Construction of a Spatial Equalization Assessment System for Medical Facilities

Abstract

The spatial equalization of medical facilities can alleviate the wastage of medical resources and improve the efficiency of medical services. Therefore, it is necessary to carry out spatially balanced planning and assessment of medical facilities in cities. Existing studies on the balanced planning, design, and evaluation of medical facilities have been conducted from the perspective of hospital buildings in terms of spatial utilization efficiency, service satisfaction, and their physical environment on one hand, and from the perspective of regional planning of medical facilities in terms of spatial accessibility to medical facilities and the suitability of medical facilities to the social environment on the other hand. This study hopes to break down the boundaries of each perspective and effectively integrate the architecture, planning, and social well-being of medical facilities, taking spatial equilibrium as the core, in order to establish a spatial equilibrium system for medical facilities and achieve a spatial equilibrium-based assessment of the current state of medical facilities. First, the factors influencing the spatial equilibrium of hospital buildings with the support of the system and environment of hospital buildings are determined. Second, the indicators of the spatial equilibrium of hospital buildings are extracted through the consideration of influencing factors, and the indicator weights are determined by discussing the degree to which they contribute to the influence of the operation of hospital building spatial equilibrium systems, thus forming a system of equilibrium indicators for hospital buildings. Finally, a spatial equilibrium evaluation model for hospital buildings is established to assess the effects of equilibrium. The results obtained in this study provide insights into the regional planning of medical facilities and the design of hospital buildings.

1. Introduction

Medical facilities are a form of integration between public health and the planning of urban public service facilities [1]. They play an important role in cities, in terms of public safety, residents’ health, and social services [2,3]. The service efficiency and fairness of public health spaces can be improved by enhancing the role of medical facilities’ spatial equilibrium [4]. To establish the spatial equilibrium of medical facilities, it is important to systematically assess the current spatial service condition of hospital buildings, establish reasonable assumptions, and find key elements [5]. Overall, the existing literature on the assessment of spatial balance in healthcare facilities involves three disciplines: architecture, urban planning, and public health [6,7,8].

In the field of architecture, the balanced evaluation of hospital buildings revolves around the rational use of space [9,10]. For example, Rose, SJ et al. (2022) have used the Post-occupancy Evaluation method for evaluation of the use of nurses in an acute care nursing unit before and after relocation to a new hospital. The survey questions included work efficiency and productivity, the design of the patient room and support spaces, information systems, and environmental conditions [8]. Nimlyat, PS et al. (2018) have studied indoor environmental quality (IEQ), methods of comparison through subjective or objective assessment, and the internal environment of buildings in a way that was related to health, comfort, and well-being [11]. Related studies also include the quality of hospital premises and user satisfaction, the physical environment of hospitals, the efficiency of the use of healthcare space, and assessment of the comfort of healthcare environments [12,13,14,15].

In the field of urban planning, studies on the spatial equilibrium of healthcare facilities are more focused on exploring the accessibility and siting of facilities [16,17,18]. Hu, W et al. (2018), taking the city of Shenzhen as an example, constructed a comprehensive assessment method that included three dimensions: supply and demand, travel convenience, and equilibrium [19]. Nakamura et al. (2017) used both distance measures and the enhanced two-step floating catchment area (E2SFCA) method to compare the number of hospitals in the neighborhood and the E2SFCA score with regard to the amount and equity of access to hospitals [20]. Xing, LJ et al. (2024) attempted to explicitly define and classify urban health resources considering active and passive health demands through building a conceptual framework. An integrated approach framework, including the global collaborative location quotient (GCLQ), the Gaussian 2SFCA method, and Gini coefficients, was constructed to evaluate the proximity, complementarity, accessibility, and equity of multi-tiered health resources in Guangzhou [21].

In public health, assessment of the equilibrium of healthcare facilities is focused on multidimensional indicators and categories of elements, usually including one or more of the social, economic, health, and environmental dimensions [22,23,24]. Social and economic assessment studies include social health benefits, financial expenditures for the construction of healthcare facilities, service volume, and hospital class, while health and social environment assessments include the number of facilities in the region, the surrounding environment, land-uses, the health needs of the population, and the experience of accessing healthcare [25,26,27]. Conley et al. (2023) have shown that hospitals can improve the quality of healthcare and population health through addressing equity and the social and structural determinants of health. They performed a cross-sectional analysis of non-profit hospital community health needs assessments (CHNAs) and implementation strategies (ISs) from a national sample of 474 non-profit hospitals in the U.S. [28]. Singh, SR et al. (2023) employed a multivariate logistic regression model to examine the association between hospitals’ use of equity as a guiding theme in the assessment of community health needs and binary indicators of alignment for six common community health needs: access to care, chronic illness, obesity, mental health, substance use, and social determinants of health. This study explores the relationship between non-profit hospitals’ use of equity as a guiding theme in the development of their community health needs assessments and the level of alignment between the health needs identified in the community health needs assessment and those addressed in a hospital’s implementation strategies [29]. JW et al. (2018) developed and applied a measure to categorize and estimate the potential impact of a hospital’s community health activities on population health and equity [30].

The studies have their own focus, and the general issues related to evaluation can be summarized into the site evaluation of medical facilities in the field of urban planning, the service efficiency of hospital buildings, and the evaluation of the healing capacity of the environment, as well as the post-use evaluation of hospitals in the field of public health, satisfaction with medical services, coverage, and assessment of the types of medical functions [5,9,31,32]. However, although specialized assessment is considered an effective way to update and develop the design of hospital buildings, it lacks relevance and therefore is not effective in practical application. In addition, rational hospital building planning is not a problem that can be solved independently at the level of urban planning, monolith construction, or public health; it is a complex system from planning to monoliths to internal structures.

Therefore, the main purpose of this study is to effectively integrate the architecture, urban planning, and social well-being of healthcare facilities taking the spatial equilibrium as a core concept, in order to establish an assessment system for the spatial equilibrium of healthcare facilities and vertically sort out the planning and architectural dimensions of healthcare facilities. This is expected to facilitate practical assessment of the spatial equilibrium of healthcare facilities, including the regional basic conditions, the location of hospitals, the environment of the hospital, the organization of the moving line, and the functional setup. As a result, this study mainly discusses three questions: (1) What are the elements that affect the spatial balance of hospital buildings? (2) How does one extract effective evaluation indices of spatial balance for hospital buildings? And (3) How does one systematically and flexibly assess the balanced effect of hospital buildings?

2. Methods and Data

2.1. Research Methods

This study regards the spatial equilibrium of hospital buildings as a system. Additionally, under the guidance of system synergy theory, in order to extract the spatial equilibrium indicators of hospital buildings, we first need to determine the factors affecting the spatial equilibrium of hospital buildings and analyze and extract them with the support of the system and the environment from the macro–medium–micro point of view [33,34]. Second, considering the self-organization relationship of each subsystem within the system—and with the help of the factors influencing the equilibrium within the hospital building space—we further extract indicators affecting the spatial equilibrium of the hospital building. Moreover, through discussing their synergistic and correlative roles within the system, as well as the degree of their contribution to the impact of the system’s operation, we determine the weights of the indicators reflecting the spatial equilibrium of the hospital building. Finally, with reference to the subordination relationships between the various sub-systems of the hospital building, we establish the index dimensions with reference to these relationships and form the spatial equilibrium index system of hospital buildings. On this basis, the spatial balance assessment model of hospital buildings is formed by applying the method of multiple linear regression. This method effectively combines the qualitative and quantitative spatial balance of hospital buildings, uses mathematical models to address the fuzzy and subjective problems related to the spatial balance of hospital buildings, and transforms the subjective evaluation of multiple factors in hospital buildings into a scientific and effective evaluation model in order to enhance its operability and applicability [35,36].

We summarize the basic process as follows (see Figure 1). First, we extract the factors influencing the spatial equilibrium of hospital buildings. Then, we determine the indicators of spatial equilibrium (focus group discussions and expert interviews were used to find indicators, and the data processing method was SPSS- Statistical Product and Service Solutions). Next, we establish the basic dimensions of the indicators, then form the index system for the spatial balance of hospital buildings. Finally, using the method of multiple linear regression, we form the spatial balance measurement model for hospital buildings.

• Focus group method

This is a qualitative research method which is commonly used in social science research. It is conducted by a research-trained investigator, who talks to a group of respondents using a semi-structured approach (i.e., one in which some of the interview questions are pre-determined). In this study, first, the information that had been summarized in advance and ready for discussion was made available to the group members through the establishment of a focus group. The moderator stated that the main purpose of the discussion was for the initial extraction of influencing factors from the two levels of spatial equilibrium research in hospital buildings, and the members were asked to list the relevant factors as exhaustively as possible.

• Exploratory factor analysis (EFA)

This is a commonly used method for data reduction and exploratory data analysis to identify potential variable structures and measurement dimensions. In this study, the corresponding functional relationships in SPSS were used to perform exploratory factor analysis for the selection of indicators through the process of balanced indicator extraction. The focus was on four indicators of the factor entries: eigenvalues of the factors, included entries of the factors, maximum loadings and differences, and factor loadings of the dimension in which they are located.

• Multiple linear regression

Multiple linear regression modeling is a statistical method used to study the relationship between a dependent variable and multiple independent variables. In this study, the spatial balance measurement model of hospital buildings was constructed using multiple linear regression. The spatial equilibrium index of hospital buildings was considered as the independent variable, and linear regression was used to fit the spatial equilibrium of hospital buildings. Equation (1) shows the form of the general expression of the multiple linear regression model:

Y = β0 + β1X1 + β2X2 + …… + βiXi + μ

(1)

Y—predicted value of dependent variable;

Xi—independent variable input values;

i—number of explanatory variables, i = 1, 2, …, n;

βi—regression coefficient;

β0—constant term;

μ—random error constant.

2.2. Screening of Factors Influencing Spatial Equilibrium in Hospital Buildings

2.2.1. Data Extractions

In the form of functional clusters, hospital monoliths, and regional planning suites, variables impacting the spatial equilibrium of hospital buildings were screened.

• Functional cluster dimension

Users of hospital buildings are directly impacted by functional groups. Using a general hospital as an example, the functional circle of a hospital building can include an outpatient functional circle, an emergency functional circle, and an inpatient functional circle, based on the demand for medical care by the public. The formation of functional clusters is based on the delineation of the functional circle and consideration of the connection efficiency between the functions and the frequency of use issues. The balanced factors influencing functional groupings were extracted from the functional groupings of general hospitals and primary healthcare institutions, which are drawn and arranged in Figure 2. (Qing Han, Beijing Architecture University, drew a schematic diagram of the functional circle and functional groups of the general hospital in a master’s thesis (MSc) and elaborated the drawing method. Our research takes this as the basis for collating and drawing).

• Dimensionality of a single entity

The monolithic dimension—which is based on the functional grouping dimension—first treats the hospital district as a whole. It then determines the relationship between the building monoliths at the sites of the inpatient department, outpatient building, infectious disease building, and so on and extracts the factors that influence the spatial equilibrium of these monoliths through regulatory analysis of the floor area, functional location, and site flow line, among others. Second, various hospital types with varying medical levels—such as general hospitals, specialized hospitals, and primary medical and healthcare institutions—are extracted as influencing factors, based on the medical level.

• Regional planning dimension

The hospital building’s accessibility, density, and other features are the primary focal points of the characteristic refinement of the balanced influencing factors at the level of hospital building planning. In the regional planning layout, the hospital building is regarded as a rational and balanced form of spatial point coordinates. This is particularly evident in the balanced relationship between the number of hospital buildings and the population.

2.2.2. Specific Operations

Focus group discussions and expert interviews were carried out for the extraction of impact factors. First, the initial extraction of the influencing factors was carried out based on the focus group methodology, through conducting a discussion on the aggregated information from the three areas mentioned above. The focus group members included 5 hospital architects, 2 staff members from the urban public space planning department, 1 academic in the field of public architecture research, 4 students in urban and environmental construction-related disciplines, 1 doctor, and 3 nurses, a total of 16 people, who were randomly divided into 2 groups for the discussion. The meeting lasted 2 h and was recorded by a note taker.

After the impact factors were determined twice and the impact factor data tables were finally organized, the impact factors that were discussed in the focus groups were organized as Excel tables and sent to the 5 experts via email and paper copies. The five experts first needed to check the initial extraction of the influencing factors and discern the reliability of the influencing factors. Secondly, the experts were to categorize the extracted influencing factors and provide advice and guidance on the subsequent hierarchy of influencing factors.

In summary, the features of the factors influencing the spatial equilibrium of hospital buildings at each level were defined and refined in accordance with the hierarchical division of influencing factors. The factors influencing the spatial equalization of hospital buildings shown in

Table 1. Factors affecting the spatial balance of hospital buildings.

Tier 1 Composition	Tier 2 Composition	Factors Influencing Spatial Equilibrium
Regional planning	Quota	Number of hospitals in the region
		Number of people in the region
		Number of hospital beds
	Site selection	Distance to medical care
		Relevance among hospitals
		Scope of Coverage
Hospital building levels	Environment	Parking spaces
		Barrier-free design
		Environmental healing capabilities
	Kinetic organization	Efficiency of rescue and treatment
		Differentiation of streamlines
	Function setting	Hospital level
		Spatial resilience
		Type of function
		Spatial scale

were generated using the index screening of multidimensional equalization influencing factors, based on the characteristics of the influencing factors.

2.3. Scale Creation for the Extraction of Indicators of Spatial Balance

To derive the specific indicators of spatial equilibrium, an indicator extraction scale must be prepared. The indicators of hospital buildings’ spatial equilibrium can then be obtained by scoring the indicators in the indicator scale and statistically analyzing the data.

2.3.1. Research Objective

The audience and the hospital environment are the primary foci of research on the scale of the balance of the hospital building space. First, the waiting area, the diagnosis and treatment area, the ward area, and other transportation spaces are the spatial objects of the scale development and questionnaire research [37,38,39]. Second, as this research uses two types of questionnaires—the expert questionnaire and the social questionnaire—the target respondents include professionals involved in hospital planning and management services; hospital users such as medical staff, patients, and their families; and administrators, as well as those connected to the expert questionnaire.

2.3.2. Statistical Methods

Using the SPSS 24.0 software, entry analysis, exploratory factor analysis, correlation analysis, reliability and validity analysis, and validation factor analysis were carried out on the gathered data. The Amos 24.0 software was used for validation factor analysis. The first test sample (n = 128) was used for entry analysis, exploratory factor analysis, factor and total score correlation analysis, validation factor analysis, the validity scale validity test, and the reliability test. The formal administration sample (n = 238) was used for these analyses.

2.3.3. Calibration Tools

Cronbach’s alpha coefficient was utilized in conjunction with the discrimination and correlation coefficients as calibration tools for item analysis in order to assess the reliability of the items. The KMO measure and Bartlett’s spherical test were used in the exploratory factor analysis of the items to identify the factors. A KMO value between 0.9 and 0.5 can be used for the factor analysis: values greater than 0.9 are very suitable for the factor analysis, while values below 0.5 are discarded. The higher the value, the higher the factor’s contribution rate. These findings align with the reference value range used in related studies.

2.3.4. Scale Creation

The single unit itself, medical function grouping, and hospital building regional planning were all included in the extraction of spatial balance indicators. Numerous levels and types of influencing factors are involved in each aspect. The indicators were compiled from earlier research, and those that appeared four or more times on average were initially kept. The role of spatial balance is also considered in the emergency medical service, along with the actual research conducted in its early stages and the opinions gathered from focus groups. Two indicators of reserved emergency land and emergency conversion space were added and, in accordance with the state of the integration of network medical service at the moment, an indicator of the network consulting service in the function setting was also added. Two indicators—the hospital’s functional diversion situation and the length of time it takes for an admission to a consultation in the flow organization—should be added in accordance with the research characteristics of spatial equilibrium. Using the information above as a guide, this paper first numbered the indicators with question items to represent the spatial balance indicators of medical facilities, which are displayed in Figure 3.

2.4. Extraction of Equilibrium Indicators

2.4.1. Design of Questionnaires

The importance of the indicators was ranked one by one in the form of a list of questions in an importance questionnaire. The questionnaire was divided into seven levels, ranging from unimportant to very important, with values from 1 to 7. Simultaneously, a link to enhance and expand the indicators by adding or changing them as desired was included.

2.4.2. Sample Features

In the first sample, 150 questionnaires were distributed. Of these, 132 were returned, and 128 valid questionnaires were obtained through screening, yielding an 85.3% validity rate. The screening criteria were as follows: ① the entire questionnaire missed ≥ two entries; ② the tendency to answer was constant; and ③ the answers showed regularity. There were 48 men and 80 women, with ages between 28 and 67 and an average age of 42 ± 10 years old, among the valid questionnaires.

The formal administration sample received 300 questionnaires in total. Of these, 254 were returned, and 238 valid questionnaires (or 79.3% of the total) were obtained after screening. A total of 129 men and 109 women, aged 24–65 with an average age of 37 ± 17 years, completed the valid questionnaires.

2.4.3. Analysis of Entries

The questionnaire scale questions are described in such a way that the following conclusions were reached: in the topic-to-total-score correlation; the correlation coefficients of T17, T18, T25, T26, T27, T28, T29, T30, T35, and T36 and the entry value were less than three in the discriminant method analysis; and no statistical significance was found for deletion in the high and low subgroups. For all T17s, T25s, T27s, T28s, T29s, T30s, T35s, and T36s, the Cronbach Alpha after entry deletion was greater than or equal to 0.890, and the correlation coefficient of the total score was less than 0.400. Therefore, it was recommended that T17, T25, T27, T28, T29, T30, T35, and T36 be excluded, and the scale was adjusted to 28 entries (

Table 2. Analysis of spatial equilibrium indicator entries for hospital buildings.

Serial Number	Deterministic Value	p	Correlation Coefficient	Cronbach’s A	Remark
T1	5.984	0.000	0.454 **	0.887	reservation
T2	7.000	0.000	0.553 **	0.885	reservation
T3	6.034	0.000	0.502 **	0.886	reservation
T4	6.153	0.000	0.480 **	0.886	reservation
T5	5.179	0.000	0.443 **	0.887	reservation
T6	6.827	0.000	0.510 **	0.886	reservation
T7	6.309	0.000	0.559 **	0.885	reservation
T8	5.596	0.000	0.580 **	0.884	reservation
T9	7.839	0.000	0.605 **	0.884	reservation
T10	7.319	0.000	0.620 **	0.884	reservation
T11	7.425	0.000	0.572 **	0.885	reservation
T12	7.632	0.000	0.606 **	0.884	reservation
T13	6.809	0.000	0.575 **	0.884	reservation
T14	6.030	0.000	0.586 **	0.884	reservation
T15	6.712	0.000	0.590 **	0.884	reservation
T16	6.512	0.000	0.597 **	0.884	reservation
T17	2.311	0.024	00.150	0.893	exclude
T18	3.767	0.000	0.343 **	0.889	reservation
T19	5.025	0.000	0.486 **	0.886	reservation
T20	5.727	0.000	0.539 **	0.885	reservation
T21	5.319	0.000	0.499 **	0.886	reservation
T22	3.641	0.001	0.408 **	0.888	reservation
T23	5.276	0.000	0.514 **	0.886	reservation
T24	5.717	0.000	0.542 **	0.885	reservation
T25	2.663	0.010	0.334 **	0.890	exclude
T26	3.618	0.001	0.386 **	0.888	reservation
T27	3.434	0.001	0.252 **	0.889	reservation
T28	2.057	0.044	0.195 *	0.891	exclude
T29	2.747	0.008	0.246 **	0.890	exclude
T30	2.830	0.006	0.233 **	0.891	exclude
T31	4.920	0.000	0.437 **	0.887	reservation
T32	5.165	0.000	0.494 **	0.886	reservation
T33	6.021	0.000	0.512 **	0.886	reservation
T34	6.302	0.000	0.504 **	0.886	reservation
T35	2.407	0.019	0.194 *	0.891	exclude
T36	2.854	0.006	0.261 **	0.890	exclude

* p < 0.05, ** p < 0.01.

).

2.4.4. Exploratory Factor Analysis (EFA)

The factor entries in this study were determined using the following four criteria.

• The factor’s eigenvalue must be greater than 1.
• Each factor has at least three entries.
• The item’s maximum loading value on both dimensions is greater than 0.4 and the difference is less than 0.1.
• The factor loadings of the dimension where the item is located are lower than 0.4.

These factors suggest that the item does not have a high degree of differentiation. The factor loadings of T18 and T26 were less than 0.4 in the exploratory factor analysis; however, the KMO values prior to the exploratory factor analysis were all above 0.5, and Bartlett’s spherical test values all reached the significance level.(

Table 3. KMO values and Bartlett’s test for sphericity.

KMO Quantity of Sampling Suitability		0.890
Bartlett’s sphericity test	rough chi-square	2689.744
	degrees of freedom	325
	significance	0.000

) As a result, we continued to analyze the 26 entries while excluding the question items T18 and T26.

Ultimately, the variables exhibited strong correlation, Bartlett’s spherical test rejected the initial hypothesis, and the scale’s KMO statistic of 0.890 was appropriate for factor analysis. The first four male factors that were extracted after a second ANOVA on the scale’s question items revealed four male factors with eigenvalues larger than 1. With a good degree of explanation, the four male factors accounted for 74.631% of the variance of all the variables, according to their cumulative variance contribution rate of 74.631%. The 26 question items underwent factor rotation to obtain the matching factor loading tables.

In order to create a table of rotated factor loadings, factor rotation was applied to the four extracted common factors. The results showed that T10, T15, T12, T8, T13, T16, T11, T14, and T9 had high loadings on the first factor; T1, T3, T2, T5, T4, T6, and T7 had high loadings on the second factor; T24, T19, T21, T20, T22, and T23 had high loadings on the third factor; and T34, T31, T33, and T32 had high loadings on the fourth factor. These results were consistent with the expected division of dimensions, indicating good validity. This allowed for the determination of the hospital building’s spatial equilibrium index and dimensions (

Table 4. The rotated component matrix.

Serial Number	Ingredients
	1	2	3	4
T10	0.873
T13	0.855
T12	0.854
T15	0.851
T8	0.847
T16	0.844
T11	0.826
T9	0.824
T14	0.804
T1		0.872
T3		0.868
T2		0.846
T5		0.833
T4		0.826
T6		0.820
T7		0.802
T19			0.865
T21			0.863
T24			0.860
T20			0.853
T22			0.851
T23			0.817
T34				0.894
T31				0.889
T33				0.870
T32				0.846

).

The indicators are crucial for the spatial balance of hospital buildings, according to the results of the Cronbach’s a test for the overall scale and sub-dimension of the spatial balance scale (Cronbach’s a = 0.885).

2.4.5. Validation of Indicators

• Structural validity

The structural validity of the spatial balance indices of hospital buildings was good, and the validation factor analysis diagram is displayed in Figure 4. As indicated in

Table 5. Index validity analysis.

Fitness Index	X2/df	RMR	RMSEA	CFI	TLI	IFI	GFI
Fitting values	1.161	0.048	0.024	0.990	0.989	0.990	0.918

, the spatial balance index X²/DF of hospital buildings was lower than 3; the RMR and RMSEA were lower than 0.08; and the CFI, TLI, IFI, and GFI were all greater than 0.9.

• Convergent validity

Table 6. Indices convergence analysis.

Dimension	AVE	CR
Site selection	0.656	0.93
Function setting	0.637	0.94
Kinetic organization	0.634	0.912
Environment	0.634	0.874

reveals that the factor loadings corresponding to the topics of site selection, functional settings, flow organization, and site environment were all greater than 0.5, suggesting that the topics corresponding to each latent variable are highly representative. The convergent validity analysis was performed on the spatial balance indices of hospital buildings. Furthermore, the convergent validity was optimal, as each latent variable’s mean variance (AVE) was greater than 0.5 and the combined reliability (CR) was greater than 0.7.

• Distinguishing validity

Table 7. Discriminant validity of indicators.

	Site Selection	Function Setting	Kinetic Organization	Environment
Site selection	0.810
Function setting	0.147	0.798
Kinetic organization	0.170	0.198	0.796
Environment	0.125	0.103	0.185	0.796

displays the results of the distinguishing validity analysis for the spatial balance index of hospital buildings. It can be seen that the correlation coefficients for site selection, functional settings, flow organization, and site environment were all less than the square root of the corresponding AVE. This suggests some degree of differentiation and correlation between the latent variables, meaning that the distinguishing validity of the scale data is reasonable.

• Establishment of indicators

Consequently, the hospital building’s spatial balance indicator system was created, and the weights of each indicator were determined based on the validation analysis of the aforementioned indicators of spatial balance, in conjunction with the analysis of the indicators of structural validity, convergence validity, and zoning validity. The specific calculation formulas are as follows: first, the standardized path coefficients of each observed variable measured in accordance with the model were weighted to obtain the indicator weights of each observed variable.

There are a total of 26 index factors and 4 categories of influencing factors in the hospital buildings spatial balance evaluation index system. The four categories of influencing factors were classified in accordance with the characterization of the spatial equilibrium analysis of hospital buildings in the preceding section, with reference to the construction specifications of the hospital buildings. Each indicator factor was then interpreted to establish the evaluation standard.

Table 8. Weight of indicators.

Dimension	Subject	Weights	Interpretation of Indicators
Site selection	Distance to hospital	0.139	The greater the distance, the lower the grade; ideally, general hospitals should be reachable by car in thirty minutes, and primary healthcare facilities should be reachable on foot in fifteen minutes.
	Convenience of referrals	0.145	The ease of referral routes to upper (lower) level hospitals that facilitate prompt referral is preferred; otherwise, the larger the gap, the lower the rank. The availability of ambulance vehicles in the hospital area is also preferred.
	Coverage	0.143	In other words, the larger the gap, the lower the grade. General hospitals are able to efficiently connect medical services with the primary healthcare institutions under their control, and the primary healthcare institutions are able to meet all community health services with superior focus, covering more than three kilometers.
	Surrounding transportation convenience	0.142	The wider the gap, the lower the grade; alternatively, convenient public transportation in the area and a direct rail connection to the compound are preferred.
	Building site reserved for future development	0.147	This considers whether any land in the hospital’s vicinity has been set aside for development and construction, and how the grade is determined based on that area while also considering the hospital’s present state.
	Reserve land for emergencies	0.147	If a site is successfully integrated with the infectious disease area and the hospital area is designated for emergency medical care, it receives a higher grade; if not, it receives a lower grade.
	Site area	0.137	The larger the gap, the lower the grade; therefore, it is better to have a hospital that serves medical needs without placing undue strain on the surrounding land and environment.
Function setting	Hospital level	0.113	Level 3A hospitals are preferred (and so on, in descending order), based on the hospital’s rating.
	Emergency transition space	0.111	The hospital has areas such as wards, labs, operating rooms, and so on that can be temporarily converted in an emergency. The more areas that can be used for this purpose, the higher the grade.
	Daily clinic volume	0.110	Preferably, general hospitals should have more than 1000 outpatient visits per day.
	Function type	0.113	All three of the aforementioned aspects are deemed to be excellent, failing which they will be eliminated one-by-one. Functional rooms are fully furnished and have room set aside for emergencies, and the functional settings satisfy hospital-level functional requirements.
	Functional partition	0.112	Functional zoning is clearly established, along with the hospital area’s superior efficiency of medical services, as opposed to the principle that the wider the gap, the lower the grade.
	Orientation of wards and consultation rooms	0.110	It is ideal if 80% of the wards and consultation rooms face south; if not, the impact on medical operations and the amount of light in the wards and consultation rooms are determining factors.
	Web-based consultation services	0.113	The higher the rank, the more online medical service items (e.g., online booking, online billing, online consultation, hospital ward registration, and so on) that are offered.
	Corridor dimensions	0.108	To meet the superior standard, waiting areas should accommodate patient needs for consultation and treatment, as well as wheelchair mobility. The larger the gap, the lower the rating.
	Functional room scales	0.109	Based on meeting the regulated area, the higher the grade, the more effectively it is used.
Kinetic organization	Functional streaming	0.160	The hospital area features distinct areas for outpatient care, emergency care, medical examinations, maternity and child healthcare, wards, infectious disease control, and other functions of the diversion line or entrance. The more gaps there are in the function of the exhaustive flow line, the worse the grade will be.
	Time from admission to consultation	0.160	The sooner a patient is seen, the better; general hospitals want to see them within 30 min of admission and primary care organizations within 10. The larger the gap, the lower the grade.
	Pedestrian–vehicle separation	0.171	It is preferable to have distinct pedestrian and vehicle flow lines with distinct lanes for each type of traffic; otherwise, the grade will be lower when the gap is larger.
	Patient–doctor triage	0.172	There is never a perfect point where patient flow and healthcare workers meet; there are some places where staff-only access is advantageous, and vice versa.
	Clean-sewage diversion	0.168	Using smart rail logistics vehicles may vary, depending on the situation. No crossing of personnel and dirt flow lines is excellent; some crossing of personnel and dirt flow lines is good, and vice versa.
	Ease of access to the medical process	0.170	According to the medical treatment flow, everything goes smoothly, every area is understood, and less folding is preferred—the larger the gap, the worse the grade.
environment	Aboveground parking setup	0.248	Temporary parking spaces, parking spaces for emergency vehicles, staff parking spaces, patient parking spaces, parking spaces for logistics vehicles, and temporary parking spaces (or set up in the underground), along with the hospital area of vehicles parked in an orderly manner, are required for the organization of the best outcome, or else decreasing one by one.
	Accessible design	0.241	Facilities free of barriers, such as elevators, accessible restrooms, barrier-free ramps, and barrier-free handrails, are arranged well or excellently; the more gaps, the worse the grade.
	Healing space setting	0.254	According to real senses, each room should have a comfortable and balanced temperature; if not, the rating will be lower.
	Number of entrances and exits	0.257	To meet the preferred standard, general hospitals should have three entrances and exits; otherwise, the larger the gap, the lower the grade.

displays the index weights and interpretations.

3. Results and Discussion

3.1. Spatial Equilibrium Measurement Model Construction for Hospital Buildings

Using the multiple linear regression method, the spatial balance assessment model for hospital buildings at the single-unit level was formed based on the established spatial balance index system for hospital buildings.

3.1.1. Variable Selection

First, through the establishment of the spatial equilibrium index system for hospital buildings, the independent variables of the spatial equilibrium model of hospital buildings were set as follows: site selection; function setting, flow organization, and site environment.

Second, the Pearson correlation coefficient test revealed a significant positive correlation (p < 0.05) between site selection, functional settings, flow organization, site environment, and the hospital building’s spatial balance, further supporting the relationship between the independent variables and spatial balance. It is evident that the indicator system can be established and that the relationships between the study variables have been validated (

Table 9. Test of correlation.

	Site Selection	Function Setting	Kinetic Organization	Environment	Spatial Equilibrium of Hospital Buildings
Site selection	1
Function setting	0.140 *	1
Kinetic organization	0.160 **	0.186 **	1
Environment	0.115	0.094	0.165 **	1
Spatial equilibrium of hospital buildings	0.473 **	0.366 **	0.393 **	0.400 **	1

* p < 0.05, ** p < 0.01.

).

3.1.2. Model Construction

First, the spatial equilibrium of hospital buildings was set as the dependent variable (Y), and the important relevant variables—site selection, functional settings, flow organization, and site environment—were taken as independent variables (X). Equation (2) illustrates how the relevant variables were substituted into Equation (1) to obtain the assumed regression model:

Spatial equilibrium of hospital buildings (Y) = β0 + β1 × site selection (X1) + β2 × Function Setting (X2) + β3 × kinetic organization (X3) + β4 × environment (X4) + μ

(2)

Second, using the least squares method with the assumption that the sum of squares of the errors is minimized, the regression coefficients of the multivariate regression model were estimated. The model fit of the regression coefficients was solved using the linear regression function of the statistical program SPSS 24.0 in order to construct the model (the confidence interval for parameter setting was set to 95%, or p < 0.05). The linear relationship between the explanatory variables and the established explanatory variables was significant, as indicated by the regression equation statistic F value of 63.520 and the p-value of 0.000 (see

Table 10. One-way ANOVA.

	Square Sum	Degrees of Freedom	Equalize the Square	F	Significance
Regression	143.831	4	35.958	63.520	0.000
Residuals	159.071	281	0.566
Total	302.901	285

). On this basis, we concluded that a linear regression model could be established for the spatial equilibrium model of hospital buildings.

Third, the coefficients of all of the dependent variables in this linear regression model were determined and tested for significance.

Table 11. Coefficient test of regression equation.

	Unstandardized Coefficients		Standardized Coefficient	t	Significance	Covariance Statistics
	B	Standard Errors	Beta			Tolerances	VIF
(Constant)	−1.450	0.372		−3.900	0.000
site selection	0.385	0.046	0.367	8.300	0.000	0.955	1.047
Function setting	0.265	0.049	0.242	5.451	0.000	0.950	1.053
Kinetic organization	0.255	0.048	0.241	5.363	0.000	0.929	1.076
Environment	0.286	0.043	0.295	6.698	0.000	0.962	1.040

displays the findings. The constant term β0 and the regression coefficients βi in Equation (2) must be solved to obtain the unstandardized coefficient B. Consequently, Equation (3) illustrates the regression equation of the spatial equilibrium of hospital buildings.

The multiple linear regression analysis indicated that the spatial equilibrium of hospital buildings is significantly influenced positively by site selection, functional settings, flow organization, and site environment. As a result, the following model was derived:

y = −1.450 + 0.385× Site selection + 0.265 × Function Setting + 0.255 × Kinetic organization + 0.286 × Environment

(3)

Fourth, the residuals of the regression model were analyzed. The residual of the model is the difference between the predicted value obtained after solving and the actual value, which represents the error of model fitting. As shown in Figure 5a, the model’s residuals basically conform to the normal distribution. The relationship between the measured cumulative probability and the predicted cumulative probability is depicted in the residual normal P-P plot in Figure 5b. As the residual distribution is essentially distributed along the graph’s diagonal, the residual distribution’s normality is confirmed. The residuals were dispersed, rather than clustered, in the scatter plot of the residuals displayed in Figure 5c. Each of these outcomes demonstrates the model’s validity and the reasonableness of the residuals.

Fifth, the goodness-of-fit test results are displayed in

Table 12. Multiple linear regression fit test.

R	R-Square	Adjusted R-Square	Errors in Standardized Estimates
0.689	0.475	0.467	0.752

. According to the table, the explanatory variables in the model have an explanatory strength for the explanatory variables, to a certain extent, with explanatory strength reaching 47.5%. The R-square value was 0.475, and the adjusted R-square was 0.467.

3.2. Spatial Balance Evaluation Rating for Hospital Buildings

In this paper, an assessment system for hospital building spatial equilibrium was established, the factors that influence a hospital building’s spatial equilibrium were extracted, and an index system was created. A better fit was also established for the purpose of predicting hospital building spatial equilibrium. A multivariate linear regression model was then constructed, and its validity was confirmed. On this basis, the hospital building spatial equilibrium prediction score was divided into five levels.

Table 13. Evaluation grade of spatial equilibrium of hospital building and its explanation.

Level	Level Description	Point Value
A	Excellent: the hospital building units that have been evaluated effectively fulfill the requirement for spatial balance with respect to site environment, flow organization, functional settings, and so on.	117–90
B	Better: the assessed hospital building units, taking into account site selection, functional settings, flow organization, site environment, and so on, satisfy the requirement for spatial balance.	89–80
C	Medium: in terms of site selection, functional settings, flow organization, site environment, and so on, the evaluated hospital building units essentially satisfy the requirement for spatial balance.	79–70
D	General: in terms of siting, functional settings, flow organization, site environment, and so on, the spatial balance of the assessed hospital building units is average.	69–60
E	Mediocre: in terms of site selection, functional settings, flow organization, site environment, and so on, the spatial balance of the assessed hospital building units is unsatisfactory and urgently needs to be improved.	59–0

displays the degree to which each level (i.e., A, B, C, D, and E) is represented.

3.3. Comparison of Research Results

The spatial equilibrium assessment model of medical facilities shows that the spatial equilibrium of medical facilities is influenced by the location of the medical facilities, the environment of the hospital, the functional settings, and the organization of the flow lines, with the degree of influence decreasing in order. The reason for this is that the functional settings and flow organization are basically the same for hospitals of the same level under the hierarchical system of Chinese hospitals, so the differentiation is not obvious. On the contrary, there is relative flexibility for the environment and location of hospitals. Therefore, to improve the balance of medical facilities, it is necessary to improve the rationality of the functional configuration and flow organization of hospitals at the national macro-control level, and at the meso-level of medical facilities, it is more important to focus on the site selection in the pre-construction stage, as well as the design of the hospital’s environment.

At the same time, the spatial balance influence factor of medical facilities is more targeted than the factors obtained from related studies in various disciplines in previous studies, which can be regarded as a systematic organization and secondary refinement of the factors from related studies in individual fields, with more emphasis on the correlation between the factors [40,41,42]. For example, in previous studies, the factors extracted from the architectural point of view would include the scale of functional rooms, emergency space conversion, etc., but would not be related to the distance to medical care and the accessibility of the surrounding traffic; in fact, they are related from the point of view of the accessibility and fairness of medical care. Therefore, this study achieves a systematic approach to spatial equilibrium and produces an assessment system and evaluation model with more practical value than previous independent studies in separate subject areas. However, due to the consideration of the size of the assessment system, the number of factors influencing the assessment of spatial equilibrium is small compared to the number of factors obtained from the previous studies in each subject area. This is also a problem of the depth and breadth of the study, which needs to be further explored and refined in subsequent studies.

4. Conclusions

The spatial equilibrium of medical facilities reflects the fairness of social public services. In this paper, the spatial equilibrium of medical facilities was first extracted, and the factors influencing the spatial equilibrium of medical facilities were obtained. After that, an index scale for the spatial equilibrium of medical facilities was formulated according to the influencing factors, which was tested and examined to extract the spatial equilibrium index of medical facilities. The indices were further verified and weighted to establish a spatial equilibrium index system for medical facilities. The spatial equilibrium assessment model for medical facilities was established with multiple linear regression, based on the spatial equilibrium index system for medical facilities.

The study of spatial equilibrium of medical facilities is an interdisciplinary, multilevel, complex, and lengthy research work. In subsequent research, the first step is to evaluate exemplary hospitals using the evaluation model established in this study, conduct an empirical study of the evaluation model, and make adjustments and additions to the model accordingly. This empirical study has already been carried out and will be described in our next paper. Second, as the sampling data used in this study mostly originated from the same region, data from other regions can be sampled in the next step of the study in order to consider geographical characteristics and conditions, test the universality, and further improve the accuracy of the model. It is hoped that further research by more scholars will improve the study of the spatial balance of medical facilities in the future, thus enhancing the fairness and balance of China’s public health services from the perspective of the health environment and public space.