𝑖𝑗 (𝑖 =1, 2, . . . , 𝑚), and its DEA weight is 𝜈𝑖𝑗 . Similarly, the 𝑖th output(2)

For 𝐷𝑀𝑈𝑘 in (1) where the objective value of a DEA
problem < 1 , when the objective variables 𝜆𝑗𝑘 , (𝑗 =1, 2, … , 𝑛) of the dual problem are 𝜆jk > 0 , we treat
𝐷𝑀𝑈𝑘 as a subordinate set of 𝐷𝑀𝑈𝑗 and include them inthe subordinate set of that reference group.

3.3 Classification Database Structure
The classification database is constructed as shown in Fig. 5.

data element is 𝑦𝑟𝑗 (r = 1, 2, ..., s), and its DEA weight is 𝜇𝑟𝑗 .

Using this structure, it is possible to perform classification

The formula for calculating a 𝐷𝑀𝑈𝑘 (𝑘 = 1, 2, . . . , 𝑛) as ancalculations in the same way for any type of object. First, theobject is as follows.

information required for the classification is prepared in DMU
table and DMU elements table. Next, the results of the DEA for[Primary Problem for 𝐷𝑀𝑈𝑘 ]𝑠max ∑ 𝜇𝑟𝑘 𝑦𝑟𝑘
𝑟=1ⓒ2019 Japan Social Data Science Society

all DMUs are stored in the combination, result, and result relationtables. When DEA calculation is performed, the calculation result
uses the primary key of the combination table, and the primary29

日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）
problem calculation result is stored in the primary problem table

DMU.

and weight table. The result of the dual problem is stored in the
dual problem results table and 𝜆 table. A reference set is stored

Table 2 Reference numbers of subordinate DMUs

in the references table, and its subordinate set is contained in theNo. of Elements insubordination table.

reference set
Number of DMUs

5

4

3

2

1

9

122

144

36

1

4.3 Indicator acquisition process for improvement of
medical service provision
Here, we examine how to improve from the obtained DEA
analysis result.
4.3.1 Characteristics of elected reference set
We obtain a reference set including 32 DMUs. These 32 DMUs
Fig. 5 Classification Database Structure

selected as the reference set are characteristic and are second
medical areas for reference. However, four of them are

4. Evaluation of the medical service
environment for second medical area
Here, we conduct the evaluation of the medical service
environment for a second medical area using DEA. We calculate
the reference set using DEA and determine the second medical
area to serve as a model. Based on the model area, the second
medical area is divided into clusters.
4.1 Dataset used in DEA
We conduct an analysis using the following items:


Inputs (Inpatient rate, Elderly people rate, Inpatient outflow
rate)



Output (Doctor rate, Young people rate, Inpatient inflow
rate)
Here, the inpatient rate is the number of hospitalized patientsin each second medical area divided by the population. The young

unreferenced sets. Therefore, we consider 28 DMUs to bereferenced. 𝜆 is the reference rate from the dependent set to thereference set. The higher this value, the stronger the reference
value. The 𝜆 average is the sum of the weights for the target setof the dependent set divided by the reference number. The second
medical area with ID 274 has the highest 𝜆 average, 0.480.
However, the number of DMUs referring to ID 274 is 1, and it is
not a reference set widely affecting. So, consider ID 169 where
the average value of 𝜆 s is 0.291 and is 6th and the reference
number is 122, which is the 1st place. As shown in the Fig.6, theaverage number of input items (𝑥1 , 𝑥2 , 𝑥3 ) is small and it isexcellent. Also, the output items(𝑦1 , 𝑦2 , 𝑦3 ) are good,

especially young people rate, Inpatient inflow rate. The 32 areas
selected as the reference set for this study are shown in Appendix
A.

people rate includes those aged from 0 to 15 years and the elderly
people rate includes those aged 65 years and over in each second
medical area. Inpatient inflow and outflow rates are calculated forthe degree of inflow and outflow of the estimated number ofhospitalized patients in each second medical area in Table 1. The
doctor rate is the number of physicians divided by the population.
These data sets were analyzed in Section 2 (see Figs. 1 to 4).
In this case, we calculate using an input-oriented CCR model.
If we can lower the inpatient and elderly population rates, we can
expect that the medical service in the second medical area will
improve. Additionally, lowering the inpatient outflow rate will
benefit the second medical area. On the other hand, we believethat if the doctor rate, young people rates, and inpatient inflow
rate are high, medical services are being provided.
4.2 Second medical area evaluation using DEA

Fig. 6 Input output item of ID 169(Compared with average value that is bold line)

We perform the DEA calculation on 344 second medical areas.
Table 2 is a classification of the reference number of subordinateⓒ2019 Japan Social Data Science Society

30日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）
4.3.2 Principal component analysis of the reference set

Inpatient outflow rate x3 and output item Young people rate y2.

In order to grasp the tendency of the reference set, we carried out

Also, ID 16, 63 which is the reference set shows that Doctor ratea principal component analysis, leaving out areas where 𝜆 wasof the 1st output item y1 is excellent. ID 163 refers to these two

0. From Fig. 7, we can see that the weight of the input items wasreference sets with respect to this item. As can be seen from thehigh for principal component 1. The weights were as follows:

In Table 3, the ID 163 strongly refers to the ID 169. Thus, we see

inpatient rate: -0.50; elderly people rate: -0.37; and inpatientthat ID 163 should first proceed with the improvement process

outflow rate: 0.50; the inpatient rate and elderly people rate werewith reference to ID 169 widely.

in the same direction. The inpatient inflow rate of pc1 was also
0.44, and the inpatient flow rate was effective. In principal
component 2, the output items and weights were as follows:
doctor rate: -0.67; young people rate: 0.22; inpatient inflow rate:
0.38; number of references: -0.46; and 𝜆 average: -0.23. In thisanalysis, as seen in Appendix A.1, ID 169, ID 192, etc., wereexcellent for the input items, references increased, and it was anarea that was easy to reference. By category, the doctor rate andnumber of references were in a proportional trend, and thecorrelation coefficient was calculated to be 0.5. We found thatareas with high doctor rates tended to be model areas. Areas withhigh young population and patient inflow rates (located in theupper-right corner of the figure) were distinctive areas but weredifficult to reference.
Fig. 8 Comparison between ID 163 and reference sets

Table 3 The reference rate of ID 163

ID

Reference rate

16

0.091

63

0.187

169

0.504

5. CONCLUSION
In this research, we conduct a basic analysis for each item. We
show that there are many concerns in terms of providing medical
services for each second medical area. We get that currently theservice provision capacity of the second medical area varies.
Fig. 7 Result of principal component analysis

Although there are few areas with high inflow of patients, outflow
of patients occurs in many areas. This indicates that the medical

4.3.3 Improvement using reference set

service capability concentrates in a specific area. In many areas

Next, we consider the process by which the second medical area

the young generation rate is low, but the elderly population

utilizes the reference set to improve. As an example, the second

spreads at a high level. Then, to improve the medical service of

medical area with ID 163 refers to ID 16, 63, 169. The Fig. 7

the second medical area, we use DEA to calculate the referenceshows input output items of these four DMUs. The bold line is of

set as a future model. As a result, we obtain a reference set

ID 163, and it is understood that the second element (Young

including 32 DMUs that are further clarified by their dependent

people rate, 𝑦2 ) of the output item is very low. Since ID 169 is asets. Based on the obtained results, we show the process ofvalue superior to ID 163 in Inpatient outflow rate third in theacquiring the index to improve the medical services provided by

input item 𝑥3 , ID 163 strongly refers mainly to input item

a second medical area. This evaluation incorporates the youngⓒ2019 Japan Social Data Science Society

31日本ソーシャルデータサイエンス論文誌
第 3 巻 第 1 号（2019 年 3 月）
people rate and the elderly rate. It becomes a policy index of
population composition as well as medical service, using as amodel a second medical area that becomes a reference set. It is
possible for all second medical areas to improve medical services
in the same way that shows how to aim for an effective second
medical area.

ACKNOWLEDGEMENT
This work was a part of research outcomes supported by the
JSPS Research Grant (KAKENHI), number 16K06659 (Principal
investigator: Atsuo Kakehi).

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Appendix A The 32 areas selected as the reference set
ID

Name

4
16
19
20
21
28
38
49
52
54
59
63
71
75

Sapporo
Souya
Tokachi
KushiroNemuroMorioka
Sendai
Murayama
Shounai
Kenchuu
Iwaki
RokkouUtsunomiya
MaebashiHigashikazura
nanbu
Ichihara
Kuchuuoubu
Nishitama
Jouetsu
Ishikawachuu
ou
Suntoutagata
Fuji
Owarichuubu
Owaritoubu
Nishimikawak
itabu
Higashimikaw
a nanbu
Ootsu
Kouga
Izumo
Shimonoseki
Matsuyama
Kumamoto

96
103
104
111
133
140
168
169
176
177
181
185
190
192
238
260
274
307

Table A.1 Information on the 32 second medical areas selected as a reference set
Number of λ average
Inpatient
Elderly
Inpatient
Doctor rate
referencesrate
people rate outflow
rate
41.212 (134)20.6 (302)
2.2 (343)
343.8 (298)0.471
840.953 (224)26.38 (152)38.4 (73)1112.8 (4)0.196
31.119 (162)
24.95 (191)
5.9 (328)
578.1 (153)0.260
131.253 (127)25.49 (180)
6.2 (326)
615.2 (117)0.260
71.117 (164)22.91 (239)38.4 (73)1032.9 (5)0.216
1.128 (156)23.3 (229)
3.3 (339)
339.3 (299)34
0.283
0.758 (304)19.11 (321)
4.7 (335)
360.4 (290)18
0.278
1.1 (171)26.22 (160)
2.4 (341)
356.9 (293)2
0.119
0.952 (227)29.1 (94)
7.6 (317)
573.4 (159)00.000
0.888 (254)
21.98 (261)
8.1 (313)
549.5 (181)78
0.250
1.14 (153)
24.98 (189)
8 (314)611.2 (123)17
0.143
0.788 (291)
21.92 (264)
50 (22)1139.5 (3)51
0.228
0.86 (264)19.33 (318)18.3 (242)545 (188)74
0.215
0.882 (260)23.36 (227)28.5 (151)
227 (340)
2
0.069

Young
people rate

Inpatientinflow rate

0.017 (341)0.447 (266)0.17 (316)0.418 (270)0.976 (176)
0.891 (190)
0.051 (336)0.17 (315)0.568 (242)0.252 (294)13.667 (6)2.165 (107)13.956 (5)13.481 (7)12.7 (232)
2.8 (327)
3.5 (322)
11.2 (245)
1.2 (338)
23.4 (109)18.1 (163)
8.8 (268)
2.5 (330)
19.6 (148)
8.7 (270)
20.8 (137)31.7 (62)43.7 (20)

53

0.274

0.602 (340)18.6 (328)26.8 (171)639 (98)

1.575 (133)34.4 (46)

11
9
86
0

0.388
0.186
0.260
0.000

0.678 (328)0.752 (308)0.884 (257)
0.941 (234)

20.91 (291)
18.79 (327)22.83 (240)27.83 (125)32.3 (118)56.6 (8)26.7 (173)10.4 (299)586.6 (141)72.6 (344)622.3 (110)620 (113)

12.749 (10)1.989 (116)
0.107 (328)9.609 (22)28.9 (76)78 (1)
47.2 (10)
4.1 (316)

3

0.240

1.161 (145)

20.41 (306)

2.4 (341)

289.9 (321)0.549 (245)

19.9 (147)

14
122
67
56

0.229
0.291
0.159
0.193

0.757 (306)0.777 (300)0.68 (327)0.65 (330)

22.99 (236)22.01 (258)20.1 (310)19.5 (316)

10.3 (300)
19.4 (232)73 (3)
37.9 (78)494.5 (225)740.9 (46)1207 (2)281.6 (326)0.42 (269)
9.625 (21)1.366 (146)
1.591 (132)24.2 (105)18.5 (159)50.5 (6)61.8 (2)

27

0.296

0.623 (336)

16.14 (344)25.1 (183)681.2 (77)2.316 (94)19.6 (148)

100

0.388

0.922 (239)21.04 (289)

9 (309)594.4 (132)

1.247 (150)

11.5 (243)

1
91
0
0
1
10

0.029
0.194
0.000
0.000
0.480
0.107

0.918 (242)0.95 (228)1.05 (183)1.78 (30)
1.103 (170)
1.375 (104)20.38 (307)19.94 (311)
26 (167)
28.55 (110)22.77 (241)20.75 (297)24.9 (185)29.4 (142)
12 (292)
7.2 (319)
2.1 (344)
11.5 (295)282.5 (325)813.9 (26)221.3 (342)392.9 (279)309.5 (313)240.8 (339)

14.628 (1)5.461 (37)
14.23 (2)12.011 (13)0.448 (265)
0 (344)29.2 (75)31.8 (61)27 (86)6.6 (292)
14.6 (205)32.8 (54)ⓒ2019 Japan Social Data Science Society

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