Evaluation Method of Equalization of Basic Medical Services from the Spatial Perspective: The Case of Xinjiang, China

Abstract

Protecting residents’ health and improving equality are important goals of the United Nations Sustainable Development Goals. The recent outbreak of COVID-19 has placed a heavy burden on the medical systems of many countries and been disastrous for the low-income population of the world, which has further increased economic, health, and lifelong inequality in society. One way to improve the population’s health is to equalize basic medical services. A scientific evaluation of the status quo or the equalization of basic medical services (EBMS) is the basic prerequisite and an important basis for realizing the equitable allocation of medical resources. Traditional evaluation methods ignore the spatial characteristics of medical services, mostly using the indicator of equal weight evaluation, which restricts the objectivity of the evaluation results. Given this, this research proposes a set of EBMS evaluation methods from a spatial perspective and takes the Xinjiang Uygur Autonomous Region of China (Xinjiang) as an example for studying the status quo of EBMS. This study puts forward a set of EBMS evaluation methods from a geospatial perspective and makes full use of spatial analysis and information theory techniques to construct a two-level evaluation indicator that takes into account the spatial characteristics of EBMS. The entropy weight method and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method have been used to reveal the current status quo of EBMS in Xinjiang to objectively reflect the differences in EBMS. When using the entropy and TOPSIS methods, the evaluation is always based on the data so that the results can more objectively reveal the medical resources available to the residents. Therefore, the government can realize a reasonable allocation of medical resources.

1. Introduction

The United Nations Sustainable Development Goals (SDGs) consist of 17 development goals to guide global development work from 2015 to 2030, which include ensuring a healthy lifestyle, promoting good health and well-being of people of all ages, and reducing inequality within and between countries. This is an important element in achieving SDGs. Access to basic medical services is one of the basic rights of citizens. Realizing the scientific and reasonable allocation of medical resources and maximizing their utility cost-effectively is an important goal of the public health and planning departments [1,2]. The EBMS is based on John Rawls’stheory of equity and justice, which refers to the fair and convenient access of all citizens to roughly equal basic medical services after removing the ability to pay factor, with the core of promoting equal opportunities and focusing on guaranteeing people’s access to fair basic medical services [3]. Therefore, scientific and objective evaluation of the equalization of basic medical services in various regions is an important basis for realizing the reasonable allocation of medical resources and achieving the equalization of basic medical services.

In addition, with the improvement of the level of social and economic development and the impact of sudden epidemics, people’s demand for medical and health services has continued to increase. During the COVID-19 pandemic, countries experienced varying degrees of utilization and availability of basic medical services [4,5]. Not only was medical equipment (e.g., ventilators) unevenly distributed, but basic health services (e.g., immunization) were also disrupted [6,7,8]. These disruptions have led other researchers to associate the lack of services with higher mortality rates among low-income groups [9,10,11]. In addition, China’s experience in fighting the epidemic also shows that the syndromic surveillance of fever, cough and other symptoms by primary medical institutions can effectively warn the community of COVID infection, especially in areas where nucleic acid testing laboratories are scarce [12,13]. These medical resource allocation problems have become barriers to achieving the SDGs [14,15,16]. It generates a situation in which healthcare resources such as diagnostic kits, drugs, and basic healthcare infrastructure were in shortage throughout the period, along with the negative impact on the socioeconomic system [16,17]. It is necessary to objectively evaluate the equalization of basic medical services in each region, and scientifically guide the allocation of government medical resources to ensure the robustness of the medical system in response to emergencies, so that everyone can have equal medical access opportunities. This is the foundation to ensure people’s basic health rights in response to the COVID pandemic [17,18].

1.1. Social Science

The social medicine field has long paid attention to the level of medical deployment and its influencing factors [17]. Related research evaluates the equalization of basic medical services by analyzing statistical data such as the number of hospitals, medical staff, hospital scale, etc. For example, R. Marten, D. McIntyre, et al. use life expectancy, maternal mortality ratio, under-five mortality rate, the prevalence of HIV in adults aged 15–49 years, physicians’ density, and other indicators to evaluate the progress of Brazil, Russia, India, China, and South Africa in EBMS [19]. R. Miao, X. Xiang, et al. use DEMATEL and information entropy to quantify the degree of mutual influence between system indicators and the differences in medical market performance, respectively, to obtain the objective index weight [20]. G. Yang, Y. Xue, et al. use the system generalized method of moments (SYS-GMM), mediation effect, and linkage effect to investigate the relationship among social organization participation, government governance, and the equalization of basic public services from 2007 to 2017 in China. The equalization level of basic public services in China is evaluated by analyzing the participation of social organizations and government governance behaviors in different periods, including research on the equalization of medical services [21]. H. Liu selected nine sample provinces in China by stratified random sampling, and their current situation of basic medical services’ equalization was evaluated by the TOPSIS method and the rank sum ratio (RSR) method. The equalization of basic medical services was evaluated by measures and dimensions of universal health coverage (including economic affordability, service availability, service attainability, and system effectiveness) proposed by the World Health Organization (WHO) [22]. From the perspective of studying the behavioral model of families’ use of health services, Anderson studied the relationship family characteristics and health service use, which is expected to facilitate the development of a more equitable distribution of health care consumption. Grossman also studied this from the perspective of health demand models [23,24].

1.2. Health Geography

The health/medical geography field has done many wonderful researches, such as the spatial organization of medical services or facilities, the relationship between the spatial distribution of medical services and people’s needs, etc. [25,26]. Furthermore, research allocation methods have been applied to health geography problems to establish the fundamental theoretical issues of whether the distribution of resources affects health outcomes [27,28,29,30,31], coverage of medical facilities, minimum travel time (distance), cost-effectiveness, etc. are the basis of geographic allocation studies [3,32,33]. Daisuke Shinjo, Toshiharu Aramaki, et al. examined the geographical distribution of healthcare resources, healthcare service provision, and interregional patient flow in Japan, to improve Japan’s healthcare policy [34]. Hong Wu, Xingbo Rong, et al. explored the impact of opening high-speed rails on the allocation level of urban medical resources and concluded that opening high-speed rails has significantly increased the allocation level of medical resources in the city [35]. Nael Aoun, Hirotaka Matsuda, et al. studied the relationship between travel time to a health center and variations in height for children less than five years of age in eastern Rwanda, and concluded that there was a significant and negative association between height-for-age z-scores and travel time to the health center [36]. In addition, some scholars focused on studying the accessibility of medical and health services in geographical space and examined the level of medical construction through analysis of accessibility, thereby reflecting the equalization of urban basic medical services [37,38,39,40,41,42,43,44,45,46]. The research of all medical service facilities considers many factors such as the hospital‘s grade, capacity, and facilities level [47]. Accessibility, as a key indicator to measure the spatial layout of public service facilities, can indeed effectively evaluate the spatial allocation of medical resources and services [27]. In the research on the influencing factors of healthcare utilization behavior in the social medicine field, the accessibility of medical facilities is mainly abstracted as Euclidean distance, and less consideration is given to the spatial structure of the urban or rural environment.

1.3. Current Limitations of Approaches

However, accessibility can only evaluate a part of the EBMS, such as the convenience of citizens’ access to medical services, which focuses on transportation accessibility and the spatial distribution of medical facilities [37,38,40,41]. The EBMS emphasizes that all citizens have access to roughly equal basic medical services in a fair and accessible manner. It requires consideration of factors including the number of people and their age structure, the scale, service radius, convenience (spatial layout) of medical institutions, etc. [48]. Therefore, accessibility cannot be a complete substitute for EBMS.

For the research of evaluation methods, some scholars use the factor analysis method, TOPSIS method, rank sum ratio method, and grey relational analysis method to calculate the degree of equalization of basic medical services [22]. After analyzing the literature, many scholars have different considerations of the indicator weight in the evaluation method. Some of them use the equal weight method to calculate, or use the analytic hierarchy process and expert experience method to weight the indicator, which has a certain impact on the objectivity of the evaluation result [49].

In general, many studies on the evaluation of the equalization of basic medical services are too one-sided, either lacking a spatial perspective or focusing too much on spatial relationships, without integrating the spatial as well as the quantitative features of medical resources.

1.4. Our Contribution

Compared with previous studies, this article fully considers the advantages and limitations of the research results on the equalization of basic medical services in social science and medical geography, constructs a two-level indicator evaluation system for the equalization of basic medical services from a spatial perspective, overlaying analyses the precise spatial distribution, service radius, and scale of medical institutions with the spatial distribution of residential areas and population (instead of only computing aggregates for regions), to comprehensively reflect the allocation level of medical institutions and the convenience of medical treatment for residents. This research is innovative in the perspective of analysis theory, using the entropy weight method and the TOPSIS method in information theory and statistics to ensure the objectivity of the equalization evaluation of basic medical services.

This article takes the Xinjiang Uygur Autonomous Region (hereafter referred to as Xinjiang), China as the empirical research object, and calculates and quantifies the level of equalization of basic medical services in each prefecture-level administrative region within Xinjiang. The results will provide a scientific reference and theoretical basis for guiding the government’s medical service allocation decisions and realizing the equalization of basic medical services throughout the autonomous region.

2. Study Area and Methods

2.1. Study Area

The choice of the Xinjiang Uyghur Autonomous Region as the study area is based on the following considerations: Firstly, Xinjiang is the largest province in China, and the area of it exceeds that of Alaska. The settlements in the province are very far apart, most of which are located in river valleys and oasis, separated by deserts and Gobi, which places high demands on the rationalization of medical resources. Secondly, Xinjiang is an economically underdeveloped region in China, and the level of medical services in this region lags behind other regions of China. Achieving the goal of equalization of basic medical services has become a huge challenge. Thirdly, Xinjiang is expected to become an important economic growth area in Central Asia. Promoting the equalization of basic medical services in Xinjiang will become an important part of achieving SDGs. Therefore, there is an urgent need to understand the disparity in the level of equalization of basic medical services among the various prefecture-level regions in Xinjiang, and in this way, the corresponding policy adjustments can be made in the 14th (2021–2025) Five-Year Plan for Basic Public Services in Xinjiang. In summary, the study area is defined as the 14 prefecture-level administrative regions (regions, autonomous prefectures, and prefecture-level cities) in Xinjiang. The 14 prefecture-level administrative regions involved in the study are shown in Figure 1.

2.2. Data Preprocessing

The study adopted the data of geo-information and sectors on the study area, such as surface coverage classification data, geographic factor data, population data, hospital data at all levels, health care worker data, health risk population data, and road network data. Among them, the geographic information data are derived from the Xinjiang Oasis Regional Geographical Conditions Monitoring Project (The Xinjiang Oasis Regional Geographical Conditions Monitoring Project collects the surface coverage and geographical elements of Xinjiang at two to three-year intervals, covering all the surface nature and human geographical elements such as hospitals, residential areas, roads, administrative divisions, etc. The average spatial resolution of the images is 1 m), population data, medical staff data, and health risk population data from Xinjiang Statistical Yearbook. The data sources are shown in

Table 1. Data adopted inventory.

Data Name	Source	Data Format	Time
Surface coverage classification data	2019 Xinjiang Oasis regional geographical situation monitoring data	.shp	December 2019
Geographic factor data	2019 Xinjiang Oasis regional geographical situation monitoring data	.shp	December 2019
Population data	Xinjiang Statistical Yearbook 2019	.xlsx	December 2018
Hospital data at all levels	2019 Xinjiang Oasis regional geographical situation monitoring data	.shp	June 2019
Health worker data	Xinjiang Statistical Yearbook 2019	.xlsx	December 2018
Health risk population data	Xinjiang Statistical Yearbook 2019	.xlsx	December 2018
Road network data	2019 Xinjiang Oasis regional geographical situation monitoring data	.shp	June 2018

.

According to the Xinjiang Statistical Yearbook 2019, the medical care in each prefecture-level region in Xinjiang is counted (See

Table A1. Basic medical conditions of all districts in Xinjiang.

Statistical Unit	Medical Institutions	Grade II Hospitals	Grade III Hospitals	Number of Sickbeds per 10,000 People	Medical Staff	Health Risk Population
Urumqi	1773	31	28	145	35,185	676,988
Karamay	77	4	1	69	3140	87,975
Turpan	433	9	1	62	3829	164,998
Hami	447	7	1	57	5175	137,786
Changji	1244	24	2	69	11,652	348,327
Bortala	462	8	0	54	3793	111,495
Bayingol	1011	20	3	77	10,828	312,154
Aksu	1485	17	0	57	10,689	663,449
Kizilsu	352	7	1	64	3619	170,796
Kashgar	3190	28	2	58	18,640	1,240,992
Hotan	1728	8	3	69	8439	616,029
Ili	1454	26	4	54	17,836	677,179
Tarbagatay	1132	19	1	59	7032	306,071
Altay	695	11	0	53	4845	159,854

in Appendix A for details). According to the “Hospital Hierarchical Management Standard of China”, research counts hospitals’ data of Grade I, II, and III (The Grade I hospital is a local hospital that provides medical, prevention, rehabilitation and health care services directly to the community. The Grade II hospital is a regional hospital that provides medical and health services across several counties and is a regional medical technology center. The Grade III hospital is a hospital that provides medical and health services across cities and is a medical technology center with comprehensive medical, teaching and scientific research capabilities).

Before starting the statistical analysis of EBMS, we must spatially distribute the population data and health risk population data for the calculation and evaluation of EBMS indicators. In this study, the population and health risk population were spatially processed by the pycnophylactic dasymetric mapping method using the Monte Carlo simulation (CITE). This is a stochastic method that can be combined with GIS to discretize population data onto a raster of 1 km*1 km size (or other grid sizes) [50]. Since the size of the raster is the same, the probability ${\mathit{P}}_{\mathit{i}}$ of assigning the data to a particular raster is calculated as follows according to the basic principles of probability statistics.

$${\mathit{P}}_{\mathit{i}}=\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{k}}}{{{\displaystyle \sum }}_{\mathit{i}=1}^{\mathit{m}}{\mathit{W}}_{\mathit{i}}^{\mathit{k}}}$$

The number of people assigned to a particular raster is:

$${\mathit{P}}_t=\frac{{\mathit{W}}_{\mathit{i}}^{\mathit{k}}}{{{\displaystyle \sum }}_{\mathit{i}=1}^{\mathit{m}}{\mathit{W}}_{\mathit{i}}^{\mathit{k}}}{\mathit{P}}_s$$

where ${\mathit{W}}_{\mathit{i}}^{\mathit{k}}$ is the weight of the $\mathit{k}$-th land use type in the $\mathit{i}$-th density zone; ${\mathit{P}}_s$is the total population; ${\mathit{P}}_t$ is the number of people in the raster. The method has been studied in depth in the literature [51,52,53]. Compared with the point-based interpolation method [54,55], the simple surface domain weighting method [56,57], the modified surface domain weighting method [50], and the maximization retention method (pycnophylactic) [58], this pycnophylactic dasymetric mapping method using CITE introduces urban land use, which is highly correlated with urban population distribution as the weight for the discretization of population data, and can discretize the population to rasters of different resolutions as needed, and for which the total population before and after discretization remains unchanged. It can meet the needs of urban micro-modeling for spatial change analysis of population [59].

The population, health risk population after spatialization is shown in Figure 2 (The enlarged version is shown in Appendix B Figure A1, Figure A2 and Figure A3). The scales of the Xinjiang regional map in this article (Figure 2 and Figure 9) are 1:5,500,000.

2.3. Method

The methods used in this research consist of the development of evaluation indicators, the entropy weight method, and the TOPSIS method.

The evaluation indicator system of equalization of basic medical service was constructed first, then the weights of each indicator of the entropy were adopted, and finally, the TOPSIS method was used to evaluate the level of basic medical service in each region.

2.3.1. Design of Comprehensive Evaluation Indicator System

(1)

Development of Evaluation Indicators

This study identifies two classes of indicators to characterize the equalization of basic medical services: the allocation level of medical institution and the convenience of medical treatment. The allocation level of medical institution refers to the allocation of medical institutions in a region in terms of grade, number, spatial distribution, population coverage, number of medical and nursing staff, etc. It is mainly used to reflect the fairness of medical resource allocation. The convenience of medical treatment refers to the time residents would have to travel to access medical services. The study distinguishes between different levels of healthcare facilities, correlates healthcare facilities with health-risk populations, and adds indicators that show how well healthcare facilities match the population they serve. Taking into account the results of the study on the equalization of basic health services in the field of medicine and healthcare, indicators such as the ratio of health care staff to the population covered and the average number of hospital beds have been added, which is one of the most important parameters in the calculation of accessibility and is therefore not presented separately. In addition, considering the spatial structure of urban traffic, this paper adopts path distance to measure the coverage of residential areas and populations by healthcare providers.

The research designed the evaluation indicator system which included 2 first-grade indicators (allocation level of medical institution, convenience of medical treatment) and 13 s-grade indicators. The allocation level of medical institution layer includes 11 indicators. The convenience of medical care is expressed in terms of accessibility and distance to the nearest medical path. Accessibility is the number of available hospital beds per capita within the travel radius of residential area, reflecting the ease of access to medical institutions [60]; proximity reflects the spatial layout of medical institutions. The system of indicators for the equalization of basic medical services is shown in

Table 2. Evaluation Indicator System for Equalization of Basic Medical Services.

First Indicator Layer	Secondary Indicator Layer
Allocation level of medical institution	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{residential} \mathrm{areas} \mathrm{within} \mathrm{hospital} \mathrm{service} \mathrm{radius} ({\mathit{D}}_1$)
	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{administrative} \mathrm{villages} \mathrm{within} \mathrm{hospital} \mathrm{service} \mathrm{radius} \left({\mathit{D}}_2\right)$
	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{residential} \mathrm{areas} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{Grade} \mathrm{II} \mathrm{hospitals} ({\mathit{D}}_3$)
	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{residential} \mathrm{areas} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{Grade} \mathrm{III} \mathrm{hospitals} ({\mathit{D}}_4$)
	$\mathrm{Population} \mathrm{coverage} \mathrm{within} \mathrm{hospital} \mathrm{service} \mathrm{radius} ({\mathit{D}}_5$)
	$\mathrm{Population} \mathrm{coverage} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{Grade} \mathrm{II} \mathrm{hospitals} ({\mathit{D}}_6$)
	$\mathrm{Population} \mathrm{coverage} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{Grade} \mathrm{III} \mathrm{hospitals} ({\mathit{D}}_7$)
	$\mathrm{Health} \mathrm{risk} \mathrm{population} \mathrm{coverage} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{hospital} ({\mathit{D}}_8$)
	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{health} \mathrm{risk} \mathrm{population} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{Grade} \mathrm{II} \mathrm{hospitals} ({\mathit{D}}_9$)
	$\mathrm{The} \mathrm{coverage} \mathrm{rate} \mathrm{of} \mathrm{health} \mathrm{risk} \mathrm{population} \mathrm{within} \mathrm{the} \mathrm{service} \mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{Grade} \mathrm{III} \mathrm{hospitals} ({\mathit{D}}_{10}$)
	$\mathrm{The} \mathrm{ratio} \mathrm{of} \mathrm{medical} \mathrm{staff} \mathrm{to} \mathrm{population} \mathrm{covered} ({\mathit{D}}_{11}$)
Convenience of Medical Treatment	$\mathrm{Accessibility} ({\mathit{D}}_{12}$)
	$\mathrm{Traffic} \mathrm{distance} \mathrm{to} \mathrm{nearest} \mathrm{medical} \mathrm{facility} ({\mathit{D}}_{13}$)

.

The hospital service radius is determined by the residents’ willingness to travel. In life, the first and most frequent choice of residents is with hospitals near their communities, of which the largest number are Grade I hospitals [61]. Grade I hospitals are generally built around communities and administrative villages, including community hospitals, township hospitals, village health clinics, and others. In the case of hospitals in the vicinity of residential communities, residents generally get services within a walking distance. The relationship between travel time and path distance using the ArcGIS traffic network analysis tool based on some researches [62,63,64] is shown in

Table 3. The service radius (time and path distance) based on hospital size.

Hospital Level	Time (min)	Path Distance (km)
Grade I hospital	15	1.2
Grade II hospital	9	6
Grade III hospital	36	24
Township health center	11.5	3.8

. The walking speed is set at 80 m/min (4.8 km/h), and the average drive speed (including peak periods) can be calculated based on the road type. For example, highway 80 km/h, national highway 60 km/h, provincial highway 60 km/h, municipal road 40 km/h, county road 40 km/h, and village road 20 km/h.

Therefore, the study set the radius of the residential areas served by the Grade I medical institutions involved in the indicator at 1.2 km, the radius of the residential areas served by Grade II hospitals at 6 km, and 24 km for those served by Grade III hospitals. The radius is 3.8 km for the medical institutions provided by administrative villages,.

(2)

The indicator value calculation

Statistical methods and spatial analysis methods are mainly used for the calculation of indicator values,. Spatial analysis methods include overlay, buffer zone, and traffic network analysis. The calculation methods for each indicator are shown in

Table 4. Equalization evaluation indicators and calculation method of basic medical service.

Indicators	Description of the Calculation Method	Unit	Indicator Meaning
${\mathit{D}}_1$	The ratio of the number of residential areas covered within the hospital’s service radius (1200 m) to the number of residential areas within the prefecture-level region.	%	Reflects the distribution and coverage of the hospital
${\mathit{D}}_2$	The ratio of the number of administrative villages covered within hospital service radius (3800 m) to the number of administrative villages within the prefecture-level region.	%	Reflects the distribution and coverage of the hospital
${\mathit{D}}_3$	The ratio of the number of residential areas covered within Grade II hospital‘s service radius (6000 m) to the number of residential areas within the prefecture-level region.	%	Reflects the distribution and coverage of Grade II hospitals
${\mathit{D}}_4$	The ratio of the number of residential areas covered within Grade III hospital‘s service radius (24,000 m) to the number of residential areas within the prefecture-level region.	%	Reflects the distribution and coverage of Grade III hospitals
${\mathit{D}}_5$	The ratio of the population covered within hospital’s service radius (1200 m) to the population within the prefecture-level region.	%	Reflects the situation of the health risk population served by hospitals.
${\mathit{D}}_6$	The ratio of the population covered within Grade II hospital‘s service radius (6000 m) to the population within the prefecture-level region.	%	Reflects the situation of the health risk population served by Grade III hospitals.
${\mathit{D}}_7$	The ratio of the population covered within Grade III hospital service radius (24,000 m) to the population within the prefecture-level region.	%	Reflects the situation of the health risk population served by Grade III hospitals.
${\mathit{D}}_8$	The ratio of the health-risk population covered within hospital‘s service radius (1200 m) to the health-risk population of the prefecture-level region.	%	Reflects the situation of the population served by hospitals.
${\mathit{D}}_9$	The ratio of the health risk population covered within Grade II hospital‘s service radius (6000 m) to the health risk population of the prefecture-level region.	%	Reflects the situation of the population served by Grade III hospitals.
${\mathit{D}}_{10}$	The ratio of the health risk population covered within Grade III hospital‘s service radius (24,000 m) to the health risk population of the prefecture-level region.	%	Reflects the situation of the population served by Grade III hospitals.
${\mathit{D}}_{11}$	The ratio of the total number of medical staff to the number of population per 10,000 people within the prefecture-level region	people/10,000 people	Reflects the matching status of medical staff and service staff.
${\mathit{D}}_{12}$	See Equation (3).		Reflects the opportunities and convenience of residents to enjoy medical services.
${\mathit{D}}_{13}$	The ratio of the sum of the transportation distance from each residential area to the nearest hospital to the number of residential areas within the prefecture-level region	m	Reflects the convenience of medical treatment for residents

In calculating individual indicators, all statistical elements within the coverage area shall not be counted twice or more, such as residential areas covered within the hospital’s service radius, administrative villages covered within the hospital’s service radius, the residential areas covered within the Grade II hospital‘s service radius, etc. Population and health risk population data are raster data processed by the pycnophylactic dasymetric mapping method using CITE (see Section 2.2 for details).

.

The accessibility indicators are calculated using a two-step floating catchment area (2SFCA), originally proposed by Radke J. and Mu L., an improvement compared with the earlier floating catchment method in terms of the considerations of both supply and demand [43]. In fact, 2SFCA is a spatial accessibility measure based on the idea of opportunity accumulation, using the principle of quantifying the facilities or resources accessible to residents within a set threshold range: the greater the number, the better the accessibility [44,65,66]. Therefore, the results can be used to evaluate the appropriateness of the allocation of services in a certain area [43,44,45]. Specific steps are as follows:

First, taking hospital j as the center, determine the time or distance threshold, search for all the residential points (residential area geographic centroids) k that fall within the search radius, and calculate the supply-demand ratio, as shown in Equation (1).

$${\mathit{R}}_{\mathit{j}}=\frac{{\mathit{S}}_{\mathit{j}}}{{{\displaystyle \sum }}_{\mathit{k}\in \left\{{\mathit{d}}_{\mathit{k}\mathit{j}}\le {\mathit{d}}_0\right\}}{\mathit{P}}_{\mathit{k}}}$$

(1)

${\mathit{R}}_{\mathit{j}}$ is the supply-to-demand ratio of health service at the location area $\mathit{j}; {\mathit{S}}_{\mathit{j}}$ is the size of supply at $\mathit{j}$, expressed in hospital beds’ number; ${\mathit{P}}_{\mathit{k}}$ is the size of demand at point $\mathit{k},$ expressed in population; ${\mathit{d}}_{\mathit{k}\mathit{j}}$ is the cost of access to health services between points k and j, usually expressed in terms of distance or time (distance used in this study, which is the average of the nearest distances that residents have to travel to reach a health point); ${\mathit{d}}_0$ is the search radius.

Second, centered on resident point $\mathit{i}$, searching for all medical points j that fall within the search radius and add up the services ${\mathit{R}}_{\mathit{j}}$ provided by all medical points to get the accessibility ${\mathit{A}}_{\mathit{i}}^{\mathit{F}}$ at the resident point $\mathit{i}$. (Equation (2))

$${\mathit{A}}_{\mathit{i}}^{\mathit{F}}={\displaystyle \sum }_{\mathit{j}\in \left\{{\mathit{d}}_{\mathit{i}\mathit{j}\le }{\mathit{d}}_0\right\}}{\mathit{R}}_{\mathit{j}}={\displaystyle \sum }_{\mathit{j}\in \left\{{\mathit{d}}_{\mathit{i}\mathit{j}\le }{\mathit{d}}_0\right\}}\frac{{\mathit{S}}_{\mathit{j}}}{{{\displaystyle \sum }}_{\mathit{k}\in \left\{{\mathit{d}}_{\mathit{k}\mathit{j}}\le {\mathit{d}}_0\right\}}{\mathit{P}}_{\mathit{k}}}$$

(2)

${\mathit{A}}_{\mathit{i}}^{\mathit{F}}$ is the accessibility of health service at point $\mathit{i}$; ${\mathit{d}}_{\mathit{i}\mathit{j}}$ is the time cost of access to health services between points i and j. The equation can be used to express the accessibility of health care providers of administrative regions after transformation, see Equation (3)

$${\mathit{D}}_{12}=\frac{\mathit{S}}{\mathit{P}}$$

(3)

Indicator ${\mathit{D}}_{12}$ is the accessibility of medical institutions in the prefecture-level region, $\mathit{S}$ is the product of the average number of hospitals covered within the service radius of each residential plot or administrative village and the average number of hospital beds, and $\mathit{P}$ is the average plot population size (per 10,000 people).

2.3.2. The Entropy Method

Entropy was first introduced by German physicist Crawus in thermodynamics, which was later applied to information theory, indicating uncertainty of things or issues. In information theory, information is a measure of the degree of order of a system and entropy is a measure of the disorder degree of a system, both equal in absolute value and opposite in sign [67]. In this study, the entropy weighting method is used to calculate the indicator weights for the equalization of basic medical services in each prefecture-level region, that is using the information given by the indicator matrix to calculate the indicator weights. The calculation steps are as follows:

Step 1: Establish a multi-attribute decision matrix A. Assuming that there are $\mathit{n}$ evaluation indicators (basic medical service equalization evaluation indicators), $\mathit{m}$ evaluation objects (basic medical service equalization situation in Xinjiang prefecture-level regions), and a multi-attribute decision matrix X made up of raw data:

$$\mathit{X}=\left[\begin{array}{c}{\mathit{X}}_{\mathit{i}\mathit{j}}\end{array}\right]=\begin{array}{c}{\mathit{A}}_1\\ {\mathit{A}}_2\\ ⋮\\ {\mathit{A}}_{\mathit{m}}\end{array}\left[\begin{array}{cccc}{\mathit{x}}_{11}& {\mathit{x}}_{12}& \cdots & {\mathit{x}}_{1\mathit{n}}\\ {\mathit{x}}_{21}& {\mathit{x}}_{22}& \cdots & {\mathit{x}}_{2\mathit{n}}\\ \cdots & \cdots & \cdots & \cdots \\ {\mathit{x}}_{\mathit{m}1}& {\mathit{x}}_{\mathit{m}2}& \cdots & {\mathit{x}}_{ \mathit{m}\mathit{n}}\end{array}\right]$$

(4)

Step 2: Establish the normalized decision matrix B. The second step requires that the decision matrix of step 1 be normalized. The procedure for normalization is outlined in Equation (5). To eliminate the influence of the different dimensions of each indicator on the equalization of basic medical service, it is necessary to normalize the decision matrix of step 1 as Equation (5) shown and get the normative decision matrix B. ${\mathit{r}}_{\mathit{i}\mathit{j}}$ represents the contribution of the $\mathit{i}$th prefecture-level region ${\mathit{A}}_{\mathit{i}}$ under the $\mathit{j}$th indicator.

$${\mathit{r}}_{\mathit{i}\mathit{j}}=\frac{{\mathit{x}}_{\mathit{i}\mathit{j}}}{{{\displaystyle \sum }}_{\mathit{i}=1}^{\mathit{m}}{\mathit{x}}_{\mathit{i}\mathit{j}}}$$

(5)

$$\mathit{B}=\left[\begin{array}{cccc}{\mathit{r}}_{11}& {\mathit{r}}_{12}& \cdots & {\mathit{r}}_{1\mathit{n}}\\ {\mathit{r}}_{21}& {\mathit{r}}_{22}& \cdots & {\mathit{r}}_{2\mathit{n}}\\ \cdots & \cdots & \cdots & \cdots \\ {\mathit{r}}_{\mathit{m}1}& {\mathit{r}}_{\mathit{m}2}& \cdots & {\mathit{r}}_{ \mathit{m}\mathit{n}}\end{array}\right]$$

(6)

Step 3: Calculate the entropy ${\mathit{E}}_{\mathit{j}}$ of the $\mathit{j}$th indicator, reflecting the degree of variability of indicator $\mathit{j}$.

$${\mathit{E}}_{\mathit{j}}=-\mathit{K}{{\displaystyle \sum }}_{\mathit{i}=1}^{\mathit{m}}{\mathit{r}}_{\mathit{i}\mathit{j}}\mathbf{ln}{\mathit{r}}_{\mathit{i}\mathit{j}}, \mathit{i} = 1,2,3,\dots ,\mathit{m} \mathrm{and} \mathit{j} = 1,2,3,\dots ,\mathit{n}$$

(7)

where $\mathit{K}=\frac{1}{\mathbf{ln}\left(\mathit{m}\right)}$, m is the number of prefecture-level regions, therefore, the value of ${\mathit{E}}_{\mathit{j}}$ is between 0 and 1. From Equation (7), it is clear that ${\mathit{E}}_{\mathit{j}}$ converges to 1 when the values of a certain indicator converge across prefecture-level regions. When ${\mathit{E}}_{\mathit{j}}$ is equal to 1, which means that indicator $\mathit{j}$ is the same for all prefecture-level regions, the indicator $\mathit{j}$ can then be excluded from the evaluation indicators. It can therefore be seen that the weighting factor of the indicator is determined by the size of the difference between the indicators for the equalization of basic medical services in all prefecture-level regions. Therefore, the ${\mathit{d}}_{\mathit{j}}$ (see Equation (8)) can be defined and introduced to represent the degree of consistency of the contribution of indicator $\mathit{j}$ to the equalization of basic medical services in each region, which can also be interpreted as the degree of diversification [68].

$${\mathit{d}}_{\mathit{j}}=1-{\mathit{E}}_{\mathit{j}}$$

(8)

Step 4: Calculate the weight ${\mathit{W}}_{\mathit{j}}$ of each indicator

$${\mathit{W}}_{\mathit{j}}=\frac{{\mathit{d}}_{\mathit{j}}}{{{\displaystyle \sum }}_{\mathit{j}=1}^{\mathit{n}}{\mathit{d}}_{\mathit{j}}}=\frac{1-{\mathit{E}}_{\mathit{j}}}{{{\displaystyle \sum }}_{\mathit{j}=1}^{\mathit{n}}\left(1-{\mathit{E}}_{\mathit{j}}\right)}, \mathit{j}=1,2,3,···,\mathit{n}$$

(9)

When ${\mathit{d}}_{\mathit{j}}$is 0, the $\mathit{j}$^th indicator can be excluded from the evaluation indicators, the weight ${\mathit{W}}_{\mathit{j}}$ of this indicator is 0, which means the condition is the same for all prefecture-level regions, therefore, as an indicator, it is meaningless for the evaluation.

2.3.3. The TOPSIS Method

The conceptual framework for the TOPSIS methodology was developed by Hwang and Yoon [69]. TOPSIS ranks the evaluation objects by sorting them based on their proximity to an idealized target. The procedure is as follows:

Step 1: The performance matrix set up in Equation (4) is normalized using Equation (10).

$${\mathit{X}}_{\mathit{i}\mathit{j}}=\frac{{\mathit{X}}_{\mathit{i}\mathit{j}}}{\sqrt{{{\displaystyle \sum }}_1^{\mathit{m}}{\mathit{X}}_{\mathit{i}\mathit{j}}^2}}$$

(10)

Step 2: Combined with indicator weight ${\mathit{W}}_{\mathit{j}}=\left({\mathit{w}}_1,{\mathit{w}}_2,\dots {\mathit{w}}_{\mathit{j}}\right)$, establish the weighted normalized matrix $\mathit{V}$:

$${\mathit{V}}_{\mathit{i}\mathit{j}}={\mathit{W}}_{\mathit{j}}\ast {\mathit{X}}_{\mathit{i}\mathit{j}}=\left[\begin{array}{cccc}{\mathit{v}}_{11}& {\mathit{v}}_{12}& \cdots & {\mathit{v}}_{1\mathit{n}}\\ {\mathit{v}}_{21}& {\mathit{v}}_{22}& \cdots & {\mathit{v}}_{2\mathit{n}}\\ \cdots & \cdots & \cdots & \cdots \\ {\mathit{v}}_{\mathit{m}1}& {\mathit{v}}_{\mathit{m}2}& \cdots & {\mathit{v}}_{ \mathit{m}\mathit{n}}\end{array}\right], \mathit{i} = 1,2,3,\dots ,\mathit{m}, \mathit{j} = 1,2,3,\dots ,\mathit{n}$$

(11)

Step 3: According to the normalized matrix, use Equations (12) and (13) to determine the ideal best solution (extreme performance on each indicator) ${\mathit{V}}_{\mathit{j}}^{+}$ and ideal worst solution (reverse extreme performance on each indicator)${\mathit{V}}_{\mathit{j}}^{-}$ [70].

$${\mathit{V}}_{\mathit{j}}^{+}=\mathit{m}\mathit{a}\mathit{x}{\mathit{V}}_{\mathit{i}\mathit{j}},\mathit{j}=1,2,3,\dots ,\mathit{n}$$

(12)

$${\mathit{V}}_{\mathit{j}}^{-}=\mathit{m}\mathit{i}\mathit{n}{\mathit{V}}_{\mathit{i}\mathit{j}},\mathit{j}=1,2,3,\dots ,\mathit{n}$$

(13)

${\mathit{V}}_{\mathit{j}}^{+}$ is the maximum value of indicator $\mathit{j}$, and ${\mathit{V}}_{\mathit{j}}^{-}$ is the minimum.

Step 4: For the basic medical service situation ${\mathit{V}}_{\mathit{i}}$ of prefecture No.$\mathit{i}$, Equations (14) and (15) can be used to calculate the Euclidean distances of ${\mathit{V}}_{\mathit{i}}$ with the ideal best solution and the ideal worst solution. Equation (16) can give the basic medical service situation composite indicator ${\mathit{P}}_{\mathit{i}}$ of region No.$\mathit{i}$.

$${\mathit{S}}_{\mathit{i}}^{+}=\sqrt{{\displaystyle \sum }_{\mathit{j}=1}^{\mathit{n}}{\left({\mathit{V}}_{\mathit{j}}^{+}-{\mathit{V}}_{\mathit{i}\mathit{j}}\right)}^2}$$

(14)

$${\mathit{S}}_{\mathit{i}}^{-}=\sqrt{{\displaystyle \sum }_{\mathit{j}=1}^{\mathit{n}}{\left({\mathit{V}}_{\mathit{j}}^{-}-{\mathit{V}}_{\mathit{i}\mathit{j}}\right)}^2}$$

(15)

$${\mathit{P}}_{\mathit{i}}=\frac{{\mathit{S}}_{\mathit{i}}^{-}}{{\mathit{S}}_{\mathit{i}}^{+}+{\mathit{S}}_{\mathit{i}}^{-}}$$

(16)

The value of ${\mathit{P}}_{\mathit{i}}$ is between 0 and 1, and the smaller the ${\mathit{S}}_{\mathit{i}}^{+}$, the smaller the distance between the primary care equalization situation in the area and the idealized best solution, and, therefore, the larger the ${\mathit{P}}_{\mathit{i}}$; conversely, the smaller the ${\mathit{S}}_{\mathit{i}}^{-}$, the smaller the distance between the primary care equalization situation in the area and the idealized worst solution, and consequently, the smaller the ${\mathit{P}}_{\mathit{i}}$.

3. Results

We calculated the value of each indicator according to the constructed evaluation indicator system of equalization of basic medical services, the weight of each indicator, and finally used the TOPSIS method to analyze the equalization of basic medical services in each area in Xinjiang.

3.1. Result of Indicator Value Analysis

3.1.1. Allocation Level of Medical Institution

According to the basic medical service equalization indicator design in Table 2, this research sets various medical institutions as the center and uses buffer analysis to calculate the coverage of residential areas, coverage of administrative villages, population and health risk populations within the service radius of hospitals in various administrative regions of Xinjiang. The indicator values of the allocation level of medical institution are obtained in

Table A2. The coverage of residential areas, administrative villages, population, health risk population, and the proportion of medical staff within the service radius of medical institutions in various administrative regions of Xinjiang.

Statistical Unit	${\mathit{D}}_1$	${\mathit{D}}_2$	${\mathit{D}}_3$	${\mathit{D}}_4$	${\mathit{D}}_5$	${\mathit{D}}_6$	${\mathit{D}}_7$	${\mathit{D}}_8$	${\mathit{D}}_9$	${\mathit{D}}_{10}$	${\mathit{D}}_{11}$
Urumqi	73.78	76.49	91.86	97.18	54.71	81	92.62	54.66	80.96	92.58	131.82
Karamay	42.64	67.91	76.14	62.94	27.2	60.62	56.09	27.25	60.74	55.9	106.15
Turpan	66.16	32.08	87.88	0	19.97	44.11	0	20.03	44.22	0	58.63
Hami	68.4	40.08	77.08	82.99	32.52	50.03	62.55	32.57	49.99	62.36	83.89
Changji	70.76	34.04	81.2	48.3	27.36	40.16	27.29	27.34	40.13	27.32	82.49
Bortala	56	32.67	80.67	0	24.12	34.62	0	24.34	34.86	0	76.8
Bayingol	47.92	30.4	80.21	14.58	24.95	54.1	22.95	25.01	54.17	22.92	77.41
Aksu	80.36	12	91.07	0	18.61	37.99	0	18.65	38.03	0	42.24
Kizilsu	63.83	17.99	91.49	38.3	18.02	39.36	26.88	17.93	39.41	26.95	60.68
Kashgar	76.86	20.91	90.91	47.11	24.73	39.3	21.6	24.69	39.33	21.64	41.53
Hotan	80.22	19.97	45.05	41.76	15.38	12.85	35.74	15.39	12.85	35.67	37.37
Ili	60.35	32.81	84.57	60.35	26.32	44.63	38.85	26.24	44.62	38.95	59.27
Tarbagatay	67.84	15.58	73.47	16.43	26.74	40.13	11.71	26.66	40.1	11.72	66.88
Altay	67.86	12.91	89.29	0	24.17	34.36	0	24.01	34.26	0	71.69

. Figure 3 shows the histograms of indicator values for the allocation level of medical institutions in various prefecture-level regions.

In Xinjiang, the average coverage of residential areas within the hospital’s service radius is 68.41%. The prefecture-level administrative regions with higher coverage are Aksu, Hotan, and Kashgar, with coverage between 76.86% and 80.36%. The average coverage of administrative villages within the hospital’s service radius is 27.31%. The prefecture-level administrative regions with higher coverage are Urumqi and Karamay, with coverage rates of 76.49% and 67.91%, respectively. The average coverage of residential areas within the service radius of Grade II hospitals is 84.78%. The prefecture-level administrative regions with higher coverage are Urumqi, Aksu, Kizilsu, and Kashgar, with coverage between 90.91–91.86%. The average coverage rate of residential areas within the service radius of Grade III hospitals is 61.86%. The prefecture-level administrative regions with higher coverage rates are Urumqi and Hami, with respective coverage rates of 97.18% and 82.99%.

The average population coverage rate within the service radius of prefecture-level administrative district hospitals is 27.08%. The prefecture-level administrative districts with higher coverage rates are Urumqi and Hami, with coverage rates of 54.71% and 32.52%, respectively. The average population coverage rate within the service radius of Grade Ⅱ hospitals is 43.70%. The prefecture-level administrative districts with higher coverage rates are Urumqi and Karamay, with coverage rates of 81% and 60.62% respectively. The average population coverage rate within the service radius of Grade Ⅲ hospitals is 31.42%. The prefecture-level administrative region with the highest coverage rate is Urumqi, with a coverage rate of 92.62%.

The average coverage rate of people with health risks within the hospital service radius is 26.89%. The prefecture-level administrative regions with relatively high coverage rates are Urumqi and Hami, with coverage rates of 54.66% and 32.57%. The average coverage rate of people with health risks within the service radius of Grade Ⅱ hospitals is 43.31%. The prefecture-level administrative regions with higher coverage rates are Urumqi and Karamay, with coverage rates of 80.96% and 60.74% respectively. The average coverage rate of people with health risks within the service radius of Grade Ⅲ hospitals is 31.06%. The administrative regions with higher coverage rates are Urumqi and Hami, with coverage rates of 92.58% and 62.36% respectively.

3.1.2. Convenience of Medical Treatment

In the research, we take residential areas and administrative villages as centers to calculate the number of medical institutions available for residents within the travel radius of residential areas and administrative villages as well as the distance between nearby medical treatments, by using buffer zone analysis and traffic network analysis. The accessibility of medical institutions in each statistical unit can be calculated according to Equation (3). The parameter values for calculating accessibility refer to

Table A3. Parameters for calculating the accessibility of medical institutions in Xinjiang.

Statistical Unit	Average Number of Hospitals within the Residential Areas‘ Service Radius (1200 m)	Average Number of Hospitals within the Administrative Village Service Radius (3800 m)	Number of Residential Areas	Number of Administrative Villages	Population (10,000 People)
Urumqi	3.16	5.58	1473	1021	222.26
Karamay	0.71	2.72	197	134	30.77
Turpan	2.35	1.65	198	240	63.34
Hami	1.85	3.66	290	247	55.94
Changji	2.27	3.18	623	642	139.37
Bortala	2.13	2.07	150	300	47.85
Bayingol	0.76	0.96	97	601	124.21
Aksu	2.71	0.77	149	1250	256.17
Kizilsu	1.06	0.53	47	289	62.45
Kashgar	3.11	1.96	282	2604	463.38
Hotan	2.27	1.27	91	1517	253.06
Ili	1.44	3.63	543	894	293.06
Tarbagatay	1.26	0.55	522	918	99.25
Altay	0.96	0.25	76	609	65.95

in Appendix A, and the indicator values of medical convenience refer to

Table A4. Indicator of equalization of basic medical services and convenience of medical treatment in all districts.

Region\Indicator	Accessibility	Distance of Nearest Medical Treatment
Urumqi	1.42	1.87
Karamay	0.25	2.62
Turpan	0.17	3.14
Hami	0.3	2.05
Changji	0.34	1.84
Bortala	0.21	2.43
Bayingol	0.07	1.82
Aksu	0.11	4.02
Kizilsu	0.05	2.77
Kashgar	0.18	1.06
Hotan	0.16	1.07
Ili	0.13	1.87
Tarbagatay	0.15	2.25
Altay	0.07	4.53

, including accessibility and nearest medical transportation distance, as shown in Figure 4.

The average accessibility value of residents to medical institutions is 0.26 in Xinjiang. Urumqi, Changji, Hami, and Karamay have the best accessibility, with an accessibility value between 0.25 and 1.42. On the contrary, the poorest accessibility appears in Bayingol, Altay, and Kizilsu, with an accessibility value between 0.05 and 0.07.

The average travel distance for the nearest medical treatments in all districts of Xinjiang is 2.01 km. Among them, Urumqi, Changji, Bayingol, Kashgar, Hotan, and Yili have shorter medical distances, ranging from 1.06 to 1.87 km.

3.2. Indicator Weight Calculation

According to Equations (4)–(9), the weights of the equalization indicator of basic medical services in each district of Xinjiang can be calculated, referring to the indicator data of Table A2 and Table A4.

The decision matrix (

Table 5. Standardized decision matrix.

Indicator\Region	D1	D2	D3	D4	D5	D6	D7	D8	D9	D10	D11	D12	D13
Urumqi	0.080	0.172	0.081	0.191	0.150	0.132	0.234	0.150	0.132	0.234	0.132	0.391	0.056
Karamay	0.046	0.152	0.067	0.123	0.075	0.099	0.142	0.075	0.099	0.141	0.106	0.070	0.079
Turpan	0.072	0.072	0.077	0	0.055	0.072	0	0.055	0.072	0	0.059	0.047	0.094
Hami	0.074	0.090	0.068	0.163	0.089	0.082	0.158	0.089	0.081	0.157	0.084	0.083	0.061
Changji	0.077	0.076	0.071	0.095	0.075	0.065	0.069	0.075	0.065	0.069	0.083	0.094	0.055
Bortala	0.061	0.073	0.071	0	0.066	0.056	0	0.067	0.057	0	0.077	0.059	0.073
Bayingol	0.052	0.068	0.070	0.029	0.068	0.088	0.058	0.069	0.088	0.058	0.078	0.020	0.055
Aksu	0.087	0.027	0.080	0	0.051	0.062	0	0.051	0.062	0	0.042	0.030	0.121
Kizilsu	0.069	0.040	0.080	0.075	0.049	0.064	0.068	0.049	0.064	0.068	0.061	0.015	0.083
Kashgar	0.083	0.047	0.080	0.092	0.068	0.064	0.055	0.068	0.064	0.055	0.042	0.050	0.032
Hotan	0.087	0.045	0.039	0.082	0.042	0.021	0.090	0.042	0.021	0.090	0.037	0.043	0.032
Ili	0.065	0.074	0.074	0.118	0.072	0.073	0.098	0.072	0.073	0.098	0.059	0.037	0.056
Tarbagatay	0.074	0.035	0.064	0.032	0.073	0.065	0.030	0.073	0.065	0.030	0.067	0.043	0.067
Altay	0.074	0.029	0.078	0	0.066	0.056	0	0.066	0.056	0	0.072	0.018	0.136

) is constructed according to Equations (4) and (5). Then according to Equations (7)–(9), ${\mathit{E}}_{\mathit{j}}$,${\mathit{d}}_{\mathit{j}}$, and${\mathit{W}}_{\mathit{j}}$, are calculated respectively as shown in

Table 6. Calculation results.

Indicator\ Parameter	D1	D2	D3	D4	D5	D6	D7	D8	D9	D10	D11	D12	D13
${\mathit{E}}_{\mathit{j}}$	0.995	0.942	0.996	0.825	0.980	0.978	0.814	0.980	0.978	0.814	0.978	0.816	0.971
${\mathit{d}}_{\mathit{j}}$	0.005	0.058	0.004	0.175	0.020	0.022	0.186	0.020	0.022	0.186	0.022	0.184	0.029
${\mathit{W}}_{\mathit{j}}$	0.006	0.062	0.005	0.188	0.021	0.024	0.200	0.021	0.024	0.200	0.023	0.197	0.032

, in which $\mathit{k}=\frac{1}{\mathbf{ln}14}=0.379$.

Table 6 shows that the indicator weights of D₁–D₁₃ are 0.6%, 6.2%, 0.5%, 18.8%, 2.1%, 2.4%, 20%, 2.1%, 2.4%, 20%, 2.3%, 19.7%, and 3.2%. Figure 5 shows the comparison of values.

The information entropy of the indicators D₁ and D₃ are 0.995 and 0.996 respectively, which are close to 1, indicating that those indicators have the lowest degree of variation, reflecting that Xinjiang medical institutions and Grade Ⅱ hospitals have very nearly the same coverage of urban residential areas, which means that urban residents have almost equal access to services on those indicators. The information entropy of indicators D₅, D₆, D₈, D₉, D₁₁, and D₁₃ is between 0.971 and 0.98, and the degree of indicator variation is small, reflecting that medical institutions have nearly the same coverage of population, risk groups, and medical staff, and basically achieve equal service on those indicators.

The entropy value of the four indicators D₄, D₇, D₁₀, and D₁₂ in the equalization indicator system of Xinjiang basic medical services is between 0.814 and 0.825, with the largest utility value, the largest amount of information reflected, and the largest weight. Analyzing the reasons, the three indicators D₄, D₇, and D₁₀ are directly related to Grade III hospitals. The consistency of the indicator data is low, and the data varies greatly. The average variance of the indicator data is 28.02 (the average variance of the remaining indicators is 11.5). At the same time, the indicator data has a high degree of dispersion and indicator variability, indicating that Grade III hospitals are the core factor affecting the equalization of basic medical services, and the distribution is the most uneven. Therefore, the number of Grade III hospitals and their coverage are the most important factors affecting the equalization of basic medical services in various prefecture-level regions, which means whether residents have the same opportunity to receive higher-level medical treatment services.

Indicator D₁₂ indicates the accessibility of medical institutions in various regions, and comprehensively reflects the rationalization of the spatial layout of medical institutions. It can be seen from Figure 6 that 42% of the accessibility of medical institutions in various regions of Xinjiang is concentrated in the interval [0.05, 0.15], and 35% is concentrated in the interval [0.15, 0.25]. Except for Urumqi, the distribution of medical institutions in other regions is uneven, the overall convenience indicator for medical treatment fluctuates greatly (from 0.07 to1.42), and the spatial layout is unreasonable, which greatly affects the residents’ opportunity for equal medical services.

3.3. TOPSIS

We standardize the basic medical service equalization indicators according to Equations (10) and (11) in each region and obtain the weighted standardized indicator matrix (shown in

Table A5. Weighted normalized TOPSIS table.

Indicator\Regions	D1	D2	D3	D4	D5	D6	D7	D8	D9	D10	D11	D12	D13
Urumqi	0.0018	0.0344	0.0015	0.1018	0.0111	0.0112	0.1278	0.0111	0.0112	0.1278	0.0108	0.1777	0.0062
Karamay	0.0010	0.0305	0.0012	0.0660	0.0055	0.0084	0.0774	0.0055	0.0084	0.0772	0.0087	0.0313	0.0087
Turpan	0.0016	0.0144	0.0014	0.0000	0.0041	0.0061	0.0000	0.0041	0.0061	0.0000	0.0048	0.0213	0.0105
Hami	0.0016	0.0180	0.0013	0.0870	0.0066	0.0069	0.0863	0.0066	0.0069	0.0861	0.0068	0.0375	0.0068
Changji	0.0017	0.0153	0.0013	0.0506	0.0056	0.0056	0.0376	0.0056	0.0056	0.0377	0.0067	0.0425	0.0061
Bortala	0.0013	0.0147	0.0013	0.0000	0.0049	0.0048	0.0000	0.0050	0.0048	0.0000	0.0063	0.0263	0.0081
Bayingol	0.0012	0.0137	0.0013	0.0153	0.0051	0.0075	0.0317	0.0051	0.0075	0.0316	0.0063	0.0088	0.0061
Aksu	0.0019	0.0054	0.0015	0.0000	0.0038	0.0053	0.0000	0.0038	0.0053	0.0000	0.0034	0.0138	0.0134
Kizilsu	0.0015	0.0081	0.0015	0.0401	0.0037	0.0055	0.0371	0.0036	0.0055	0.0372	0.0049	0.0063	0.0092
Kashgar	0.0018	0.0094	0.0015	0.0494	0.0050	0.0055	0.0298	0.0050	0.0055	0.0299	0.0034	0.0225	0.0035
Hotan	0.0019	0.0090	0.0007	0.0438	0.0031	0.0018	0.0493	0.0031	0.0018	0.0493	0.0030	0.0200	0.0036
Ili	0.0014	0.0147	0.0014	0.0632	0.0054	0.0062	0.0536	0.0053	0.0062	0.0538	0.0048	0.0163	0.0062
Tarbagatay	0.0016	0.0070	0.0012	0.0172	0.0054	0.0056	0.0162	0.0054	0.0056	0.0162	0.0055	0.0188	0.0075
Altay	0.0016	0.0058	0.0014	0.0000	0.0049	0.0048	0.0000	0.0049	0.0048	0.0000	0.0058	0.0088	0.0151

) after getting calculated weight values. It can be seen from Table A5 that we get the optimal solution ${\mathit{V}}^{+}$ and the worst solution ${\mathit{V}}^{-}$ for each indicator in each region, as shown in

Table 7. ${\mathit{V}}^{+}$ and ${\mathit{V}}^{-}$ values of various indicators.

	D1	D2	D3	D4	D5	D6	D7	D8	D9	D10	D11	D12	D13
V+	0.0019	0.0344	0.0015	0.1018	0.0111	0.0112	0.1278	0.0111	0.0112	0.1278	0.0108	0.1777	0.0151
V−	0.0010	0.0054	0.0007	0	0.0031	0.0018	0	0.0031	0.0018	0	0.003	0.0063	0.0035

. After obtaining ${\mathit{V}}^{+}$ and ${\mathit{V}}^{-}$, we respectively calculate the Euclidean distance between the medical service equalization indicator in each region and the ideal best solution (${\mathit{S}}^{+}$) and the ideal worst solution(${\mathit{S}}^{-}$) of each indicator by using Equations (14) and (15). According to Equation (16), the equalization indicator of basic medical services(${\mathit{P}}_{\mathit{i}}$) in various regions is calculated, which reflects the Euclidean distance between the equalization level of medical services in various regions and the ideal state. The greater the ${\mathit{P}}_{\mathit{i}}$-value, the shorter the distance between the equalization level of medical services in the region and the optimal solution, and the farther the distance from the inferior solution, the higher the level. The level of equalization of medical services in various regions is shown in

Table 8. Basic medical service equalization scores in various regions.

Region\Value	${\mathit{S}}^{+}$	${\mathit{S}}^{-}$	${\mathit{P}}_{\mathit{i}}$
Urumqi	0.009	0.271	0.968
Karamay	0.167	0.133	0.443
Turpan	0.261	0.020	0.071
Hami	0.154	0.160	0.509
Changji	0.194	0.083	0.299
Bortala	0.258	0.023	0.083
Bayingol	0.235	0.049	0.173
Aksu	0.266	0.013	0.048
Kizilsu	0.225	0.067	0.229
Kashgar	0.217	0.067	0.237
Hotan	0.204	0.084	0.290
Ili	0.198	0.100	0.336
Tarbagatay	0.241	0.032	0.118
Altay	0.269	0.013	0.047

. The comparison of ${\mathit{S}}^{+}$,${\mathit{S}}^{-}$ and${\mathit{P}}_{\mathit{i}}$ in each region is shown in Figure 7.

3.4. Regional Statistics on the Level of Equalization of Basic Medical Services

Standard deviation is often used in probability statistics as a measure of the degree of the statistical distribution of data. It can reflect the degree of dispersion of a dataset and it has the same units as the data within the group. In the medical field, the standard deviation is commonly used to measure the range or level of medical reference values [71]. The ideal result of the EBMS level is that each prefecture-level region has approximately the same ${\mathit{P}}_{\mathit{i}}$ value (mean close to 1 and standard deviation close to 0) in our study. Given that the standard deviation can be understood as a kind of average distance from the sample data to the mean, the study uses the standard deviation of ${\mathit{P}}_{\mathit{i}}$ values as a statistical interval to classify EBMS level classes for each region from large to small. Moreover, in the subsequent more in-depth study of the effect of ${\mathit{P}}_{\mathit{i}}$ index changes on the level of EBMS, when the effect of each 1-unit increases in the ${\mathit{P}}_{\mathit{i}}$ index on the level of EBMS is not significant, it can also be considered to convert it to an increase of one standard deviation for the study. After calculation, the standard deviation of${\mathit{P}}_{\mathit{i}}$ is about 0.2. The distribution interval and frequency of${\mathit{P}}_{\mathit{i}}$ are shown in Figure 8.

It can be concluded from Table 8 and Figure 8, the research divides Xinjiang’s basic medical service equalization level into four levels according to the distribution interval of ${\mathit{P}}_{\mathit{i}}$ values in each region. Level I is Urumqi. Level II is Hami. Level III has four prefecture-level regions: Hotan, Changji, Ili, and Karamay. Level IV has eight prefecture-level regions: Altay, Aksu, Turpan, Bortala, Tarbagatay, Bayingol, Kizilsu, and Kashgar.

At the same time, the use of GIS technology to perform regional spatial processing of ${\mathit{S}}^{+}$,${\mathit{S}}^{-}$ and${\mathit{P}}_{\mathit{i}}$ in each region can more intuitively reveal the spatial distribution of basic medical services in each region, as shown in Figure 9, the enlarged version is shown in Appendix B Figure A4.

Analysis of Figure 9 shows that 57.1% of regions (prefecture-level regions) of Xinjiang are at level IV of equalization of basic medical services, 28.6% are at level III, and only 14.3% are at level I and II.

4. Discussion and Conclusions

This research designed the EBMS’ evaluation indicator system which included 2 first-grade indicators (allocation level of medical institution, convenience of medical treatment) and 12 second-grade indicators under the spatial perspective, and uses the entropy method and the TOPSIS evaluation model to calculate the current spatial distribution and level of EBMS in Xinjiang.

In contrast to the numerical evaluation method in medical resource analysis [72,73], this paper proposes an EBMS evaluation method from a spatial perspective, taking into account the advantages of medical geography spatial accessibility [1,74]. The level of medical institutions can be analyzed by fusion analysis of their precise spatial distribution, scale, the number of medical staff, and other data with residential area distribution, population density, and medical needs, to comprehensively reflect the allocation level of medical institutions and the convenience of residents for medical treatment from a spatial perspective. This can reflect the equal opportunities for residents to access basic medical and health services. Given the reliability of the research methodology, the main conclusions obtained in this paper are as follows:

(1) The higher EBMS indices in Urumqi and Hami indicate that the spatial distribution of medical institutions in the region is more reasonable than in other prefecture-level regions. It also has higher coverage, better accessibility, and more convenient access to basic medical services for residents, and a stronger ability to respond to public health emergencies. The government can therefore appropriately reduce the later planning investment. Conversely, lower EBMS indices in Altay and the other seven cities indicate that medical institutions are poor in spatial distribution, accessibility, coverage, and convenience. From this result, the main reason for low EBMS is the insufficient coverage of Grade Ⅲ hospitals. The large area of the jurisdiction and the dispersed population distribution have resulted in low EBMS in eight cities, including Altay.

(2) The research found that the EBMS level is low in most prefecture-level regions of Xinjiang, and the distribution of basic medical service resources is extremely uneven between prefecture-level regions in Xinjiang.

(3) The EBMS level in the northern part of Xinjiang is significantly higher than that in the south. There were also obvious differences between prefecture-level cities within them.

Therefore, the ability to deal with large-scale emergencies (such as COVID-19) is limited. Only a few areas have essentially achieved equalization of medical services.

This paper suggests that:

(1) For the follow-up investment, the government should fully integrate the residents’ spatial distribution characteristics and medical needs, rationally plan the layout of medical institutions and medical resources investment, and further enhance the equality and convenience of residents’ medical treatment opportunities.

(2) Urumqi and Hami have a better level of EBMS. The government should therefore focus on directing public health service resources to remote mountainous areas and rural groups to narrow the urban-rural gap in medical and health services. At the same time, medical and health service facilities should be reasonably laid out to avoid the crowding-out effect of population gathering on medical and health services as much as possible.

(3) For prefecture-level regions other than Urumqi and Hami where the EBMS is weak, the government should gradually increase the intensity of public health investment, accelerate the urbanization process, and give full play to the role of population gathering and public health investment in promoting the equalization of medical and health services.

It seems that the above recommendations are measures to improve the level of regional EBMS. We will further argue for their reliability in a follow-up study. In addition, we also clearly recognize the limitation that the evaluation methods proposed in this paper (e.g., ${\mathit{P}}_{\mathit{i}}$) can only reflect the ranking and disparity of the level of EBMS in each region, and cannot indicate the severity of inequality. In our subsequent work, we will monitor the changes in EBMS levels within the prefecture-level region in Xinjiang annually, by using the results of the long time series monitoring and the Atkinson index or the Gini Coefficient to study the inequality for each [75], to better guide the government to perform its medical resource redistribution function.