An Equity Evaluation of Healthcare Accessibility across Age Strata Using the G2SFCA Method: A Case Study in Karamay District, China

Abstract

Equitable access to healthcare services is essential for residents’ well-being and social equity, requiring the rational spatial distribution of healthcare facilities in urban planning. Compared with major studies on the spatial accessibility and equity of healthcare services in first-tier cities, second-tier cities, which form the foundational structure of the global urban system, have not be given sufficient attention. Therefore, this study takes Karamay District in Karamay as a case study to analyze the spatial equity of healthcare services using place-based accessibility measures. For accessibility calculations, we employ the Gaussian two-step floating catchment area method to separately analyze the accessibility to hospitals and primary healthcare (PHC) institutions, considering factors such as the number of facilities, population, distance, and transportation modes. Second, we utilize global and local Moran’s I for spatial analysis to identify areas with varying levels of accessibility. Furthermore, considering the spatial equity for different social groups, this study innovatively proposes an analytical framework for assessing healthcare accessibility and equity across age groups using residential-level data and an adjusted search radius in second-tier cities, typically those with small-scale urban areas. The results reveal significant spatial clustering in healthcare accessibility, similar to that observed in most first-tier cities, as well as notable differences in the spatial distribution between hospital accessibility and PHC accessibility. Regarding age strata, results show that the elderly have lower access to hospitals but higher access to PHC institutions, which is opposite to the situation observed for children. Overall, second-tier cities demonstrate better equity in healthcare accessibility compared to first-tier cities, particularly regarding hospital accessibility. However, there are minor inequities in PHC accessibility for children aged 0–12 years. Our findings may provide valuable insights and essential data support for healthcare resource allocation and land use planning in second-tier cities.

1. Introduction

Spatial inequity permeates critical urban sectors such as housing, transportation, and public service delivery [1], significantly impacting the daily lives of individuals. Despite the ongoing debates on a universally accepted definition of equity, most scholars agree that spatial equity relies on the foundation of equality and focuses on the fair allocation of public resources among diverse social groups [2,3]. In urban planning, ensuring equitable access to public facilities stands as a fundamental objective to achieve spatial equity. Early geographers and urban planners conducted such studies from a more macro perspective to reveal urban–rural divides, while overlooking intra-urban spatial disparities [4]. With the advancement of geographic information systems (GIS) technology [5,6] and the availability of more precise demographic and spatial data [7,8,9], there has been a growing focus on public resources, especially spatial healthcare inequity. For example, more studies have focused on healthcare inequity within urban areas, paying attention to the intra-differences within cities and the differences between rural and urban [10,11]. In addition, some scholars attached more importance to achieving universal healthcare coverage [12], concentrating on the impact of national internal factors on medical accessibility, such as regional differences [13], administrative levels [14], and boundary effects [15]. These developments have enabled a more detailed analysis of intra-urban healthcare accessibility, assisting urban planners and policymakers in more effectively addressing spatial disparities.

However, currently, most healthcare inequity studies still focus solely on cities in metropolitan areas, such as Beijing, Shanghai [16], Jakarta [17], Chicago [18], and Melbourne [19]. However, non-metropolitan regions, including small- and medium-sized cities are more numerous and widely distributed, which constitute city-regions alongside large core cities [20]. Actually, cities with different geographical and historical backgrounds experience various forms of healthcare inequity. Therefore, it is significant to analyze the possible issues of healthcare inequity faced by second-tier cities.

Take China as a typical example, due to the rapid urbanization, China has witnessed a notable reduction in the regional disparities in the number of healthcare facilities per capita [21]. Moreover, this urbanization has also shifted the spatial inequality of healthcare services from a rural–urban divide to disparities between urban areas. Existing studies typically analyze healthcare facility accessibility under different transportation scenarios, explore how healthcare-seeking behavior is influenced by facility accessibility [22], and investigate supply-demand matching and spatial equity issues [11], revealing significant disparities in healthcare accessibility within first-tier cities. Similarly, these studies predominantly focus on densely populated metropolises, often overlooking healthcare accessibility and equity in second-tier cities, which constitute the majority of China’s urban landscape. In this study, we define first-tier cities as metropolitan areas, provincial capitals, and cities with populations exceeding one million. All other cities are classified as second-tier cities, which constitute over 80% of the total. These cities are not only widespread in distribution, accommodating a large number of urban residents, especially among the middle-income population, but they also serve as important carriers for future rural-to-urban migration and the advancement of China’s new urbanization. Unlike first-tier metropolises, second-tier cities are primarily regional or local in nature and often lack both economic competitiveness and sufficient employment opportunities. With a trend of continuous population migration of young people towards first-tier cities, these second-tier cities also face an escalating aging population issue. Additionally, the built environment and facility layout in these cities differ significantly, posing challenges to the direct application of accessibility rules derived from first-tier cities. Therefore, exploring the social inequities in healthcare service layouts in second-tier cities is crucial for achieving the goal of healthcare service equality and sustainable urban development.

Given that China’s healthcare system is centered around hospitals and lacks an effective hierarchical diagnosis and treatment system [23,24], urban residents tend to prefer higher-level hospitals, while PHC institutions mainly cater to the elderly and provide childhood vaccinations [25]. Therefore, this study focuses on evaluating the accessibility and equity of healthcare facilities, specifically hospitals and PHC institutions. Three primary research questions are proposed: (1) What are the healthcare accessibility patterns in second-tier cities? (2) Are there disparities in the distribution of healthcare accessibility compared to first-tier cities? (3) What inequities exist in healthcare accessibility across different age groups? To address these questions, we conducted a case study in Karamay District, which is located in the center of Karamay, a second-tier city in the northern part of Xinjiang Uygur Autonomous Region in China. Karamay District has an area of 70.6 km² and a population of approximately 271,496. Our methodology employed an improved two-step floating catchment area (2SFCA) method, utilizing residential compounds as basic demand units and integrating spatial accessibility with demographic data to reveal disparities among age groups. Initially, we constructed a GIS spatial database using publicly available data. Then, we applied the improved 2SFCA method to assess the spatial accessibility of hospitals and PHC institutions. Subsequently, we analyzed the spatial clustering of accessibility by calculating global and local Moran’s I values to identify regions with varying accessibility levels. Finally, we evaluated equity across different age groups using Gini coefficients.

This paper presents a framework for assessing healthcare facility accessibility and equity across different age demographics, providing valuable insights for medical resource distribution and urban land use planning in second-tier cities in China. The study’s findings enhance the academic understanding of healthcare accessibility and equity across various city types and scales. The paper begins with a review of relevant literature and methodologies, followed by an introduction to the study area and data. Empirical results are then presented. Drawing upon these findings, the paper concludes by discussing the planning implications derived from the empirical study and acknowledging the inherent limitations of this research effort.

2. Literature Review

2.1. Measuring Healthcare Accessibility

Healthcare accessibility refers to the relative ease with which services, specifically healthcare, can be reached from a given location [26]. The concept of accessibility was initially introduced by Hansen in the 1950s, emphasizing “potential opportunities in interactions” [27]. Other scholars have also presented similar concepts of accessibility, such as utility-based accessibility [28] and space–time accessibility [29]. Due to the multidimensional nature of healthcare accessibility, which encompasses not only the potential use of healthcare services but also the actual act of using or receiving them [30], it is necessary to highlight that accessibility should involve both spatial and nonspatial factors [31] and can be understood in terms of two main types, namely, place-based accessibility and individual accessibility [32]. This article focuses on place-based accessibility, which, although built on the work of individual accessibility, differs in its emphasis. Compared to individual accessibility, place accessibility underscores spatial attributes, including origins, destinations, and spatial impedance. It highlights the importance of spatial separation between supply (i.e., healthcare facility) and demand (i.e., population) and how they are interconnected in space [4,33].

Given that place-based accessibility measurement is a classic issue in location analysis, well-suited for GIS to address, various approaches have been employed to measure spatial accessibility to healthcare services. These include the ratio model [34,35], the minimum distance model [36], the two-step floating catchment area (2SFCA) method [24,37,38], and the potential model [39,40]. Among these, the 2SFCA method stands out as one of the most commonly utilized models in accessibility assessment [5,41,42]. Since its inception, some enhancements have been developed due to the limitations of the original 2SFCA method’s simple binary approach [26]. These improvements generally address distance–decay effects within catchments or allow for the use of variable catchment sizes [43,44]. Methods like the Kernel density function [4] or Gaussian function [45] have been suggested to model distance decay effects, reflecting residents’ declining willingness to travel. Furthermore, enhanced versions such as the 3SFCA [46] and the I2SFCA [47] methods have been extensively employed to capture facility competition intensity.

Research on measuring healthcare accessibility and equity has been conducted extensively, primarily within densely populated metropolitan areas. For example, studies have been carried out in the Chicago area in North America [5,48], as well as several Canadian metropolises [9]. Additionally, research has been conducted in European cities such as Milan [6,38] and Paris [49] and in Asian cities like Beijing [50] and Tokyo [51]. While the emphasis has been on urban areas, there has been limited attention given to non-metropolitan regions. Nevertheless, the existing minority of studies has predominantly focused on rural areas rather than other second-tier cities. McGrail and Humphreys [52] assessed primary care service accessibility across Victoria, Australia, to evaluate the effectiveness of improved methods both within and between rural and metropolitan populations over large geographical areas. Beyond regional studies, scholars have also analyzed accessibility allocation among different social groups through the lens of social spatial differentiation. For instance, Dai [45] examined residential segregation among black communities concerning spatial access to late-stage breast cancer diagnosis in metropolitan Detroit. Blumenberg et al. [53] applied the 2SFCA method to predict variations in childcare supply relative to demand across California’s Latinx neighborhoods. Hawthorne and Kwan [54] utilized GIS and perceived distance to explore the unequal geographies of healthcare in lower-income urban neighborhoods.

In China, scholars have also analyzed healthcare accessibility in different cities and regions, primarily distributed within major fist-tier cities, including metropolitan cities along the eastern coast or central and western provincial capital cities. The spatial patterns of hospital accessibility have been revealed with case studies in large cities such as Shanghai [55], Shenzhen [56], Fuzhou [57], Wuhan [58] and Nanjing, China [59], noting a gradient decrease in accessibility from urban centers to peripheries. Research has also explored PHC accessibility with different modes of transportation and for different demographic groups. For instance, studies have examined walkability to PHC institutions in Xi’an [23] and accessibility among different age groups in Wuhan [60]. However, minimal research has been directed toward second-tier cities, despite observations highlighting disparities in medical infrastructure distribution, resident mobility patterns, and healthcare service demands when compared to first-tier cities. Overall, existing research has predominantly focused on densely populated major cities, revealing common patterns in healthcare accessibility distribution. However, the available evidence may not be sufficient for studies in second-tier cities.

2.2. The Equity of Healthcare Accessibility

The equity of healthcare accessibility is a crucial component of both spatial equity and social justice, essential for crafting effective intervention strategies to improve healthcare fairness in particular areas or demographics; however, an authoritative definition remains elusive [61]. Spatial equity has been proposed since the 1960–1970s, undergoing a transition from the pursuit of spatial equality to social justice. This evolution has introduced concepts such as territorial justice [62], spatial equality [63], and location equity [64], primarily emphasizing the notion that residents in different areas should have equal per capita access to public services. Some scholars argue that the distribution of public resources, including healthcare, should be based on the social attributes and needs of individuals rather than merely striving for spatial equality. Therefore, they have proposed the concepts of horizontal equity and vertical equity [65]. The former suggests that people in the same environment should be treated equally, while the latter suggests that people in different environments should be treated differently to alleviate social inequality through the compensatory distribution of resources. This differentiation highlights the distinction between inequality and inequity [66]. Despite this, there is currently no single direct objective method to measure spatial equity, often necessitating the combination of multiple equity measurement approaches [61]. Among the most commonly used methods are the Gini coefficient and the Lorenz curve for assessing spatial equity [67,68]. Additionally, methods such as spatial autocorrelation or local indicators of spatial association (LISA), which align with demand-based definitions of spatial equity, are frequently employed [37,69]. Simultaneously, various techniques are utilized to examine the relationship between the distribution of healthcare facilities and population and socioeconomic factors, including ordinal correlation analysis, analysis of variance, bivariate spatial autocorrelation, and regression analysis [53,65,70,71].

The evaluation results indicate that affluent suburbs in certain North American urban areas have better healthcare accessibility compared to urban centers [5], while areas with low socioeconomic status are more likely to suffer from healthcare spatial inequity [45,54]. For example, an analysis of the spatial equity of community healthcare facilities in Chicago reveals that there is spatial inequity in the distribution of breast screening facilities for low-income families [72]. In Asian regions, optimal healthcare accessibility is typically concentrated in city centers and gradually diminishes toward the periphery [50,57], particularly affecting numerous urban vulnerable groups, such as the elderly, disabled, migrant workers, and low-income individuals in densely populated cities who face severe healthcare inequity issues [25,55].

In summary, the current mainstream view of spatial equity in healthcare accessibility focuses on ensuring similar spatial access while considering social attributes such as income, race, and age to achieve social equity goals [4,69,73]. In China, high-quality medical resources are predominantly concentrated in first-tier cities [21,55], making it necessary to study equity not only by region and demographics but also by city tier [74]. However, there is currently a lack of research on healthcare accessibility equity in second-tier cities. With the growing awareness of spatial equity in China, research on healthcare accessibility equity in second-tier cities and especially small and medium cities have become particularly important. Therefore, it is crucial to examine the accessibility and equity of healthcare facilities in these cities to improve this disadvantageous situation.

3. Study Area and Data

3.1. Study Area

This case study was conducted in Karamay District, which is located in a second-tier city in the northern part of the Xinjiang Uygur Autonomous Region in China (Figure 1). The city spans an area of 7334 square kilometers and has a population of 490,000, according to the seventh national population census in 2020. Established in the 1950s due to oil exploration, Karamay boasts a remarkably high urbanization rate of 99% and has a minimal agricultural population. The city is divided into four administrative districts, 14 subdistricts, and 107 communities. Karamay District has the highest population and the largest urban area, serving as the seat of the municipal government. This study specifically focuses on the urban area of Karamay District, which has a permanent resident population of 271,496 and covers approximately 70.6 square kilometers. Karamay District is divided into two distinct zones, namely, the northern and southern, separated by the Karamay River. The northern zone, including the Tianshanlu, Yinhelu, and Shenglilu subdistricts with a population of 148,739, constitutes the old city established in the 1950s, while the southern zone, including the Kunlunlu and Yingbin subdistricts with a population of 122,757, represents the new city developed from the late 20th century to the early 21st century. Significant differences exist between the northern and southern areas in terms of demographics, such as age, ethnicity, income, and other socioeconomic characteristics.

3.2. Data

3.2.1. Road Network and Healthcare Facility Data

The urban road network data required for this study were obtained from OpenStreetMap. We supplemented these data with satellite imagery and field surveys to classify the roads into five specific categories: highway, expressway, arterial road, collector road, and local road (Figure 2a). In the Chinese healthcare system, there are four main categories of institutions: hospitals, PHC institutions, specialized public health institutions, and other healthcare facilities. For this study, we focused on hospitals and PHC institutions, which are directly accessible to residents (Figure 2b). The locations of hospitals and PHC institutions were sourced from Gaode Maps (https://amap.com/) (accessed on 11 December 2023), while information regarding the supply capacity of the facilities, such as the number of beds or floor area, was gathered from publicly available online sources. In total, our study encompassed 15 hospitals and 18 PHC institutions. Among the hospitals, the number of beds ranged from 20 to 1000, with an average of 101 beds. The largest hospital, located in the southern part of the city, has a bed count that exceeds the combined total of all other hospital facilities. This hospital was relocated from the northern part of the city in 2023 and is one of the two tertiary hospitals in Karamay District. For PHC institutions, which typically do not have bed counts and for which it is difficult to obtain the number of medical staff, the building area is used as a proxy for service capacity. The building area of PHC institutions ranges from 259 to 5855 square meters, with an average of approximately 1713 square meters, indicating considerable variation. Similar to hospitals, there is a significant disparity in the size of PHC institutions (

Table 1. Statistics of demand and supply scale in different types and statistical units.

Index		Count	Statistics of Demand/Supply Scale
			Min.	Max.	Mean	SD
Supply scale	Hospitals (beds)	15	20	1000	101	275
	PHC institutions (m2)	18	259	5855	1713	1662
Demand scale	Compound access (persons)	274	114	4714	991	716
	Residential compound (persons)	160	114	7428	1697	1395
	Community (persons)	67	712	9815	4072	2040
	Subdistrict (persons)	5	38,566	71,642	54,299	12,343

).

3.2.2. Demographic Indicators

When evaluating accessibility, the size of the calculation unit impacts the accuracy of accessibility findings [4,43]. Using demographic data at inappropriate levels, such as when the data is aggregated or mismatched with the analysis scale, can lead to ecological fallacies, particularly when examining the characteristics of specific groups or community residents. In this study, to address the limitations of using geometric centroids in larger spatial units, such as administrative units, to represent demand points, which can overlook variations in accessibility within these units and may not accurately reflect the actual locations of residents, thereby reducing the precision of accessibility assessments, our study adopts residential compounds as the smallest analysis unit. Residential compounds are a common form of urban housing in China, typically characterized by enclosed boundaries and controlled entrances. Although travel times from residents’ homes to compound entrances vary due to differences in compound size and building locations within the compound, our study focuses on travel distances within the urban public road network, excluding internal roads within the compounds. Thus, demand points are located at the entrances of each residential compound. In cases where compounds have multiple entrances, the compound’s total population is evenly distributed among the entrances based on their number. In total, 274 demand points are obtained, each representing the population size of it (Figure 3a, Table 1). Demographic information regarding age groups, gender, and ethnicity within these compounds is also gathered. This information is sourced from the local civil affairs department, with accuracy at the residential compound level. Age, particularly, is a crucial variable in this study. It is divided into eight groups: four groups for children (0–18 years old) (Figure 3b), two groups for young and middle-aged adults (19–60 years old) (Figure 3c), and two groups for seniors (61 years old and above) (Figure 3d). Among these, children account for 17.8% of the population, young and middle-aged adults account for 67%, and seniors account for 15.3%. Regarding the spatial pattern of the population, it is observed that the northern zone accommodates 54.7% of the population, while the southern zone accounts for 45.3%. Considering different age groups, the proportion of children and young and middle-aged adults living in the northern zone is 54.1% and 53.5%, respectively, which is slightly lower than their overall population proportion in this zone (54.7%). However, the proportion of seniors, especially those aged 75 years and above, is notably higher at 69.4%. In contrast, in the southern zone, the proportion of preschool children exceeds the zone’s overall population proportion (45.3%) by nearly 10 percentage points, with infants and toddlers (0–3 years old) accounting for 58.3%. This indicates that the northern zone has a higher concentration of seniors, especially the elderly, while the southern zone is inhabited by more preschool children, particularly infants and toddlers (Figure 3b). This segmentation enables a detailed understanding of the population distribution within the compounds and facilitates a more precise comprehension of how accessibility varies across different age groups.

All data collection occurred at the end of 2023 to establish a temporal context for the study. Measures were implemented to ensure the reliability of the gathered data, with specific data provided in the study’s Supplementary Materials for transparency and verification purposes. However, it is important to acknowledge the possibility of changes in healthcare facilities or road networks that could affect the timeliness of the data and thus the study’s findings at the time of analysis or publication.

4. Methods

4.1. Measuring Accessibility

The fundamental concept of the traditional 2SFCA method entails conducting two searches, including one from the supply points and another from the demand points, within a designated search radius to compute accessibility. The specific calculation formulas are as follows:

(1) First search: Centered on supply point j, search for all demand points k within the service threshold d₀ of j, and calculate the supply-demand ratio R_j of point j with respect to all demand quantities D_k.

$$R_j={\displaystyle \frac{S_j}{\sum D_k}}$$

(1)

(2) Second search: Centered on demand point i, search for all supply points j within the threshold d₀. Then, accumulate the supply-demand ratios of all found points j to obtain the accessibility value A_i of point i.

$$A_i=\sum _{j\in \left\{d_{ij}\le d_0\right\}}{R}_j$$

(2)

The Gaussian two-step floating catchment area (G2SFCA) method introduces an additional distance attenuation function within the search radius to account for the non-linear decrease in residents’ willingness to seek medical care as travel distance increases. The Gaussian function shows a pattern of initially accelerating attenuation rates with increasing distance, followed by a deceleration, which is considered to more accurately reflect people’s travel behavior. Hence, this study adopts the G2SFCA method for accessibility assessment. The formula for the Gaussian function is as follows:

$$f\left(d\right)={\displaystyle \frac{e^{-\frac{1}{2}\times {\left(\frac{d}{d_0}\right)}^2 }-e^{-\frac{1}{2}}}{1{-e}^{-\frac{1}{2}}}}, d\le d_0$$

(3)

Here, d represents the actual distance between supply and demand points, and d₀ is the service threshold for the search.

The determination of the service radius d₀ is a subject of considerable debate due to its subjective nature. Generally, service thresholds should be established based on variations in different regions, travel modes, and facility types [4,26]. Residents usually select different modes of transportation to access healthcare facilities depending on the services provided. In China, hospitals primarily offer diagnostic and treatment services, and people typically use cars or public transportation to reach them. PHC institutions, on the other hand, provide services such as elderly care and children’s vaccinations and are typically accessed on foot, often by children and the elderly. Many empirical studies in China set the service radius for hospitals to a travel time of 30–50 min by car or public transportation [46,55,74]. For PHC institutions, the service radius is often set to a travel time of 15–30 min on foot [18,23]. However, it should be noted that these data mainly come from first-tier cities, and whether these thresholds are suitable for second-tier cities remains unproven. In second-tier cities, public transportation resources are very limited, with walking, electric bicycles, and private cars as the primary modes of transportation. When seeking medical treatment, residents tend to use private cars [74,75]. For PHC services, walking is the main mode of transportation, primarily due to the user groups of the elderly and children.

To determine the calculation radius of healthcare institution service areas in this case, we first plotted isochrone maps based on different modes of transportation. For hospital service, we used car travel distance, starting at 5 min (approximately 2 km) and increasing in 5-min increments. For PHC institutions, we considered walking distance, starting at 10 min (approximately 667 m) and increasing by 10-min increments until covering all demand points. The results indicate that hospitals can cover all demand points within a 15-min travel range by car (Figure 4a), while primary healthcare institutions can cover the majority of demand points within a 30-min walking range, with only two demand points not covered (Figure 4b). Therefore, the service radius for hospitals is set to a 15-min car journey, while the service radius for primary healthcare institutions is set at the maximum walking duration of 30 min for calculations.

Given the significant influence of healthcare facility tiers on residents’ healthcare-seeking behavior, this study employs a subjective weighting approach to account for this impact. Different levels of healthcare facilities are assigned distinct service weights, denoted as W. The specific allocations are outlined as follows:

$$w=\left\{\begin{array}{l}1.0, \mathrm{i}\mathrm{f} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{t}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{h}\mathrm{o}\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}\\ 0.8, \mathrm{i}\mathrm{f} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{h}\mathrm{o}\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}\\ 0.5, \mathrm{i}\mathrm{f} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y} \mathrm{i}\mathrm{s} \mathrm{a} \mathrm{p}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{y} \mathrm{h}\mathrm{o}\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}\end{array}\right.$$

(4)

Based on the above, the refined two-step floating catchment area (2SFCA) model is expressed as follows:

$$A_i^F=\sum _{j\in \left\{d_{ij}\le d_0\right\}}{R}_j=\sum _{j\in \left\{d_{ij}\le d_0\right\}}{\displaystyle \frac{S_j ·w_j}{\sum _{k\in \left\{d_{kj}\le d_0\right\}}{D}_k·f\left(d_{kj}\right)}}·f\left(d_{ij}\right)$$

(5)

Here, i and k are demand points, j is a supply point, and d_ij and d_kj are the distances from demand points i and k, respectively, to supply point j. S_j is the supply scale of supply point j, D_k is the demand scale of demand point k, and f(d_ij) and f(d_kj) are Gaussian distance decay functions, as described in Equation (2). R_j is the ratio of the facility scale of supply point j to the population served within the search radius d₀. w_j is the service weight of supply point j, and A_i^F is the accessibility value of demand point i.

In addition, in this paper, to distinguish areas with good and poor accessibility, we employed an equal interval method, using 1.60 for hospitals and 0.07 for PHC as the standard intervals. This method divides the accessibility levels of hospitals and PHC institutions into five categories: 1. Excellent (6.50–8.00 for hospitals|0.29–0.35 for PHC institutions, same below), 2. Relatively good (4.90–6.40|0.22–0.28), 3. Moderate (3.30–4.80|0.15–0.21), 4. Relatively poor (1.70–3.20|0.08–0.14), and 5. Worst (1.40–1.60|0.00–0.07).

4.2. Spatial Autocorrelation

Spatial autocorrelation analysis is a method used to study the spatial correlation within geographic datasets [76,77]. Global Moran’s I is the most commonly used indicator of global spatial autocorrelation [78,79], while Local Moran’s I is typically used to identify local clusters and spatial outliers [80]. In healthcare accessibility studies, Global Moran’s I analyzes the overall spatial clustering characteristics of accessibility, while Local Moran’s I identifies areas with high and low accessibility values, indicating regions where healthcare resources are relatively abundant or deficient. In this study, ArcGIS 10.4 software is used to compute the global and local Moran’s I for healthcare accessibility. The spatial relationship among units is defined as the inverse distance, and the Euclidean distance method is used to calculate the distance from each unit to neighboring units. Furthermore, ArcGIS 10.4’s visualization capabilities are used to display the results of these indicators, as well as the spatial clustering characteristics of medical facility distribution and the specific distribution of “medical deserts”.

4.3. Equity Analysis

Lorenz curves have been extensively employed in evaluating equity within accessibility studies [71]. By illustrating the cumulative distributions of accessibility across a population, this method effectively portrays accessibility (in)equity across various locales. In this study, we grouped populations by community and plotted Lorenz curves with cumulative population percentages on the horizontal axis and cumulative accessibility percentages on the vertical axis. If healthcare accessibility is evenly distributed among all populations, the curve would align with the diagonal. However, if disparities exist, the curve would fall below the diagonal, indicating an uneven distribution. To further assess the extent of inequity, the Gini coefficient was utilized to measure the deviation of the Lorenz curve from the diagonal. A greater deviation from the diagonal signifies higher inequality levels. Graphically, the Gini coefficient equals SA/SB, where SA represents the area between the diagonal line and the Lorenz curve, and SB represents the total area under the diagonal line. For unordered samples, the Gini coefficient is computed as follows:

$$Gi=1-\sum _{i=1}^n(X_i-X_{i-1})(Y_i-Y_{i-1})$$

(6)

Here, Gi denotes the Gini coefficient of facility accessibility, n represents the number of communities, X_i is cumulative population percentages, and Y_i is cumulative accessibility percentages. The Gini coefficient ranges from 0 to 1. A value of 0 usually indicates perfect equality, while a value of 1 suggests complete inequality. In this paper, we use the Gini coefficient to evaluate the equality of access to healthcare across all communities and age groups.

5. Results

5.1. Accessibility of Two Types of Healthcare Facilities

Figure 5 illustrates the accessibility patterns of two types of healthcare facilities: hospitals and primary healthcare institutions. The hospital accessibility pattern demonstrates a clear monocentric trend, with accessibility values gradually decreasing from the southeast to the northwest. The areas with the highest accessibility are concentrated around tertiary hospitals in the southwest, while regions with moderate to poor accessibility are predominantly located in the northern part. In contrast, the accessibility pattern for PHC institutions exhibits a multicentric clustering distribution, with areas of high and low accessibility overlap spatially. Regions with relatively good accessibility are mainly located around community health service centers, which, along with their subfacilities, including community health service stations, constitute the PHC institutions. Conversely, areas with relatively poor accessibility are predominantly on the outskirts of urban areas, displaying a scattered distribution. Additionally, there are regions with zero accessibility, indicating a lack of coverage by primary healthcare services.

Hospital accessibility primarily ranges between 1.36 and 7.76, with a mean of 4.92, while PHC accessibility mainly falls between 0 and 0.35, with a mean of 0.11 (Figure 5,

Table 2. Statistics of healthcare accessibility by subdistrict.

Subdistrict	Mean	Median	Max	Min	SD	CV
Shenglilu	4.48 0.11	4.59|0.11	5.52|0.18	3.12|0.03	0.68|0.05	0.15|0.45
Kunlunlu	6.91|0.10	7.16|0.11	7.77|0.25	5.10|0.00	0.69|0.06	0.10|0.60
Tianshanlu	3.46|0.09	3.40|0.09	5.06|0.17	1.48|0.00	0.74|0.06	0.21|0.67
Yinhelu	2.18|0.14	1.93|0.14	4.13|0.31	1.36|0.01	0.78|0.08	0.36|0.57
Yingbin	5.76|0.07	5.49|0.10	7.66|0.25	4.32|0.00	0.95|0.07	0.16|1.00
Total	4.93|0.11	5.03|0.11	7.77|0.31	1.36|0.00	1.87|0.07	0.38|0.66

Note:|separates statistics of accessibility data, with values on the left for hospitals and those on the right for PHC institutions.

). For hospital accessibility, we found that 27% of the population falls within the excellent category, with 26.5%, 22%, and 17% in the relatively good, moderate, and relatively poor categories, respectively, and only 7% in the worst category. Regarding PHC accessibility, 0.8% of the population is in the excellent category, with 7%, 21%, and 34% in the relatively good, moderate, and relatively poor categories, respectively, and 38% in the worst category (of which approximately 1.6% have zero accessibility). Although these two accessibility indicators are not directly comparable, the distribution across categories reveals that hospital accessibility predominantly falls in the upper-middle range, whereas PHC accessibility is primarily in the lower-middle range. Furthermore, we weighted and averaged the accessibility of each compound entrance within a community to obtain the accessibility data at the community level (Figure 5c,d), showing a pattern similar to the entrances of compounds.

Further analysis of accessibility data at the subdistrict level reveals significant differences in the distribution of accessibility for the two types of healthcare facilities. For hospital accessibility, Kunlunlu boasts the highest accessibility, followed by Yingbin, with values of 6.91 and 5.76, respectively. These two subdistricts are both located in the southern zone of the city. Conversely, Yinhelu has the lowest hospital accessibility, followed by Tianshanlu and Shenglilu, with values of 2.18, 3.46, and 4.48, respectively. These three subdistricts are situated in the northern zone of the city. In terms of primary healthcare accessibility, Yinhelu ranks highest, followed by Shenglilu, Kunlunlu, and Tianshanlu, with Yingbin subdistrict having the poorest accessibility. Their respective accessibility values are 0.14, 0.11, 0.10, 0.09, and 0.07. Hospital accessibility tends to be better in the southern zone compared to the northern zone, while healthcare accessibility shows the opposite trend.

5.2. Spatial Agglomeration Characteristics

The global autocorrelation analysis of the accessibility of two types of facilities shows that the global Moran’s I is 0.96 for hospital accessibility and 0.65 for primary healthcare institutions (

Table 3. Global Moran’s I summary.

Statistic	Value for Hospital Accessibility	Value for PHC Accessibility
Moran’s I Index	0.959895	0.649227
Expected Index	−0.003663	−0.003663
Variance	0.000499	0.000498
Z Score	43.135795	29.254173
p Value	0.000000	0.000000

). This result indicates that both hospital and primary healthcare institution accessibility exhibit positive spatial agglomeration characteristics, with hospital accessibility showing a more pronounced clustering feature. The local autocorrelation analysis, represented by local Moran’s I, indicates different high and low accessibility value distribution areas for each type of facility (Figure 6). High value clusters of hospital accessibility are mainly distributed in the southern area, particularly in the Kunlunlu subdistrict, while low value clusters are predominant in the northern area, mainly in the Yinhelu and Tianshanlu subdistricts. High value clusters of primary healthcare institution accessibility are primarily distributed in four different regions: the Beidou, Fangcaojiayuan, and Yinhe communities, and their surroundings in the Yinhelu subdistrict; the Zefu and Huifu communities and their surroundings in the northern part of the Yingbin subdistrict; the Nanyuan and Nanquan communities and their surroundings in the Kunlunlu subdistrict; and the Dongfeng Education, Hongqi Democracy, and Liming Shuguang communities in the Shenglilu subdistrict. Low value clusters are mainly distributed in three regions: the Qianjin North and Qianjin South communities in the Shenglilu subdistrict; the Riheyuan, Xiyuetan, and Senxiangshuian Garden communities in the Tianshanlu subdistrict; and the Ruyiyuan, Jixiangyuan, and Pinganyuan communities and their surroundings in the Kunlunlu subdistrict. Identifying high and low accessibility clusters provides visual assistance for analyzing the spatial inequality of healthcare resource distribution and formulating corresponding intervention policies.

5.3. Equity Evaluation

5.3.1. Equality of Healthcare Accessibility

The spatial patterns of hospital accessibility and primary healthcare accessibility indicate that they are unequal for people in different locations. This inequality does not necessarily imply spatial unfairness, as it must be evaluated in the context of socioeconomic factors [61]. We believe that while equity means providing vulnerable groups with preferential accessibility, it should still be based on a foundation of equality and be limited to a reasonable range of inequality. To quantify this, we use the Gini coefficient and Lorenz curve for evaluating the equality of healthcare accessibility. The Gini coefficient is frequently used as an index to reflect the inequality of income distribution. The value of the Gini coefficient varies from 0 to 1. A region with complete equality will have a value of 0, while a region with no equality will be denoted by 1. According to general international standards, a Gini coefficient that is smaller than 0.3 represents a particularly equitable condition, 0.3–0.4 is the normal condition, while greater than 0.4 raises concern, and a value greater than 0.6 indicates a dangerous state [81,82,83,84].

The Gini coefficient is 0.22 for hospital accessibility and 0.38 for primary healthcare accessibility. Both fall within the range of relative equality. However, there is significant variation in Gini coefficients across different subdistricts. Kunlunlu exhibits the lowest Gini coefficient for hospital accessibility at a mere 0.06, followed by Shenglilu, Yingbin, and Tianshanlu, with the poorest accessibility found in Yinhelu at 0.20. Regarding PHC accessibility, Shenglilu has the lowest Gini coefficient at 0.23, followed by Yinhelu, Yingbin, and Kunlunlu, while Tianshanlu displays the highest inequality at 0.43. This leads to an intriguing observation: while hospital accessibility Gini values within subdistricts are lower than the overall Gini value, the same does not hold true for PHC accessibility. There is substantial variation in PHC accessibility Gini values within subdistricts, with both the Kunlunlu and Tianshanlu subdistricts exceeding the critical threshold of 0.4, indicating inequality. Consequently, we conclude that addressing inequality in hospital accessibility should focus on inter-subdistrict disparities, whereas for PHC accessibility, both intra-subdistrict and inter-subdistrict disparities need to be addressed simultaneously.

5.3.2. Equity across Age Strata

While hospital and primary healthcare accessibility falls within a relatively equal range, it remains uncertain whether this equality translates into equity across different socioeconomic groups. Among the various factors influencing individual health equity; age stands out as particularly significant, especially considering the crucial role that age plays in shaping healthcare decisions. Therefore, it is imperative to prioritize the healthcare needs of age-vulnerable populations; such as the elderly and children. Thus, we propose to investigate whether the healthcare accessibility pattern within our study area disproportionately benefits the elderly and children.

Table 4. Healthcare accessibility and Gini coefficients by age group and subdistrict.

Age	Yinhelu	Tianshanlu	Shenglilu	Kunlunlu	Yingbin	Average
0–3	2.27|0.14	3.25|0.06	4.52|0.11	7.10|0.08	5.98|0.11	5.28|0.10
	(0.20|0.37)	(0.13|0.52)	(0.08|0.23)	(0.05|0.46)	(0.09|0.36)	(0.20|0.42)
4–6	2.25|0.15	3.23|0.06	4.45|0.11	7.12|0.08	6.05|0.11	5.14|0.10
	(0.20|0.35)	(0.12|0.52)	(0.08|0.25)	(0.05|0.47)	(0.10|0.36)	(0.22|0.43)
7–12	2.21|0.15	3.22|0.06	4.47|0.11	7.07|0.08	5.74|0.13	4.82|0.10
	(0.20|0.35)	(0.12|0.52)	(0.08|0.24)	(0.05|0.45)	(0.10|0.34)	(0.23|0.42)
13–18	2.24|0.14	3.28|0.08	4.55|0.11	6.90|0.10	5.62|0.13	4.68|0.11
	(0.20|0.34)	(0.14|0.38)	(0.08|0.23)	(0.06|0.38)	(0.09|0.32)	(0.23|0.35)
19–45	2.24|0.14	3.28|0.07	4.54|0.11	7.03|0.08	5.90|0.11	5.02|0.10
	(0.20|0.36)	(0.13|0.47)	(0.08|0.23)	(0.05|0.44)	(0.10|0.36)	(0.22|0.40)
46–60	2.26|0.14	3.32|0.08	4.52|0.11	6.85|0.10	5.76|0.12	4.86|0.11
	(0.19|0.33)	(0.13|0.40)	(0.08|0.23)	(0.06|0.37)	(0.09|0.34)	(0.21|0.35)
61–75	2.31|0.15	3.32|0.09	4.56|0.12	6.92|0.10	5.88|0.12	4.94|0.11
	(0.18|0.29)	(0.12|0.37)	(0.08|0.22)	(0.06|0.38)	(0.10|0.35)	(0.21|0.35)
76+	2.39|0.14	3.44|0.12	4.56|0.13	6.80|0.13	5.84|0.12	4.71|0.13
	(0.18|0.26)	(0.10|0.22)	(0.08|0.20)	(0.06|0.28)	(0.10|0.35)	(0.21|0.26)
Average	2.26|0.14	3.30|0.08	4.53|0.11	6.96|0.09	5.85|0.12	4.93|0.11
	(0.20|0.34)	(0.13|0.43)	(0.08|0.23)	(0.06|0.41)	(0.09|0.35)	(0.22|0.38)

Note: Gini data in (). “|” separates hospital (left) and PHC (right) data.

reveals that hospital accessibility is highest for children aged 0–3 years, exceeding the average by 7.3%, followed by children aged 4–6 years (4.4% above average) and adults aged 19–45 years (2.0% above average). The elderly aged 61–75 years are on par with the average. Accessibility for adults aged 46–60 years is 1.2% below the average, followed by children aged 7–12 years (2.0% below average), senior citizens aged 76 years and above (4.3% below average), and adolescents aged 13–18 years, who have the lowest accessibility (4.8% below average). For PHC accessibility, individuals aged 76 years and above have the highest accessibility, exceeding the average by 18.2%. Those aged 13–18, 46–60, and 61–75 years are on par with the average. Children aged 0–3, 4–6, and 7–12 years and young adults aged 19–45 years have the lowest accessibility (all 9% below average). From this evidence, we find that two demographic groups, children and the elderly, do not always occupy advantageous positions in accessibility distribution. For the elderly, they have an advantage in PHC accessibility but not in hospital accessibility, with those aged 76 years and above even showing a significant disadvantage. As for children, those aged 0–12 years have better hospital accessibility but exhibit poorer PHC accessibility. Therefore, based on the existing results, it is challenging to argue that this situation favors equity in all age groups. We can conclude that for the elderly, PHC accessibility distribution is equitable, whereas hospital accessibility is not. For children, the situation is the opposite.

Another approach based on age stratification is to examine the individual inequality of accessibility distribution within different age groups. We hope that accessibility is evenly distributed, as such equality implies equity, especially without additional socioeconomic differences. Therefore, we further examine the Gini coefficient of accessibility distribution across age groups (Figure 7). We find that the Gini coefficients of hospital accessibility mainly range from 0.20 to 0.23. This indicates a relatively equal distribution, suggesting that hospital accessibility is equitable. However, the Gini coefficients of PHC accessibility range from 0.26 to 0.43, showing significant variation among age groups. The Gini coefficients for children aged 0–3, 4–6, and 7–12 years are 0.42, 0.43, and 0.42, respectively, all exceeding the 0.4 threshold for inequality. Overall, it can be broadly concluded that healthcare accessibility distribution in the study area is relatively equal. However, the elderly face group-level inequity in hospital accessibility, while children aged 0–12 years face both group-level inequity and individual-level inequity in PHC accessibility.

6. Discussion

6.1. Interpreting Results

Studies have found that hospital accessibility demonstrates a monocentric trend, where as PHC accessibility exhibits a multicentric distribution. The areas with the highest hospital accessibility are concentrated around large hospitals, while PHC accessibility is greatest near PHC centers. These phenomena are typically attributed to three factors: supply scale, demand scale, and transportation. First, healthcare facilities impact accessibility patterns, particularly larger ones, whose locations directly determine the accessibility patterns in this case study. Similar findings have been observed in some first-tier cities. Like second-tier cities, hospital accessibility in first-tier cities also shows a pronounced centrality. However, in first-tier cities, this centrality is determined not by a single top-tier hospital but by clusters of hospitals concentrated within central urban areas [50,55,85]. A similar pattern is also observed in the distribution of PHC facilities and PHC accessibility in first-tier cities [86]. Second, in terms of demand scale, there is no clear evidence suggesting that it significantly affects the distribution of healthcare accessibility. This could be attributed to the fact that the population distribution in second-tier cities is more even, which reduces the impact of demand scale differences on healthcare accessibility distribution. Compared to the significant spatial differentiation of the population within first-tier cities, the smaller scale of non-residential functional land and the lower, more evenly distributed intensity of residential land development in second-tier cities lead to a more even population distribution. Finally, from the perspective of transportation, studies from first-tier cities indicate that high accessibility areas are often distributed along major transportation routes or around public transit nodes [55]. However, the results in this study indicate that second-tier cities do not exhibit the same pattern, which may be due to differences in transportation systems and residents’ travel modes between the two types of cities. Public transportation improves residents’ healthcare accessibility [85], but the lack of public transportation in second-tier cities makes it challenging to assess its impact on healthcare accessibility in these areas. Additionally, studies based on spatiotemporal big data are attempting to uncover patterns of population mobility within cities [87,88]. These findings provide favorable conditions for researching the affordability of healthcare-related travel [25] and spatial equity based on individual accessibility [73]. However, there is still a lack of evidence to determine whether these findings align with the travel behaviors of second-tier city residents regarding acceptable travel time, cost, and destination distance.

Due to the ambiguous nature of the concept of equity, a vast array of research methods at diverse spatial levels have been used to explore various aspects of equity [89]. A more commonly accepted viewpoint is that there are two main types of equity: horizontal equity and vertical equity [90]. This study evaluated these two types of equity: overall population equality for horizontal equity and both group-level equity among different demographic groups and individual-level equity within specific age groups for vertical equity. In terms of horizontal equity, healthcare accessibility in second-tier cities is relatively equal, which is surprisingly better than that in larger cities. A possible reason is that in smaller cities, motor vehicles greatly reduce spatial inequality due to the smaller city scale. However, PHC equality is not as good as hospital equity, likely because PHC accessibility is calculated based on walking distance and the layout of PHC facilities does not favor pedestrian access. The Chinese government’s “15-min life circle” concept aims to distribute various urban service facilities, including PHC institutions, within a 15-min walking distance for local residents [18]. However, this research indicates that for residents of second-tier cities, reaching the nearest PHC institution within 15 min on foot is quite challenging, and about 31% of the population is not covered by the 15-min service radius. Additionally, it is important to note that distance-based calculations have certain limitations, as they only consider the service area of the facility, but neglect demand and supply scale differences. Therefore, the accessibility-based analysis reveals these inequalities more accurately. In terms of vertical equity, analysis of age-vulnerable populations reveals some group-level inequities in hospital accessibility for the elderly, as well as both group-level and individual-level inequities in primary healthcare accessibility for children aged 0–12 years. This may be attributed to a spatial mismatch between healthcare facilities and the population distribution across different age groups. New urban areas, with their high-quality hospital resources, tend to attract more young adults and their children, while the elderly often prefer to remain in older zones due to lifestyle preferences and economic reasons. This phenomenon reflects a government focus on mobilizing high-quality medical resources to attract affluent populations in the development of new cities, often overlooking the healthcare needs of the elderly. Furthermore, the neglect of PHC institutions in these newly developed zones has resulted in inequities in PHC resources for residents of these urban areas.

Based on the above discussion, facility layout and supply scale significantly influence accessibility patterns, although demand scale, distance, and transportation modes also play certain roles. These findings highlight the singular dominance of healthcare facility factors (including their level and scale) in shaping the healthcare accessibility layout in second-tier cities, and suggest the direction for efforts to improve healthcare accessibility in these cities. While healthcare accessibility in second-tier cities performs relatively well in terms of horizontal equity, it has overlooked the medical needs of the elderly in some aspects, leading to vertical inequities. Enhancing the provision of PHC institutions in newly developed areas and ensuring that residents can reach the them within a 15-min walk should be key focuses of urban planning to promote healthcare equity.

6.2. Planning Implications

Our empirical research conducted in Karamay District has shed light on promising strategies for improving the distribution of healthcare resources in second-tier cities. Drawing upon our findings and subsequent discussions, a series of strategic recommendations have been developed, aiming at maximizing the impact of our research. First, it is vital to acknowledge the significant role that the layout of healthcare facilities plays in urban planning, profoundly influencing healthcare accessibility patterns. When addressing deficiencies in healthcare provision in these cities, it is essential to prioritize enhancing the quality and scale of individual facilities rather than merely increasing their quantity or altering their distribution. This approach ensures improved accessibility and the delivery of higher quality medical services to residents. Second, refining land use regulations can effectively shape the location and scale of healthcare facilities, thereby influencing the spatial distribution of healthcare services. Decision-making processes regarding the approval of healthcare facility sites should be informed by scientific analyses of accessibility and equity, moving beyond traditional metrics such as per capita or distance-based assessments. Third, for the study area, increasing the scale of hospitals in the northern part is important to improve hospital accessibility. For PHC accessibility, the focus should be on improving the walkability of PHC facilities in the southern part and adding PHC facilities in the low-accessibility clusters located in the western, northeastern, and southeastern areas. Additionally, there is a need for ongoing optimization of urban spatial structures, including enhancing walkability according to the 15-min living circle plan and improving public transportation networks to enhance healthcare accessibility. Lastly, as urban populations shifting towards newer development areas, it is crucial to focus on the healthcare needs and spatial distribution of vulnerable groups, such as the elderly and children. We believe that in improving healthcare accessibility, creating a more age-friendly environment should be prioritized. This includes providing safer street environments and public spaces that promote physical activity and social interaction and increasing healthcare facilities that offer geriatric services.

Future research should explore the healthcare-seeking behaviors of residents in second-tier cities, conduct individual-level accessibility studies, and investigate the long-term impacts of urban healthcare accessibility on health outcomes. In terms of planning practice, it is necessary to explore the impact of community participatory planning on healthcare policy and the distribution of healthcare accessibility, as well as the role of technologies such as telemedicine and digital health platforms in improving healthcare accessibility in underserved areas. The aim of these continued research efforts is to improve the spatial accessibility and equity of healthcare services in second-tier cities, thereby promoting greater health equity.

6.3. Assumptions and Limitations

This study has some limitations. First, it focuses solely on place-based healthcare accessibility and does not consider residents’ spatiotemporal behavior, which also plays an important role in measuring accessibility. Future research could explore how to utilize the G2SFCA method to better explain the dynamic accessibility experienced by individuals. Second, while focusing on second-tier cities, it is important to note that these cities vary widely. This study selects only Karamay District as a case study. Although Karamay is a typical industrial resource-based city representing a significant category of second-tier cities, it is still challenging to generalize findings to all second-tier cities based on a single case. Nonetheless, this research provides a new perspective on second-tier cities, which could guide further studies. Third, Karamay District is located in the Xinjiang Uygur Autonomous Region of China, where ethnic minorities account for more than 20% of the population. However, due to difficulties in obtaining data on ethnic minorities, this factor was not considered in the study. We believe that healthcare accessibility is a universal issue that extends beyond the context of ethnic minorities, making the results still credible and applicable to some extent.

7. Conclusions

This study utilizes the G2SFCA method to assess the spatial accessibility of hospitals and primary healthcare facilities in a second-tier city, investigating healthcare equity across various age groups. The findings reveal distinct patterns: hospital accessibility follows a monocentric distribution, while PHC facility accessibility exhibits a polycentric pattern. Both types of facilities demonstrate significant positive spatial clustering, with hospitals showing stronger clustering overall. Healthcare accessibility is relatively equal, while the elderly face group-level inequity in hospital accessibility and children aged 0–12 years face both group-level and individual-level inequities in PHC accessibility.

This research contributes methodologically by extending existing frameworks for analyzing healthcare accessibility and equity to suit second-tier cities. By separately evaluating hospitals and PHC facilities and proposing service thresholds tailored to these contexts, we provide a nuanced understanding of accessibility. Moreover, employing higher precision data enhances the accuracy of our results. Empirically, our study sheds light on healthcare accessibility distributions in second-tier cities, demonstrating similarities to patterns in large cities but with notable differences. Notably, these cities exhibit relatively better spatial equity compared to the inequities found in larger cities.

In the future, as China undergoes healthcare reforms, understanding the evolving patterns of healthcare accessibility under the hierarchical medical system becomes crucial. Future studies should also explore other socioeconomic attributes beyond age groups, depending on data availability. Lastly, as achieving the goals of “Healthy China 2030” is paramount for sustainable development, further exploration of healthcare accessibility and equity in cities remains an essential area of research.