### Data sources

The indicators of health resources were adopted in accordance with the " Statistical Communique on the Development of China’s Health Undertakings " published by the China National Health Commission every year. These indicators are commonly cited in studies on health resources in China [5, 9, 16,17,18,19]. Hospitals and PMHI are the main places for diagnosis and treatment, and they account for the vast majority proportion of medical and healthcare institutions (more than 97% in 2018 [20]). Thus, they were included as indicators of healthcare institutions in the study. Correspondingly, their beds were also included. Health personnel refers to employees engaged in the healthcare institutions. In this study, licensed doctors (LD), registered nurses (RN), and healthcare employees (HCE) were included. Total health expenditure (THE) is usually divided into three types, including government health expenditure (GHE), social health expenditure (SHE), and Out-of-pocket payments (OOPs). Data for demographic, geographical, and socioeconomic including total population, geographical area, and GDP per capita were also included for the distribution assessment of health resources. These indicators are defined in the China Statistical Yearbook and China Health Statistical Yearbook and are listed in Additional file 1.

The data related to these indicators of 31 provinces, autonomous regions, and municipalities directly under the central government originate from China Statistical Yearbook and China Health Statistics Yearbook from the year 2009 to 2018. Due to inconsistent statistical standards, Hong Kong, Macau, and Taiwan were not included in this study.

### Study design

This study was divided into three steps.

### Description of the general situation

For the first step, we described the overall condition of health resources in China over the past ten years from four categories. Ten indicators including hospital, PMHI, hospital beds, PMHI beds, HCE, LD, RN, GHE, SHE, and OOPs were studied. In addition to the above ten indicators, we also introduced the calculation of Beds per 1,000 people, HCE per 1,000 people, GHE Per Capital, the proportion of OOPs in THE, and the proportion of THE in GDP for a overview of health resources.

### Demographic and geographic distribution of health resources

For the second step, we explored the demographic and geographic distribution of health resources. Since we introduced calculation methods of per capita or per thousand people in the comparison process, this was not applicable to healthcare institutions in practice. Therefore, in this process, we mainly compared three categories of indicators, namely beds, health personnel, and health expenditure. We used maps to visually present the distribution of beds (both in hospitals and PMHI per 1,000 people), HCE per 1,000 people, and THE per capita (refers to the ratio of THE in a year to the average population) between 2009 and 2018. We also included HRDI to present the integrated health-resource distribution from the aspects of population density and geographic area. HRDI was calculated as the geometric mean of health resources per 1,000 people and per square kilometers. The following formula was used to calculate HRDI [9, 26]:

$$HRDI=\sqrt{\left(Yi/\;Pi\right)\left(Yi/\;Ai\right)}$$

*Yi* represents the health resource of unit *I*; *Pi* represents the population of unit *I*, and *Ai* represents the area of unit *I*.

The results of HRDI were also presented by maps. To measure the global autocorrelation, we introduced the global Moran’s I index. The global Moran’s I is an important index to measure spatial autocorrelation with the range of -1 to 1 [39]. If Moran’s I is larger than 0, the resources had spatial disparity, indicating that a larger (smaller) resource corresponded with easier (harder) aggregation. If Moran’s I was smaller than 0, the resources had spatial heterogeneity, indicating that a larger (smaller) resource corresponded with less likelihood of aggregation. When Moran’ I was 0 (or P > 0.05), resources were randomly distributed in space and had no spatial correlation. When the global Moran’s I is statistically significant, the local Moran’s I can be further analyzed. The local Moran’s I can analyze whether an indicator in a local area has spatial correlation, which can be divided into two parts: (1) The level of an indicator in the region compared with the overall; (2) The level of indicators in the surrounding areas compared with the overall. The global Moran’s I and local Moran’s I can be calculated by:

$$Gobal Moran\text{'}s I=\frac{n}{{S}_{0}}\text{*}\frac{{\sum }_{i=1}^{n}{\sum }_{j=1}^{n}{\omega }_{ij}({y}_{i}-\overline{y})({y}_{j}-\overline{y})}{{\sum }_{i=1}^{n}{({y}_{i}-\overline{y})}^{2}}$$

$$Local Moran\text{'}s I={I}_{i}=\frac{({y}_{i}-\overline{y})}{{\sum }_{k=1}^{n}{\left({y}_{i}-\overline{y}\right)}^{2}/(n-1)}\text{*}\sum _{j\ne i}^{n}{w}_{ij}({y}_{j}-\overline{y})$$

Where *n* is the number of the province, *yi* and *yj* are the resource of province *i* and *j*, respectively, \(\overline{y}\) is the mean of the resource of all provinces, \({S}_{0}={\sum }_{i=1}^{n}{\sum }_{j=1}^{n}{\omega }_{ij}\), and\({\omega }_{ij}\) is the spatial weight value of province *i* and *j* calculated from the spatial distance using Euclidean distance. It should be noted that the data points used for the calculation of \({ \omega }_{ij}\) were different between global Moran’s I and local Moran’s I.

### Assessment of the equity and the association between economic factor and health resources

For the third step, we used CI to quantify the degree of inequality in the allocation of health resources. We introduced a Geo-Detector model and GWR to further measure the association between GDP per capita and health-resource distribution.

CI is recognized as a superior tool to measure the equality of health-resource allocation associated with socioeconomic status [32]. The following figure was used to demonstrate the definition of CI.

The x-axis is the cumulative share of the population, ordered by GDP per capita from lowest to highest, and the y-axis represents the cumulative share of health resources. The concentration curve presents the cumulative share of the health resources against the cumulative share of the population. *A* in Fig. 1 is the area between the line of equality (the 45° line) and the concentration curve. *S* is the area under the concentration curve. The CI is calculated as twice the area *A*. The following exact computational formula was used to calculate the CI.

$$\begin{aligned}S=&\frac{1}{2}\sum_{i=0}^{n-1}\left(Y_i+Y_{i+1}\right)\left(X_{i+1}-X_i\right)\\ CI=&2\ast\left(0.5-S\right)\end{aligned}$$

The CI is bound from -1 to +1. Where 0 means complete equity, and ±1 means complete inequity. A negative value indicates health resources are disproportionately concentrated among the poorer, whereas a positive value means that health resources are disproportionately concentrated within wealthier populations.

A Geo-Detector model is used to measure structured spatial heterogeneity of health resources and determine whether the health resources within strata are more similar than that between strata. Given the q-statistic calculated by the Geo-Detector model, we can say that 100q% information of health resources can be explained by structured heterogeneity based on the independent variable (the GDP per capita here). The q-statistic has a range of 0 to 1 and can be calculated as follows [36, 37]:

$$q=1-\frac{{\sum }_{h=1}^{L}{N}_{h}{\sigma }_{h}^{2}}{N{\sigma }^{2}}$$

Where *L* is the number of strata of GDP per capita, \({N}_{h}\) and *N* is the number of provinces in strata *h* and the number of all provinces, respectively, and \({\sigma }_{h}^{2}\) and \({\sigma }^{2}\) are the variance of resources in strata *h* and all data. \({\sum }_{h=1}^{L}{N}_{h}{\sigma }_{h}^{2}\) is within sum of square and \(N{\sigma }^{2}\) is total sum of squares. Our research divided GDP per capita into four grades using lower quartile, median, and upper quartile (*L*=4).

However, the calculation of q-statistics needs to discretize the independent variables into the qualitative variable, which may cause the loss of information. Therefore, we used GWR to analyze the impact of economic factors on the distribution of health resources. In our study, Gaussian kernel was used, and the optimal bandwidth was selected using leave-one-out cross validation.

R studio software (version 4.1.1) was used to perform all analyses. *P* < 0.05 was considered statistically significant.