Research on the Spatial Pattern and Spatial Heterogeneity of Chinese Elite Hospitals

: Background: Facing the problems of unreasonable allocation of medical resources and health inequity, the layout of elite hospitals in China deserves further attention. This paper explores the unbalanced allocation of high-quality resources and its influencing factors in the development of China's health system , so as to provide reference for the rational distribution of high-quality medical resources in China and other countries, from the perspective of space. Methods: This study investigated 706 elite hospitals in 31 provinces, cities and autonomous regions in 2017. In this paper, geographic weighted regression (GWR), spatial lag model and spatial error model are used to study the influencing factors and spatial heterogeneity of spatial pattern. Results: Spatial auto-correlation of elite hospitals in China is of great significance and the results of OLS regression showed that city level, number of medical schools, urban population and resident population were its significant variables. Further, its spatial agglomeration phenomenon were confirmed through SEM and SLM model. Among them, the city level is the most important factor affecting the spatial distribution of elite hospitals in China. The influence intensity of urban level gradually weakened from northeast to southwest. And medical colleges, whose degree of influence is gradually increasing from northeast to southwest, is the second influence factor. There is a weak relationship between the distribution of elite hospitals and population size,which indicates other factors' important impact. Conclusion: China's elite hospitals are unevenly distributed and have obvious spatial heterogeneity. Therefore, we suggest that we should pay attention to the spatial governance of high-quality medical resources, attract medical elites in the region, increase investment in medical education in the scarce areas of elite hospitals and develop tele-medicine service. Through these means, we can solve the problem of unbalanced spatial distribution of medical resources and the demand of areas lacking high-quality medical resources.

is more urgent. Due to the unequal supply of health service space [2] , high-quality medical resources cannot cover the entire population (2008, WHO), which leads to the lack of access to health service space and directly damages the right to health of some people. The imbalance in the allocation of health resources is not only a worldwide problem, but also one of the major obstacles faced by China's health services [3] . Elite hospitals are one of the important indicators reflecting high-quality medical resources in the region, and their spatial distribution is directly related to the fairness of health resource allocation. At present, China is pursuing the reform of the medical system [4][5][6][7] . Taking China as an example to study the space allocation of elites is of great significance for achieving the goal of health equity and protecting citizens' right to health, and it can also provide reference for other countries.
At present, most researches on the spatial distribution and spatial allocation of medical resources are implemented by means of geographic information technology. This has become one of the frontier hotpots in international health research [8][9][10][11] . To our knowledge, the research on the space problem of medical and health resources are relative rare and mainly focuses on the following three aspects: the fairness of space distribution [12][13] , space accessibility [14][15] and hospital location and evaluation [16][17] . The specific research methods mainly include: applying the network analysis model, average center and standard distance in the geographic information system (GIS), combined with remote sensing technology or the 2SFCA method (two-step floating catchment area method) extended on the basis of GIS [18][19] and other methods.
The above method focuses on the description of the spatial pattern of medical resources, the measurement of fairness and spatial accessibility, etc., while ignoring the focus on two types of issues: (1) Lack of explanation of causality from a spatial perspective. The traditional regression method uses ordinary least squares (OLS) for model estimation, which requires the data to meet the assumptions of normality, homogeneity of variance, and independence.
However, due to the geographical difference of each study area, the study area lacks spatial homogeneity, and thus cannot satisfy the assumption of homogeneity of variance. At the same time, because the regions are not independent, but open to each other, there must be a flow of factors, which cannot satisfy the assumption of independence. Therefore, the existence of spatial effects leads to deviations in OLS estimates. The spatial econometric model can be compensated through the establishment of statistical and econometric relationships between geographic location and spatial connection, providing a new research perspective and analytical work for revealing regional differences and influencing factors [20][21][22][23][24] ; (2) Lack of spatial heterogeneity Analysis. Spatial heterogeneity is one of the important properties of spatial data [25][26] , referring to the non-stationary nature of spatial random processes. Ignoring spatial heterogeneity may cause many problems, such as loss of estimation efficiency, biased estimation, and saliency of errors. Based on the above considerations, on the basis of using the Exploratory Spatial Data Analysis (ESDA) method to study the spatial pattern of Chinese elite hospitals, this paper focuses on the analysis of their influencing factors and spatial heterogeneity from the scale of prefectural administrative units. The former uses a spatial regression model, and the latter uses a geographically weighted regression model, with a view to exploring the problems from a spatial perspective, such as the imbalance of high-quality resource distribution in the development of China's medical and health system and its influencing factors, so as to provide reference of the high-quality medical resources distribution for China and other countries.

Exploratory Spatial Data Analysis (ESDA)
Our research used spatial autocorrelation to explore the spatial pattern of elite hospitals.
Spatial autocorrelation refers to the statistical correlation between a certain attribute values where the distribution of geographical things is different from the spatial position. Generally, the closer the distance is, the greater the correlation between the two values. Generally, Moran's I and Local Moran Index are introduced to measure the global and local spatial correlation features. The former is a method for global clustering test, which tests that the adjacent areas in the entire study area are similar and different (spatial positive correlation, negative correlation) , or independent of each other; the latter is used to test whether there are similar or different observations gathered in local areas. Global spatial autocorrelation generally uses Moran's I index. Moran's I index is between -1 and 1, and its calculation formula is as follows: Local spatial autocorrelation refers to the Local Moran Index of a region to measure the degree of association between Area I and its neighbors. Note that the accumulation of j in the formula does not include the Area I itself, that is , j≠i. A positive Ii means a high value is surrounded by a high value (high-high), or a low value is surrounded by a low value (low-low); a negative Ii means a low value is surrounded by a high value (low-high), or a high value is surrounded by a low value (high-low). The calculation formula is as follows: In the formula：n is the total number of areas in the study. i  and j  are the attribute values of areas I and j; ij W are spatial weights， are the average values of the attributes， 2 x s are the variances.

Spatial econometrics method
This study mainly uses spatial constant coefficient regression models: Spatial Lag Model (SLM) and Spatial Error Model (SEM) (1) Spatial Lag Model (SLM) It mainly explores whether the explained variable Y in an area is affected by the explained variable in its surrounding area (spatial spillover effect)： Y=α+ρWY+βX+ε (5) In the formula: W represents the spatial weight matrix of the area; α is a constant term; β is the regression coefficient, which reflects the influence of the explanatory variable change on the explained variable; ρ is the spatial lag autoregressive coefficient, which is used to measure the spatial spillover effect of the explanatory variable in the geographical vicinity; X is the explanatory variable; ε is the random disturbance term, which is independent and identically distributed.
(2)Spatial error model (SEM) If the explained variable in a certain area is also affected by a set of local features and some important variables related to geographic space (called error terms) that are ignored. Then SEM reflects the explained variable is affected by the interdependent random error impact of other areas. The formula is as follows: In the formula, μ represents the spatial autocorrelation error term, λ represents the autoregressive coefficient of the spatial error term, which measures the degree of influence of the error term of the sample observation value on the explained variable.
(3) Geographically Weighted Regression. This method is based on the local regression analysis method and incorporates the spatial location of the data into the regression parameters, and uses the local weighted least square method to estimate point-by-point parameters. The spatial location. The estimated parameters of each spatial unit change with geographic spatial location, thereby directly displaying the spatial heterogeneity of the research object in the research area. Geographically weighted regression can also be regarded as an extension of the traditional global regression model. Its formula is:

Data sources
The article takes China's municipalities directly under the Central Government,

Spatial distribution of elite hospitals in China
As of December 31, 2017, a total of 705 elite hospitals had been included in the Chinese hospital ranking query system. From a regional perspective, 283 elite hospitals were located in the eastern coastal area, 166 were located in 6 central provinces, 171 were located in 12 Hangzhou (13), and Taiyuan (13) , Nanchang (13), Nanjing (12), Chongqing (11), Chengdu (11), Guiyang (11), Changchun (11), Harbin (10), Fuzhou (10); those with 5 to 10 elite hospitals There are 17 cities in total, namely Xining (9), Shenyang (9), Foshan (9), Shijiazhuang (8), Nanning (8), Jinan (7), Dongguan (7), Dalian (7), Shenzhen (6)    To further clarify the spatial distribution of Chinese elite hospitals, Moran's I statistic was used to measure the spatial autocorrelation of Chinese elite hospitals. The value of the global Moran'I statistic was 0.087, which indicates that the distribution of elite hospitals across the country was not random, but a definite positive spatial autocorrelation. That is to say, the distribution of elite hospitals in China was clustered and cities with more elites hospital were usually close geographically and vice versa. Figure    The regression results showed that four variables were significant at 5% level, including the city level, the number of medical schools, urban population and permanent population. model with larger test statistics was selected, the explanation of which was more convincing.

Analysis of spatial heterogeneity of elite hospitals in China
The above ESDA analysis showed that the distribution of elite hospitals in China exhibits significant spatial dependence. In order to explain the determinants of the spatial distribution of elite hospitals in China more comprehensively, especially focusing on the study of spatial heterogeneity at the prefecture-level city scale, this paper further used Geographic Weighted Regression (GWR) to analyze. Based on the four determinants selected in the OLS model (city level, number of medical schools, urban population and permanent population), the regression coefficient estimates of the Geographically Weighted Regression Model were used to show the degree of influence and spatial difference of each determinant.
The regression coefficients were calculated by the geographic weighted regression in ArcGIS 10.0 software (see Table 2 for the results), and the model bandwidth was calculated by using the AIC method of "adaptive" kernel function. The R-Squared of the GWR model was 0.8827, and the Adjusted R-Squared was 0.8667, which was higher than 0.8431 of the OLS model, indicating that the fitting effect of the GWR model is better than that of the OLS model.   In China's demographic system, the urban population is usually counted as the registered population. At present, with the rapid development of China's economy and society, the scale of population mobility is also rapidly expanding. Therefore, considering the mobility of the population, this article took the permanent population into the analysis framework. Figure 7 showed that the regression coefficient of the permanent population was negative, which indicated that the increase in the number of permanent residents in a region had a negative impact on the number distribution of local elites. In addition, comparing Figures 6 with    just the opposite. It shows that the regional imbalance of China's high-quality medical resources is obvious. This explains to a large extent the phenomenon of "difficult medical treatment" in China. Over the past 20 years, the focus of China's medical reform is to establish and improve the medical insurance system. It is hoped that insurance can improve the economic accessibility of health services, while spatial accessibility is neglected. This is very detrimental to patients' equal access to quality medical services. With economic development and family income growth, as well as the high incidence of major diseases, residents are increasingly demanding high-quality medical and health services, hoping to seek medical treatment in major hospitals, especially elite hospitals. A large number of patients are chasing high-quality medical resources across regions, resulting in the phenomenon of "difficult medical treatment". The essence is that it is difficult for patients to obtain high-quality medical and health services [27][28] .
Secondly Our research has its limitations. The first limitation is that the number of elite hospitals in each city is adopted as the core indicator to measure high-quality medical resources.
Although it is an intuitive indicator, it does not consider factors such as the scale of elite hospitals and service quality. In the empirical process, it is found that the urban population and permanent population have an impact on elite hospitals, but the regression coefficient is small. Therefore, only using the number of elite hospitals as the core variable of high-quality medical resources may underestimate the impact of factors such as urban population and permanent population. The second limitation is that it does not take into account the impact of floating patients or patients seeking medical care across regions [7] . Beijing, Shanghai, and resources should be ensured [29] , and the rights of every citizen to enjoy high-quality medical resources should be protected.

Conclusion
The current imbalance in the spatial allocation of high-quality medical resources in China has become a serious constraint to coordinated regional development and social equity and justice. Based on the above analysis, we make the following recommendations. First of all, attention should be paid to the spatial governance of high-quality medical resources. At the national level, it is necessary to formulate long-term plans for the construction of elite hospitals in underdeveloped cities, adjust the spatial layout of high-quality medical resources, and recommend at least one elite hospital in a prefecture-level city to alleviate the spatial imbalance in the allocation of high-quality medical resources between regions. Secondly, attracting outstanding medical talents to regions where elite hospitals are scarce. A series of incentives such as high salaries, job title evaluation, education and training can be used to attract outstanding medical professionals to "sink" to regions where elite hospitals are scarce.
Third, increasing investment in medical education in areas where elite hospitals are scarce [30]. Relying on universities and scientific research institutions in regions where elite hospitals are scarce, it is necessary to increase investment in medical education, improve the availability of local high-quality medical resources and establish the affiliated hospitals.
Finally, developing the telemedicine services [31] . With the rapid development of 5G, AI, blockchain, big data and other technologies, it provides technical support for the establishment of a partial or even a whole system of telemedicine networks. In the future, with the remoteization of core medical services and the systematization of telemedicine, the issue of spatial accessibility of high-quality medical services will be effectively resolved.

Declarations
Ethics approval and consent to participate: Not applicable.

Consent for publication: Not applicable.
Availability of data and material: Not applicable.

Competing interests:
The authors declare that they have no competing interests. Authors' contributions: BS was a major contributor in writing original draft, data analysis and framework design;YW, JX and XZ were responsible for data collection and literature retrieval; YL reviewed and edited the paper. All authors read and approved the final manuscript.