Good health and well-being is one of the sustainable development goals of the United Nations and has received extensive attention throughout the world (Agbenyo et al., 2017). Since the 1950s, with the development of public services in the western countries, health geography has received increasing attention. The health care accessibility, i.e., the ability of individuals or groups to access certain health care services, is an important instrument in health geography research (Penchansky and Thomas, 1981; Guagliardo, 2004; Peters et al., 2008; Jacobs et al., 2011). Since the World Bank advocated a balanced coverage of access to public services (Scott, 2009), the health care accessibility has increasingly become an important field of government and academic research.

Till date, several studies have explored the spatial pattern characteristics of health care accessibility at different scales (Yang et al., 2010; Rosenberg, 2014). At regional scale, Crooks and Schuurman (2012) explored the potential spatial access to primary health care physicians in five Canadian provinces and territories. At urban scale, several studies found that the areas with higher accessibility are mainly concentrated in urban areas, while those with lower accessibility are mainly concentrated in marginal areas (Brabyn and Skelly, 2002; Chen et al., 2018). At neighborhood scale, several studies indicated that accessibility significantly differs from spatial dimensions (Bell et al., 2013; Cabrera-Barona et al., 2016). However, these studies mainly focused on the regional heterogeneity of health care accessibility; nonetheless, studies exploring the accessibility to different levels of health care services are relatively fewer. Noteworthy, in-depth understanding of this aspect is important, as it has implications for public policies that change health care services. Most countries, such as China, have different levels and types of health care facilities. Primary health institutions are mainly responsible for basic services, as well as for the treatment of common and frequently occurring diseases. Public hospitals are mainly responsible for high-level health care services, providing emergency medical assistance services, which can be divided into county, municipal and provincial categories. Owing to differences in the objectives and content, it is meaningful to measure the accessibility to different levels of health care facilities, when studying the accessibility to health care services.

Some researchers examined the spatial pattern characteristics in different levels of health care accessibility. Yin et al. (2018) found that regional differences in accessibility to clinics, hospitals, or emergency centers in China are particularly evident. Health care services are mainly concentrated in areas with superior natural and economic conditions. Song et al. (2018) analyzed the public hospitals, emergency centers and surgical hospitals accessibility in Australia, and found that accessibility to all the public hospitals in remote areas is possibly higher than in metropolitan areas, which have a higher accessibility to emergency and surgical services. However, the majority of these studies focus only on the spatial patterns of health care accessibility, thereby ignoring the equity of health care accessibility (Neutens, 2015). The equity of health care accessibility can be divided into horizontal equity and vertical equity. The former indicates that the groups with the same health needs should have the same health care accessibility, while the latter refers to the corresponding changes of health care accessibility with the change of health needs. Owing to the ethical judgment, only a few studies are available on vertical equity of health care accessibility (Goddard and Smith, 2001; Oliver and Mossialos, 2004; Neutens, 2015). The existing researches on equity of health care accessibility, mainly analyzed it from the perspective of different levels and different types of health care services, as well as horizontal equity and vertical equity. Based on the census data, Rosero-Bixby (2004) analyzed the horizontal equity of Costa Ricans in access to the nearest outpatient care and hospital care, and pointed out that 12%–14% of the population was living in underserved areas. Based on the 1998–2000 health survey in England, Morris et al. (2005) analyzed the horizontal inequity in the utilization of different levels health care services for low income and ethnic minorities groups, and found that they used more primary health care services than high-level health care services. Based on the Health Interview Survey of Taiwan in China, Wang and Yaung (2013) evaluated the vertical equity of health demands in outpatient, emergency services, hospitalization, and preventive service; and pointed out that the vertical equity of preventive service was poor. Although existing studies performed quantitative evaluation of health care services, they tended to study overall equity at regional scale (Lin et al., 2009; Gu and Yin, 2010; Ding and Chen, 2017), and lack the quantization and visualization of smaller scale spatial units from the perspective of equity.

These limitations actually hamper the identification of health care underserved areas. Moreover, the identification of underserved areas is usually based on accessibility, without considering equity. Since the 1960s, several studies have been carried out to identify health care underserved areas. The identification standard for the U.S. Department of Public Health is that the population-to-primary physician ratio is less than 3500∶1, and that health care services are available within 30 min of travel time (US Department of Health and Human Services, 1998). Wang and Luo (2005) integrated transportation accessibility, socio-economic predicaments, socio-cultural barriers, and health care demand variables to identify underserved areas in Illinois. Rosero-Bixby (2004) found that half of Costa Ricans lived within 1 km from clinics and 5 km away from hospitals, with about 15% of the population identified as underserved one. Hare and Barcus (2007) conducted a study of Kentucky heart care services, pointing out that rural areas and the Appalachian Mountains are more likely to be economically and socially marginalized, if their travel time is more than 45 min. Based on raster and network accessibility, Delamater et al. (2012) identified the underserved areas of Michigan emergency centers, and suggested that the measurement model should be carefully selected. Existing studies identify underserved areas only through health care accessibility (Rosero-Bixby, 2004; Hare and Barcus, 2007; Delamater et al., 2012), thereby ignoring the impacts of equity on this identification. Combining the evaluation of accessibility and equity, it is possible to identify underserved areas more accurately, so as to provide more effective decision support for health policymakers.

Furthermore, the majority of existing studies focus on developed countries. There are significant differences in the type of health care services, health system, identification standards, and social and economic attributes of population among different countries (Wang and Luo, 2005; Delamater et al., 2012; Lang et al., 2016; Zhang et al., 2018); thus, it is essential to conduct empirical research in developing countries as well.

This study makes several important contributions to the literature. First, unlike in previous studies, in this study, the equity of health care accessibility at different levels was quantified and visualized. Second, by identifying health care underserved areas, the equity of health care accessibility was considered. Based on the travel time, the communities of Xi’an, China were selected as the research unit to measure both low- and high-level health care accessibility using the Amap by JavaScript tools. The Lorenz curve and the Gini coefficient were used to evaluate the horizontal equity of different level health care accessibility. Based on the overall equity, an attempt was made herein to quantify the equity of different levels of health care accessibility, and to identify health care underserved areas. This study identifies the health care underserved areas more accurately and can provide a better scheme in optimizing the allocation of health care services.

Numerous studies are available on the health care accessibility of cities in developed regions (Delamater et al., 2012; Cheng et al., 2016; Tao and Cheng, 2019). Compared to cities in developed regions and cities in Eastern China such as Beijing, Shanghai and Guangzhou, cities in Western China exhibit significant differences in the allocation characteristics of health care services. Xi’an is the largest central city in Northwest China, thus it is a good representative city. There are 13 districts in Xi’an: Xincheng, Beilin, Lianhu, Weiyang, Yanta, Chang’an, Baqiao, Yanliang, Lintong, Gaoling, Hu, Zhouzhi and Lantian (Fig. 1). By the end of 2017, there were 3169 communities in Xi’an, with a permanent population of 9.6167 million (Xi’an Statistical Bureau, 2018). In total, there are 322 health institutions with 61 076 beds.

Figure 1.  The distribution of different levels of health care services in Xi’an, China

The data used in this study mainly relate to hospital data, population data and travel time data. Medical insurance has an important impact on choice of treatment; therefore, hospital data were obtained from the list of designated health institutions in Xi’an (http://xahrss.xa.gov.cn/). Owing to the fact that the clinic only undertakes the primary diagnosis of common diseases and frequently occurring diseases, clinics, especially in remote areas, were not selected for further study (Delamater et al., 2012; Hu et al., 2013; Song et al., 2019). Finally, 149 primary health institutions (i.e., township hospitals and community health service centers), 63 primary hospitals, 79 secondary hospitals and 31 tertiary hospitals were selected. Most of the hospital bed-related data were attained from the official website of health institutions, while a small part was obtained through telephone consultation or field research. In view of the differences in the service functions and scale of health institutions, primary health institutions and primary hospitals are collectively referred to as ‘low-level health care services’, and secondary hospitals and tertiary hospitals are collectively referred to as ‘high-level health care services’. Population data were obtained from the compilation of the sixth population census data of Xi’an. The travel time data were attained from the driving time extracted from the Amap by using JavaScript tools. The travel time calculated by using Amap has a higher accuracy, and can provide a reliable basis for the measurement of health care accessibility (Kong et al., 2013; Yang et al., 2017).

The average elevation and slope were calculated based on a digital elevation model derived from the Geospatial Data Cloud. The land-use mix was calculated by the point of interest, including residences, shopping malls, parks, sports facilities, transport facilities, commercial buildings, financial institutions, schools and government organizations (Frank et al., 2004; Moniruzzaman et al., 2013). Bus stations, expressway entrances and exits, and road networks (including national, provincial, county and township roads) were derived from electronic maps (2017), while metro stations were derived from the Baidu Map Picking Coordinate System, including every entrance and exit of all metro stations.

The two-step floating catchment area method was implemented to assess the different levels of health care accessibility in communities (Luo and Wang, 2003; Neutens, 2015; Liu et al., 2016). The measurement was divided into the following two steps:

First, we determined the population P_k in the community k that falls within the catchment area d₀ of each health institution S_j, to calculate the supply-to-demand ratio D_j. d_kj indicates the travel time between community k and hospital j. Second, we allocated the hospitals to population i by identifying which hospital falls within d₀ of each population, and added up the product of hospital to population ratio A_i.

The impedance function f(d) is important for the spatial interaction modeling. Herein, one of the most popular impedance functions (Kwan, 1998; Cheng et al., 2016; Kanuganti et al., 2016), namely the Gaussian function, was selected to reveal the spatial behavior of population, in the following way:

where f(d) is the impedance function, d is the travel time, d₀ is the threshold of travel time, e is natural constant and k is constant.

Differences and connections exist between equity and equality. In terms of differences, equity is not equal to equality and some inequality distribution may correspond to equity in some specific cases (Johnston, 2004). Equity can be divided into horizontal equity and vertical equity. Horizontal equity indicates that the same number of people should have the same supply of health care services, which can avoid favoring a certain individual or group, thus emphasizing on facing the largest number of user groups. In contrast, vertical equity refers to allocating resources among individuals or groups with different needs, which is conducive to different social classes or specific needs, emphasizing on facing the most needed groups (Delbosc and Currie, 2011; Wang and Yaung, 2013; Welch and Mishra, 2013). Equality refers to a state in which various forces lead to changes in balance, and this concept is the core of neoclassical economics (Johnston, 2004). In geography, equality refers to the concentration degree of a geographical element in a certain region, which has been investigated in terms of different levels, multi-scale and different regions (Shinjo and Aramaki, 2012; Ma et al., 2018; Yin et al., 2018; Song et al., 2019). In terms of connection, compared to the vertical equity, horizontal equity emphasizes upon the fact that everyone has equal access to health care services and faces the largest number of user groups. The connotation of horizontal equity is consistent with the equality, that is, it emphasizes upon equal distribution of geographical elements in a certain region.

In terms of measurement, some studies analyzed the horizontal equity of health care services based on Lorenz curve and Gini coefficient. Based on the data of Ecuador Living Standards Measurement Survey and Gini coefficient, Waters (2000) found that although the implementation of general health insurance program led to the increase in the health care accessibility, it exhibited a negative impact on the equity of health care services. Based on Lorenz curve and Gini coefficient, Shinjo and Aramaki (2012) analyzed the equity of medical staff in hospitals and clinics in Japan and the values of Gini coefficient were found to be 0.209 and 0.165, respectively. Based on Lorenz curve, Ding and Chen (2017) found that the inequity of medical staff in the central urban area of Wuhan, and residents in suburban areas showed health care services than those in central urban areas. Zheng et al. (2020) used Lorenz curve and Gini coefficient to evaluate the equity of basic health care services in Beijing, and found that the equity of population distribution is better than that of geographical distribution.

Based on the above mentioned analysis, an attempt was made in this study to use Lorenz curve and Gini coefficient to analyze the overall equity of health care accessibility. Owing to the difficulty of data acquisition, the vertical equity of age, occupation, income, health status, and preferences about health care and other factors were not considered. The Lorenz curve can not only be used for graphical representation of wealth, but also for any variable accumulated by population (Lorenz, 1905). It has been widely used in various disciplines, from biodiversity to transportation research. The Lorenz curve is an intuitive expression of inequity, while the Gini coefficient is used to reflect the degree of overall equity.

where X_k is the cumulative proportion of population, k = 0, ..., n, X₀ = 0, X_n = 1; and Y_k is the cumulative proportion of health care accessibility, k = 0, ..., n, Y₀ = 0, Y_n = 1.

The gap between the supply of health institutions and the demand of population can be used to represent the specific areas of inequity (Delbosc and Currie, 2011; Delmelle and Casas, 2012; Guzman et al., 2017). The standard deviation range can be used to identify which regions have better health care accessibility relative to the population, so as to achieve the objective of quantifying the equity of health care accessibility.

where E_i is the equity in community i; x_i is the difference between accessibility percentage and population percentage in community i; and μ and σ are the mean value and the standard deviation, with i = 0, ... , n.

The key to measuring health care accessibility is to accurately assess barriers to health institutions. Distance and time are the main types of barriers. Overcoming these barriers is very important for patients, especially for acute and severe patients; an attempt was thus made herein to measure health care accessibility based on travel time.

In order to avoid the limitation of setting fixed travel speed and threshold, as traditionally done to measure health care accessibility, the Amap API (application programming interface) was used to obtain the travel time of residents. The automatic updating of road network, traffic congestion information, time delay of turning, and traffic lights were considered. There are 322 health institutions and 3169 communities; therefore, the shortest travel time can be calculated among 1 020 418 possible combinations. Although the maximum travel time to low-level and high-level hospitals is 637 and 803 min, respectively, the data less than or equal to 200 min account for 98.47%. For this reason, the statistical analysis was carried out only for the data less than 200 min (Fig. 2a).

Figure 2.  The histogram and the cumulative percentage of travel time (a) and the impedance function f(d) (b)

As mentioned in Formula (3), the impedance function was used to describe the spatial interaction between the community and health institution. It was assumed that the communities could access the health care services before reaching the average time, and the average value of 60.83 and average value of 66.61 were used as thresholds d₀ of low- and high-health care accessibility, respectively. Therefore, it was further assumed that when the thresholds are 60.83 min and 66.61 min, the constant k can be derived as 1235.18 and 1481.07 when the impedance function f(d) is 0.05 (Fig. 2b).

In the measurement of health care accessibility, number of hospital beds was used to characterize the capacity of health care services, while community population was used to characterize the demand. The number of beds in the central urban area is very dense and high, while the number of beds in the peripheral area is low and scattered (Fig. 3a). Similarly, the population density changes dramatically from the center to the periphery (Fig. 3b).

Figure 3.  Distribution of hospital beds (a) and residential density (b) in Xi’an, China

According to the data on bed allocation in the Outline of National Medical and Health Service System Planning (2015–2020) (http://www.gov.cn/index.htm), there will be 6 beds per thousand permanent residents by 2020. There are 1.2 beds in primary health institutions and 4.8 beds in hospitals, among which there are 3.3 beds in public hospitals and 1.5 beds in social hospitals. Therefore, the low-level health care accessibility was divided into low and high categories by taking 1.2 beds as the cut-off point. In order to further characterize the internal differences, the low categories were divided into the lowest, lower and low according to Natural Breaks, which are characterized by numbers 1, 2 and 3; respectively. Moreover, the high categories were divided into high, higher and the highest, represented by the numbers 4, 5, 6, respectively. Similarly, taking 3.3 beds as the cut-off point, the high-level health care accessibility can be divided into low and high categories. From low to high, the accessibility can be divided into the following six categories: the lowest, lower, low, high, higher and the highest, which are represented by numbers 1–6 in order, respectively. When the 4.5 beds were taken as the cut-off point, the comprehensive health care accessibility was divided into low and high, i.e., two categories and six subcategories, which are represented by numbers 1–6. Therefore, 1, 2 and 3 can be used to characterize the low value types of health care accessibility and their internal differences.

Clear spatial differences exist among different levels of health care accessibility. Low-level health care accessibility is high in the northern areas and low in the southern areas (Fig. 4a). This may be closely related to the topographic conditions of Xi’an, where the Qinling Mountains lie to the south and the Weihe River lies to the north. In parallel, high-level health care accessibility shows a clear core-periphery pattern, which is directly related to the distribution of high-level health institutions in the central urban areas (Fig. 4b). In terms of value, low-level health care accessibility ranges from 0 to 6.097, while the value of high-level health care accessibility ranges from 0 to 12.100, and its maximum value is about twice as much as that of low-level health care accessibility. This result clearly indicates that high-level health care accessibility exhibits a greater range of change and may contain greater spatial inequity. Comprehensive and high-level health care accessibility shows similar distribution characteristics, with a numerical range of 0–18.184, and its maximum value is about three times that of low level health care accessibility, indicating that there may be greater spatial inequity (Fig. 4c).

Figure 4.  Accessibility to low-level (a), high-level (b) and comprehensive health care services (c) in Xi’an, China

The majority of the population has only a small proportion of health care accessibility; therefore, its equity in Xi’an is relatively low (Fig. 5). Compared to low-level health care accessibility, the equity of high-level and comprehensive health care accessibility gets further aggravated. The Gini coefficient of low-level health care accessibility for the total population of Xi’an is 0.54, which indicates that 60% of population accounts for only 20% of low-level health care accessibility; however, 40% of population accounts for 80%. In contrast, the Gini coefficient of high-level health care accessibility for the total population of Xi’an is 0.69, which indicates that 60% of population accounts for 10% of high-level health care accessibility, whereas 40% of population accounts for 90% of it. The Gini coefficient of comprehensive health care accessibility is 0.57, indicating that 60% of population accounts for 19% of comprehensive health care accessibility, whereas 40% of population accounts for 81% of comprehensive health care accessibility.

Figure 5.  Lorenz curves of health care accessibility

The equity of health care accessibility can be divided into negative value and positive value. The negative value indicates that the equity of health care accessibility is poor. In order to further characterize the internal differences, the negative values were divided into the worst, worse and bad according to Natural Breaks, and represented by using the alphabets A, B and C. Positive value indicates that the equity of health care accessibility is good, which is specifically divided into good, better and the best, and it is represented by using the alphabets D, E and F. The equity of different levels of health care accessibility can be divided into six categories from bad to good, which are represented by the alphabets A–F, respectively. Herein, the range of standard deviation was used to quantify the equity of different levels health care accessibility, so the equity of health care accessibility can be summed up to characterize the equity of comprehensive health care accessibility. The specific classification method is consistent with equity of accessibility to different levels health care services. The equity of comprehensive health care accessibility is divided into negative value and positive value, i.e., two categories and six subcategories, which are represented by alphabets A–F. Therefore, A, B and C can be used to characterize the inequity types of different levels health care accessibility and their internal differences.

The equity of the different levels of health care accessibility presents diametrically opposite spatial characteristics. The areas with better equity in low-level health care are mainly located in the periphery of the central urban areas, in particular, in the northern foot of the Qinling Mountains (Fig. 6a), while areas with better equity in high-level health care are mainly concentrated in central urban areas. A total of 60.69% of communities have a positive value of standard deviation, that is, the equity of health care accessibility is good; they account for 69.26% of the total area and 20.87% of the entire population (Table 1). Although the majority of communities have relatively better equity of health care accessibility, these areas are mainly located in the northern foot of the Qinling Mountains, and have a small population. In areas with high population density (i.e., communities with a population density > 200 people/km²), there are main [–0.5, 0) standard deviation of low-level health care accessibility. A total of 1060 communities (i.e., 31.02% of all communities) occupy 26.43% of the area and account for 36.78% of total population. There are 283 communities (8.29%) with a standard deviation that is lower than –0.5 for low-level health care accessibility. These areas are mainly located in central urban and counties areas, and the equity of health care accessibility is relatively poor.

Figure 6.  The quantified equity of accessibility to low-level (a), high-level (b) and comprehensive health care services (c) in Xi’an, China

Compared to that of low-level health care accessibility, the equity of high-level health care accessibility is considerably different. There are six types of equity, and the circle structure is evident for the equity of high-level health care accessibility (Fig. 6b). There are 1292 communities with a positive value of standard deviation, that is, the equity of health care accessibility is good; they account for 37.81% of all communities. The standard deviation in the range [0.5, 1) is the largest among all communities. Although they cover an area that is equal to 9.18% of the entire territory, their population accounts for 36.43% of total population. Moreover, population is mainly distributed in the central urban areas with larger population density. However, the majority of high-level health care accessibility with a negative of standard deviation, that is, the equity of high-level health care accessibility is poor, accounting for 62.19% of the total. The standard deviation in the range [–0.5, 0) is the largest, with a total of 1111 communities, accounting for a third of all communities, a fourth of total area and a fifth of total population. These areas are mainly distributed in the peripheral of the beltway. With the increase of the distance from central urban areas, the standard deviation of high-level health care accessibility is smaller, in particular, the standard deviation range < –1, which is mainly located in the northeastern and northwestern edge areas of Xi’an. Comprehensive equity and high-level equity of health care accessibility exhibit similar distribution characteristics (Fig. 6c). The areas with equity of comprehensive health care accessibility account for 60.40%, among which the standard deviation of [0, 0.5) is the largest, accounting for 27.39% of the total. The areas with inequity of comprehensive health care accessibility account for 39.60%, among which the standard deviation of [–0.5, 0) is the largest, accounting for 22.10% of the total.

In order to further explore the inequity distribution of different levels of health care accessibility, the natural, social and economic, and built environment factors were analyzed herein. As natural factors, the average elevation and the average slope index were selected; as social and economic factors, the land-use mix index was selected; and as built environment factors, the bus station density, the metro station density, the expressway entrances and exits, and the road network density were selected. The Pearson’s correlation coefficients indicate that the average elevation and the average slope exhibit an opposite correlation under different levels of health care services. The equity of low-level health care accessibility is positively correlated with average elevation and average slope, that is, with the increase of elevation and slope, the population gradually decreases while the equity is relatively improved. This reasonably explains also the relatively high equity of most communities at the northern foot of the Qinling Mountains. However, the equity of high-level and comprehensive health care accessibility is negatively correlated with average elevation and average slope; this is related to the fact that the areas with high average elevation and average slope are far away from high-level health care services, in particular, the areas that are distributed with a large number of 0 for health care accessibility. The land-use mix is positively correlated with the equity of health care accessibility, and the correlation is stronger for high-level health care services. The equity of high-level health care accessibility is more positively correlated with built environment factors, in particular, with the density of bus stations and road network, which are 1.32 times and 1.24 times higher than those for the low-level health care accessibility, respectively. The correlation with metro station density is weak, which may be related to the smaller construction scale and coverage. The proximity of expressway entrances and exits is not significantly correlated with equity for low-level health institutions, but is significantly correlated to equity for high-level and comprehensive health institutions; this is closely related to the distribution of the beltway and its circle structure.

In general, the equity of high-level and comprehensive health care accessibility in the central urban areas is better, while low-level health care accessibility is relatively inadequate. While improving the low-level health care accessibility in the central urban areas, the functioning of high-level health institutions in county towns should be further improved, in particular, the equity of high-level health care accessibility in Zhouzhi and Yanliang districts. Specifically, the equity of accessibility at different levels of health care can be improved by increasing the land-use mix, bus station and road network density. Noteworthy, the proximity of expressway entrances and exits can effectively improve the equity of high-level health care accessibility (Table 2).

As the numbers 1, 2 and 3 can be used to characterize the low value types of health care accessibility and their internal differences, the alphabets A, B and C can be used to characterize the inequity of health care accessibility and their internal differences. Therefore, we defined all combinations between the categories 1, 2, 3 and A, B, C as the health care underserved areas.

With regard to the structure of underserved areas, the low-level underserved areas are A1, C1, C2 and C3 (Fig. 7a), while the high-level underserved areas are A1, B1, B3, C1, C2 and C3 (Fig. 7b), and the comprehensive underserved areas are A1, A2, A3, B1, B2, B3, C1, C2 and C3 (Fig. 7c). Regardless of quantity, area, or population, the proportion of high-level and comprehensive underserved areas is larger, and is 4.10, 3.87 and 1.97 times higher than those of low-level underserved areas (Table 3). In terms of spatial distribution patterns, significant differences exist between low-level and high-level health care underserved areas. Apart from the northeast region, the low-level underserved areas are scattered. These areas are dominated by C2 and C3, and the degree of underserved areas is relatively good. High-level health care underserved areas are mainly distributed outside the beltway, which can be roughly divided into eastern and western agglomeration areas. These areas are mainly A1, B1, C1 and C2; especially A1 and B1, where the degree of underserved areas is low, and thus deserve particular attention. Although the number of communities, area, and population of comprehensive health care underserved areas are slightly less than those of high-level health care underserved areas, the overall spatial distribution pattern is consistent with the high-level health care underserved areas. The types of these underserved areas are mainly A1, A2 and A3, which need more attention for health policymakers.

Figure 7.  Identification of underserved areas of low-level (a), high-level (b) and comprehensive health care services (c) in Xi’an, China. White area in the figure means served area

Health care accessibility shows not only regional heterogeneity but also hierarchical heterogeneity. The empirical results of different levels of health care accessibility in Xi’an communities show that low-level and high-level health care accessibility have different spatial distribution patterns, thus further revealing the spatial heterogeneity of the study area. According to the characteristics of different levels of health care accessibility, the reasonable allocation of health institutions is an important basis to ensure its equity.

The spatial pattern of health care accessibility tends to reflect the supply level of health care services, while the equity of health care accessibility can well reflect the unmet health care needs of residents. The results showed that the equity of health care accessibility in Xi’an is relatively low on the whole, in particular, for high-level health care accessibility. By quantifying the equity of health care accessibility in smaller spatial units, the limitations of the overall equity can be supplement, so as to provide decision-making basis for making targeted interventions. Moreover, the equity of different levels of health care accessibility can be improved by improving the built environment factors. The main reason is that the land-use mix, bus station density, road network density and the proximity of expressway entrances and exits can significantly improve the convenience of travel, especially the periphery of the central urban areas.

In general, the identification of health care underserved areas is mainly based on accessibility, thus it has certain one-sidedness (Rosero-Bixby, 2004; Hare and Barcus, 2007). Based on the equity, the health care underserved areas can be identified more comprehensively, in particular, the areas that need priority attention (i.e., A1 and B1 areas). These health care underserved areas have both lower accessibility and worse equity of health care services, so it is more urgent to specify the corresponding optimal allocation of health care services.

The inequity allocation of health care services is the main cause of social exclusion, especially the allocation of high-level health care services. Exclusion is a dynamic process, and some exclusions can lead to more disadvantages and greater social exclusion, especially in areas outside the beltway, which may eventually form lasting social deprivation. Moreover, owing to the stability of health care supply in a specific period, the reasonable allocation of health care services is an important way to promote the equity of health care accessibility and eliminate social deprivation. Attention should not only be paid to the characteristics of the areas of social exclusion, but also to the excluder, that is, the characteristics of health care underserved areas and surplus areas are comprehensively considered, so as to seek feasible ways to promote social equity and justice. Furthermore, to promote equity and justice in the allocation of health care services, it is necessary to coordinate the relationship between equity and efficiency. We should not only promote the horizontal equity of health care accessibility, but also provide corresponding health care services according to the health needs of different ages (aging), occupation, income and health status, so as to meet the vertical equity of residents. Through these targeted optimization of health care services allocation, the equity and efficiency of health care services can be unified..

Health care accessibility is a comprehensive concept, which was analyzed from the spatial perspective of transportation accessibility and availability. In the future, health care accessibility can be synthetically characterized by non-spatial factors such as socio-economic attributes and personal preferences, so that we can explore equity and health care in underserved areas more objectively and truly. Equity has many dimensions, and we evaluated the horizontal equity of health care accessibility. Owing to difficulties in data acquisition, the vertical equity of age, occupation, income, vehicle ownership and other factors were not considered. Moreover, the long time series analysis of equity for health care accessibility and the improvement path of equity deserve further study.

Based on the travel time of residents obtained by using Amap, the low-level and high-level health care accessibility in Xi’an communities were measured in a more accurate way. We not only evaluated the overall equity, but also quantified the equity of health care accessibility, and identified the health care underserved areas inside communities. The main conclusions are as follows.

Low-level health care accessibility is higher in northern areas and lower in southern areas of Xi’an. In parallel, high-level and comprehensive health care accessibility follow clear core-periphery spatial patterns, which are directly related to the concentration of high-level health institutions in central urban areas. In terms of value, the accessibility of high-level and comprehensive health care services has a greater range of change and may have greater spatial inequity than low-level health care services.

The overall equity of health care accessibility in Xi’an is relatively low. Compared to low-level and comprehensive health care accessibility, the equity of high-level health care accessibility is further aggravated, as it has a Gini coefficient of 0.69, which is 0.15 and 0.12 higher than those of low-level and comprehensive health care accessibility, respectively. Moreover, the results of equity quantification of health care accessibility show that the equity of high-level and comprehensive health care accessibility in the central urban areas is better, while low-level health care accessibility is relatively poor. Specifically, the equity of accessibility at different levels of health care can be improved by increasing the land-use mix, bus station and road network density. Noteworthy, the proximity of expressway entrances and exits can effectively improve the equity of high-level health care accessibility.

There are significant differences among different levels of health care in underserved areas. High-level health care underserved areas are mainly located outside the beltway, and can be roughly divided into eastern and western agglomeration areas. Regardless of quantity, area, or population, the proportion of high-level underserved areas is larger; and this is especially true for A1 and B1 in high-level underserved areas, which deserve the attention of policymakers.

It is essential to optimize the spatial and temporal distribution of high-level health care services. According to the characteristics of some remote areas and scattered distribution of population, the way of Internet+ health care is effective to promote the convenience of health care services and make up for the health care underserved areas. This sharing of health care services can make the high-level health care services in the central urban areas have a greater trickle effect on the surrounding areas. Moreover, optimization of the allocation of medical staff is of great significance. Through the assistance of low-level health care services, it can promote the reasonable flow of health technical personnel in different levels of health institutions, which can not only improve the quality of low-level health care services, but also the utilization efficiency of high-level health care services. At the same time, the equity and efficiency of health care services should be unified. In the process of optimal allocation of health care services, the characteristics of high investment and low benefit in public service in remote mountainous areas and sparsely populated areas should be considered. According to the topography, population structure and other regional characteristics, a better scheme in optimizing the allocation of health care services can be formulated.

We would like to thank the Health Commission of Xi’an for their valuable assistance with health care services data.