Evaluating the efficiency of primary health care institutions in China: an improved three-stage data envelopment analysis approach

Given that the low performance of PHC institutions can seriously affect the efficiency of the health care delivery system, in the past few years, scholars in China and elsewhere have conducted research on the efficiency of PHC institutions nationwide or in a particular region by applying DEA models. Such models are used in two major situations. One stream of the literature focuses on the efficiency evaluation of PHC institutions by using traditional DEA models and improved DEA models. Oikonomou et al. [13] applied a restricted DEA model to estimate the efficiency of rural Greek PHC institutions. Their results indicated that there was much room for efficiency improvement in the majority of rural PHC institutions. Cordero et al. [14] used extended DEA windows to assess 11 primary care units in the Basque Country from 2010 to 2013, and they demonstrated that the efficiency of these units improved during the study period. Liu et al. [15] used the super-efficiency SBM DEA model to analyze the efficiency of Chinese community health service institutions from 2008 to 2016 and revealed that community health service institutions in quite a few provincial areas were inefficient. Zhang et al. [16] quantified the efficiency and productivity of PHC institutions by using the traditional DEA model and the Malmquist productivity index (MPI) DEA model. Trakakis et al. [22] applied the MPI DEA model to study the productivity of 155 health centers in Greece, and the overall productivity factor was found to drop by 0.9% from 2016 to 2017 and by 5.2% from 2017 to 2018.

Another stream of the literature focuses on the efficiency evaluation of PHC institutions and on exploring the influencing factors through a two-stage DEA model, i.e., a combination of a DEA model and a regression model. Marschall and Flessa [11] assessed the efficiency of primary care in rural Burkina Faso by using the traditional DEA model, and they identified the reasons for inefficiency with the use of a truncated regression approach with a bootstrap procedure. Their research results showed that improvement in the accessibility of PHC institutions will have a significant impact on the performance of these institutions. Alhassan et al. [12] evaluated the efficiency of private and public PHC institutions in Ghana using the traditional DEA model in the first stage and then examined the factors associated with efficiency levels by employing a Tobit regression model in the second stage. Yitbarek et al. [17] adopted a two-stage DEA approach combining the use of traditional DEA models with the Tobit regression model to gauge the efficiency of neonatal health services in PHC institutions in Southwest Ethiopia and to identify the drivers of efficiency. They concluded that available resources could be utilized for additional newborns in the institutions, and a positive correlation was found between the years of experience of the health center head and the population served by the institutions and efficiency. Mohammadpour et al. [18] conducted an efficiency evaluation of rural PHC centers in Hamadan and explored the determinants of efficiency using the traditional DEA model and Tobit regression model. Zhong et al. [19] employed the traditional DEA model to estimate the efficiency of PHC institutions in Hunan Province, China, over the 2009–2017 period in the first stage and estimated the influencing factors using a Tobit regression model in the second stage. The results showed that the total population, the level of urbanization, and the proportion of beds exerted significant impacts on efficiency. Cao et al. [25] quantified the efficiency of basic public health services in Shandong Province, China, using the traditional DEA model and explored the influencing factors by means of a panel Tobit regression approach. Hou et al. [26] examined the efficiency of the hierarchical medical system, including PHC institutions and secondary and tertiary hospitals, by using the super-efficiency SBM DEA model. Then, the efficiency scores were regressed on a group of environmental and management factors through bootstrap truncated regressions.

The studies above can help us understand to some extent the performance of PHC institutions in China and other countries. However, based on the analysis of the available literature, there is still room for improvement in the methods used to assess the efficiency of PHC institutions. First, both traditional DEA models and two-stage DEA models fail to obtain efficiency values that exclude the effects of environmental factors and random noise. As a nonparametric estimator, DEA models are based on a finite sample of observations and do not consider the measurement errors in efficiency estimation, with the potential consequence of erroneous conclusions [27, 28]. Additionally, DEA models assume that DMUs are homogeneous in terms of the environment under which they operate [29, 30]. When DMUs are not homogeneous, the efficiency scores may reflect the underlying differences in environments rather than any inefficiencies. There are significant differences in the socioeconomic development of China's 31 provinces. Therefore, it is essential to control for the effects of environmental factors and random noise to obtain real efficiency values when measuring the efficiency of PHC institutions in China’s 31 provinces. The three-stage DEA method proposed by Fried et al. [31] can be applied to obtain efficiency values that exclude the effects of environmental factors and random noise, and it has been used for efficiency assessment in medical and health industry [21, 32, 33]. However, the model used to measure efficiency in the first and third stages of the three-stage DEA model is the traditional DEA model, which does not consider the slack and the super-efficiency problem [34‐37]. Additionally, when using panel data to analyze dynamic changes in efficiency, another key issue should be fully considered, namely, the comparability of interperiod efficiency values. Contemporaneous benchmarking techniques or cross-benchmarking techniques are often used in the literature. However, as a result, efficiency scores measured in different periods lack interperiod comparability, and the reliability of the results can be affected [35, 36, 38, 39]. For slack and the super-efficiency problem, the super-efficiency SBM DEA model proposed by Tone [34] has been shown to be a good tool for addressing these two issues, and it has been applied for the efficiency measurement of Chinese community health service institutions [15], public hospitals [40], and hierarchical medical systems [26]. For the problem of the comparability of interperiod efficiency values, the GBT proposed by Pastor and Lovell [38] can address this issue by treating the same samples from different observation periods as different DMUs and combining them into one sample set, and it has been used extensively to evaluate efficiency [35, 36, 39]. To accurately measure the efficiency of PHC institutions, a better option is to consider the abovementioned issues in DEA models. However, thus far, this remains an unresolved problem. To fill this gap, this study constructs a global super-efficiency SBM DEA model that combines the advantages of the super-efficiency SBM DEA model and GBT to simultaneously address the issues represented by slack, the super-efficiency problem and the comparability of interperiod efficiency values. Then, the global super-efficiency SBM DEA model is used to measure the efficiency of PHC institutions in the first and third stages of the three-stage DEA model, different from the traditional three-stage DEA model, which uses the traditional DEA model to calculate efficiency in the first and third stages. This study refers to the improved model as an improved three-stage DEA approach. The improved three-stage DEA approach combines the advantages of the super-efficiency SBM DEA model, GBT, and three-stage DEA model, simultaneously taking into account slack, the super-efficiency problem, environmental factors, random noise, and the comparability of interperiod efficiency values in the efficiency measurement. This method can provide a feasible approach to measuring the real efficiency of PHC institutions or other health care institutions.

Suppose that there are \(n\) DMUs and that the observation period is \(\tau =1,\cdots ,T\), with the input and output matrices being \(X=\left({\times }_{kj}\right)\in {R}^{m\times n}\) and \(Y=\left({Y}_{rj}\right)\in {R}^{s\times n}\) respectively. The input-oriented global super-efficiency SBM DEA model can be established as follows [34]:subject to where \({x}_{kj\tau }\) and \({y}_{rj\tau }\) represent the \(k\)-th input variable and the \(r\)-th output variable of the \(j\)-th DMU in period \(\tau\), respectively. \({\lambda }_{j\tau }\) is a nonnegative vector of the \(j\)-th DMU in period τ.

The input-oriented global BCC model can be established as follows [31, 47]:subject to where the subscript of the evaluated producer’s data contains the letter “\(o\)”. The meanings of \({\lambda }_{j\tau }\), \({x}_{kj\tau }\), and \({y}_{rjt}\) are the same as those mentioned above.

The input slacks computed in the first stage demonstrate the disparities between the real and targeted inputs, impacted by three effects: managerial inefficiency, environmental influences, and statistical noise [31]. The SFA model, which considers the environmental variables as explanatory variables and the input slack variables as explained variables to control for the effects of nonmanagement factors on the input slacks, is established as follows:where \({S}_{ij}\) is the slack value for the \(i\)-th input of the \(j\)-th DMU, derived from the first stage; \({Z}_{j}\) represents the vector of the environmental variables of the \(j\)-th DMU, \({Z}_{j}=({Z}_{1j}, {Z}_{2j}, \cdots , {Z}_{pj})\); \(p\) is the number of environmental variables affecting the efficiency of PHC institutions; \({\beta }^{i}\) is the coefficient of every environmental variable; \({f}^{i}\left({Z}_{j};{\beta }^{i}\right)\) denotes the function of environmental parameters calculated by \({f}^{i}\left({Z}_{j};{\beta }^{i}\right)={Z}_{j}{\beta }^{i}\);\({v}_{ij}+{u}_{ij}\) is the mixed error term; and \({v}_{ij}\) and \({u}_{ij}\) are the random noise component and managerial inefficiency term for the \(i\)-th input of the \(j\)-th DMU, respectively. Assuming that the distributions of \({v}_{ij}\) (\({v}_{ij} \sim N(0,{\sigma }_{vi}^{2})\) and \({u}_{ij}\) (\({u}_{ij} \sim {N}^{+}(0,{\sigma }_{ui}^{2})\)) are independent from each other, \({\gamma }_{i}={\sigma }_{ui}^{2}/{(\sigma }_{ui}^{2}+{\sigma }_{vi}^{2})\) is defined. The paremeters (\({\beta }^{i},{\sigma }_{i}^{2},{\gamma }_{i}\)) are estimated using Frontier 4.1 software, and the inputs are adjusted in accordance with the regression results of the SFA model. The adjustment formula is as follows:where \({X}_{ij}^{A}\) is the adjusted input value and \({X}_{ij}\) is the initial input value in the first stage. The term \(\left[max\left(f\left({Z}_{j};{\widehat{\beta }}_{i}\right)-f\left({Z}_{j};{\widehat{\beta }}_{i}\right)\right)\right]\) shows the adjustment assigning all DMUs under the most unfavorable environment confronted by DMUs. The component \(\left[max\left({v}_{ij}\right)-{v}_{ij}\right]\) places all DMUs under a normal natural condition described as the most unfortunate environment confronted by DMUs. Such adjustments allow all DMUs to be under the same external environment and random noise.

In this stage, the adjusted input values computed at the second stage and the original output data used at the first stage are utilized to recalculate the efficiency value of PHC institutions through the input-oriented global super-efficiency SBM DEA model. The efficiency scores obtained in the third stage are more accurate than those obtained in the first stage due to the elimination of the influence of external environmental factors and statistical noise.

The efficiency of PHC institutions in Chinese provinces is influenced not only by internal inputs and outputs but also by external environmental factors, such as social and economic factors. Based on the studies of Yi et al. [53] and Auteri et al. [48], this paper selects seven indicators as external environmental variables in terms of the economy, population, and education. The seven indicators include residents’ annual average income, per capita GDP, the proportion of the urban population, population density, the percentage of the population aged 0–14, the percentage of the population aged 65 and older, and the number of people with a college education and above per 100,000 residents.

Based on the consistency and availability of indicators, the input and output data for PHC institutions in 31 provincial‒level regions in mainland China from 2012 to 2020 are selected as the sample for this study. All data used, including the data on the input‒output variables and external environmental variables, are collected from the “China Health Statistics Yearbook (2013–2021)” and the “China Statistical Yearbook (2013–2021)”. The descriptive statistics of the data on the input‒output variables and external environmental variables are presented in Table S1 and Table S2, respectively.

In this stage, the input-oriented global super-efficiency SBM DEA model in MaxDEA 8 Ultra software is used to calculate the efficiency scores of PHC institutions in 31 provinces in China from 2012 to 2020. The average scores of TE, PTE, and SE in the observation period were 0.721, 0.776, and 0.931, respectively (Table 1). SE was significantly greater than PTE, revealing that PTE has great potential for improvement, and this result is similar to that of Chen et al. [54], who calculated the efficiency of PHC institutions by using the traditional DEA model. It can be presumed that the inefficiency of PHC institutions in recent years was mainly due to the low levels of medical technology and management in PHC institutions. As a graphical supplement to the efficiency scores of PHC institutions in Table 1, Fig. 2 illustrates the dynamic changes in efficiency from 2012 to 2020. As shown, the TE of China’s PHC institutions decreased from 0.807 in 2012 to 0.546 in 2020, PTE decreased from 0.870 to 0.594, and SE decreased from 0.934 to 0.917, showing an unexpected downward trend. The downward trend in all three types of efficiency indicates that the growth in input in PHC institutions failed to generate efficiency gains. Although China has significantly expanded financial investment and introduced favorable policies to strengthen its PHC system, the development of PHC institutions still faces great challenges, such as inferior facilities and equipment, ineffective management, the poor capacity and skills of physicians at the primary level, and the inadequate construction level of information technology [5].

In the second stage, the SFA model is applied to separate the influences of the external environment, random noise, and managerial inefficiency on the input slack variables. The slack variables of inputs calculated in the first stage are treated as the dependent variables, and the seven external environmental variables (population density, the percentage of the population aged 0–14, the percentage of the population aged 65 and older, the number of people with a college education and above per 100,000 residents, the proportion of the urban population, residents’ annual average income, and per capita GDP) are taken as independent variables to construct the regression models. Table 2 displays the SFA estimation results, which are obtained using Frontier 4.1 software. First, the one-sided likelihood ratio (LR) value of each regression model obeys the mixed chi-squared distribution, and all results are significant at the 1% level, supporting the robustness of the SFA model. Second, the γ values of the four regression models are all close to 1 and significant at the 1% level, implying that low levels of medical technology and inefficient management were the main reason for the inefficiency of PHC institutions. Additionally, most regression coefficients of environmental variables on input slack variables are significant at the 1% level, and only a few are significant at the 5% or 10% level, which demonstrates that the environmental variables exert critical influences on the input slack variables. Thus, it is necessary to separate the influences of managerial factors, statistical noise, and environmental factors by using the SFA model to obtain the real efficiency of PHC institutions. In this model, the positive and negative signs of the regression coefficients denote different relationships between environmental indicators and input slack variables. Specifically, a positive regression coefficient implies that an increase in the value of an environmental variable will bring more input redundancy, with more resource waste and less efficiency. Conversely, a negative coefficient indicates that an increase in the value of an environmental variable will lead to less waste of inputs or more outputs. Next, the impacts of the environmental variables are analyzed separately.

The real efficiency scores of PHC institutions in China from 2012 to 2020 computed based on the adjusted input data derived from the second stage are presented in Table 3. The average scores of TE, PTE, and SE are 0.593, 0.927, and 0.636, respectively. Here, PTE is significantly larger than SE, indicating that the inefficiency of PHC institutions in recent years was mainly due to the low level of SE. This result differs from the results of the first stage and of Chen et al. [54], who calculated the efficiency of PHC institutions by using the traditional DEA model. This difference indicates that not taking into account the effects of environmental factors and random noise can introduce bias into the results. From 2012 to 2019, all three types of efficiency showed a small decline, while a greater drop occurred between 2019 and 2020 (Fig. 3). The main reason for the greater decrease from 2019 to 2020 was the COVID-19 pandemic. To reduce the risk of cross-infection during the COVID-19 pandemic, medical and health institutions had strict requirements for patient access procedures, such as taking body temperature, showing travel codes and health codes, and providing 24-h or 48-h nucleic acid-negative certificates. In addition, the rigorous control measures of the pandemic caused people to be fearful of the new coronavirus and to develop the mindset of not going to a medical institution unless their condition was serious and urgent. These measures greatly reduced the outputs in 2020, including visits and admissions to PHC institutions.

In both the first and third stages, from 2012 to 2020, the efficiency of PHC institutions displayed a downward trend from, indicating that the relevant policies and measures used to strengthen the grassroots in recent years did not meet expectations. This result is similar to that of Xu et al. [71], meaning that there are still many unresolved issues in promoting the development of PHC institutions. For example, in the construction of medical associations, there are serious conflicts of interest between hospitals and PHC institutions, and hospitals and PHC institutions have not become a real community of responsibility, management, services and interests [72]. Thus, high-quality medical and health resources are not really sunk into PHC institutions. The problems of serious staff turnover in PHC institutions, the lack of quality health care personnel and relatively simple and outdated medical equipment are still prominent [73]. These problems have significantly limited the improvement in efficiency of PHC institutions in China. Therefore, in future reforms, relevant systems should be continuously established and improved to strengthen the deeper coordination between PHC institutions and hospitals, especially the alignment of economic interests [5]. Additionally, a reasonable performance incentive system, a title promotion channel, and social security measures should be explored to attract high-quality health professionals to work at the grassroots level, with a certain degree of autonomy granted to PHC institutions to give full play to their talent.

Compared with the first stage, the average value of the TE of PHC institutions decreased from 0.721 to 0.593, PTE increased from 0.776 to 0.927, and SE declined from 0.931 to 0.636 (Tables 1 and 3). PTE increased, while SE decreased significantly, resulting in a decrease in TE. This result means that external environmental factors have a marked impact on the efficiency of PHC institutions, especially on SE.

The natural breaks method [74] is used to divide the efficiency scores of PHC institutions in the first stage and the third stage from 2012 to 2020 into four grades. As shown in Fig. 4, from the first stage to the third stage, i.e., before and after the removal of environmental values and stochastic disturbances, the TE of PHC institutions in each region had certain changes, but the relative levels of TE in all regions did not differ much. The TE of PHC institutions also exhibited a certain clustering, as did the distribution of the TE of public hospitals [40], indicating that the efficiency of medical and health institutions in an area might be related to the efficiency of medical and health institutions in adjacent areas. The reasons for the clustering phenomenon may be related to the construction of regional medical centers and the competition among neighboring medical institutions. As the construction of regional medical centers progresses, medical and health institutions with high TE will lead and radiate to the medical institutions in surrounding areas, and the agglomeration phenomenon will become more obvious.

To analyze the differences in the efficiency of PHC institutions across China, China’s 31 provinces are divided into four groups of regions based on their geographical location and economic development [75], as shown in Fig. 5. These groups are the eastern region (including Beijing (BJ), Tianjin (TJ), Hebei (HEB), Shanghai (SH), Jiangsu (JS), Zhejiang (ZJ), Fujian (FJ), Shandong (SD), Guangdong (GD), and Hainan (HAN)), the central region (including Shanxi (SX), Anhui (AH), Jiangxi (JX), Henan (HEN), Hubei (HB), and Hunan (HN)), the western region (including Chongqing (CQ), Shaanxi (SAX), Inner Mongolia (IM), Guangxi (GX), Sichuan (SC), Guizhou (GZ), Yunnan (YN), Tibet (TB), Gansu (GS), Qinghai (QH), Ningxia (NX), and Xinjiang (XJ)), and the northeast region (including Liaoning (LN), Jilin (JL), and Heilongjiang (HLJ)). Figure 6 illustrates the three types of efficiency for each region over the 2012–2020 period. As illustrated, changes in efficiency from the first stage to the third stage are evident, with a decrease in TE in most provinces (22 out of 31), indicating that the TE in these provinces is overestimated under the influence of environmental factors and random noise. Chen et al. [21] obtained different findings when measuring the TE of public hospitals using the traditional three-stage DEA model, concluding that most provinces (28 out of 31) had higher TE in the third stage. The application of different research methods and differences in the effects of the same environmental variables on the TE of public hospitals and PHC institutions may lead to different conclusions. Hence, more environmental variables should be explored in future studies to determine their impact on the efficiency of different health care institutions. Next, a comparative analysis of the efficiency of PHC institutions across regions is presented.

First, the TE of PHC institutions in GD in the third stage is 0.961, higher than that in other provinces in the eastern region. The highest TE of PHC institutions in GD is mainly due to its high level of economic development and innovation in management. As the most economically developed region in China, GD has ranked first in GDP for 34 consecutive years, providing a good material basis for the development of PHC institutions. Second, GD has actively created a new model for the management of PHC institutions and reformed the performance pay system of PHC institutions, which has greatly mobilized the enthusiasm of primary medical staff [76]. At the same time, to encourage high-quality health talents to serve in PHC institutions, GD has set up special positions for primary general practitioners, and it has offered generous welfare benefits. These measures have led to the high efficiency of PHC institutions in GD. Although PHC institutions in TJ have a PTE of 0.990 in the third stage, which is ahead of that of some other provinces, its SE is only 0.319, putting it well behind some other provinces in terms of TE. Compared with the first-stage results, the TE of PHC institutions in BJ, TJ, SH, HAN, ZJ and FJ shows a certain decline, with BJ and TJ experiencing larger declines of 0.525 and 0.528, respectively. These results indicate that the efficiency of PHC institutions in BJ and TJ is more influenced by environmental factors.

In the central region, the TE value of PHC institutions in SX in the third stage is 0.373, lagging far behind the values of the other five provinces. Chen et al. reached a similar conclusion when evaluating the TE of regional public hospitals and concluded that public hospitals in SX have the lowest TE [21]. Overall, the development of public hospitals and PHC institutions in SX is relatively backward, and the efficiency of public hospitals and PHC institutions needs further improvement. After taking into account the effect of external environmental factors and statistical noise, the SE of PHC institutions in HB, JX, AH, and SX showed a decrease, with SX experiencing the largest decrease, from 0.965 to 0.491. This result indicates that the SE of PHC institutions in SX is more influenced by environmental factors.

In the western region, PHC institutions in TB, QH, and NX have relatively low TE in the third stage, with all of these provinces obtaining values lower than 0.2. After excluding the effect of environmental factors and statistical noise, the TE of PHC institutions in TB, NX, and QH showed a significant decrease, which is due to the significant decline in SE. This result indicates that the SE of PHC institutions in TB, NX, and QH is more influenced by environmental factors. This phenomenon can be explained by the fact that TB, NX, and QH are less developed areas in China, and their external environment improved after the adjustment. Thus, they need to invest more health care resources to reach an efficient scale to improve their SE. In addition, the TE of PHC institutions in GZ declines the least, from 0.721 to 0.676, indicating a minimal influence of environmental factors.

In the northeast region, PHC institutions in LN, JL, and HLJ are relatively inefficient in the first and third stages, with PHC institutions in JL being the least efficient. The possible reasons for this phenomenon are the low level of economic development and the serious lack of quality medical and health professionals in the northeast region. The lack of dynamism in economic development and the low level of wages and social security in the northeast region have led to a serious brain drain problem, resulting in a lack of quality health professionals in PHC institutions [77]. The brain drain rates of graduates in LN, JL, and HLJ reached 15.56%, 40.65%, and 32.03%, respectively, which are higher than those in other provinces [76]. Among the three northeastern provinces, the brain drain of college graduates is more prominent in JL and is a critical reason for the lowest efficiency of PHC institutions in JL. In addition, affected by various factors such as the natural environment, the geographical environment, and economic and social development, the population loss in the in the northeast region is the most serious [78]. After taking into account the effect of external environmental factors and statistical noise, the PTE of PHC institutions in JL improves by 0.422, indicating that the PTE in JL under the influence of environmental factors is greatly undervalued.

As depicted in Fig. 7, the line graphs of the scores of the three types of efficiency in the four groups of regions calculated in the first and third stages reflect the tendency of efficiency. First, from the perspective of TE, the TE values of the four regions calculated in the first stage exhibit a pronounced downward trend over time, while the values calculated in the third stage display a relatively slight decrease, both indicating much room for efficiency improvement. The differences in the efficiency of PHC institutions between regions are evident, and the northeast region has remained in the most backward position, which is consistent with the conclusion reached by Yi et al. [53] when measuring the efficiency of health care facilities nationwide. The obvious difference in efficiency is likely due to the differences in the level of economic development and the resource endowment between the four regions. Second, from the perspective of PTE, the PTE values in the first and third stages exhibit a decreasing trend that fluctuates over time. This result demonstrates that there is still much room for improvement in PTE, and more effective measures should be taken to improve the medical technology and management of PHC institutions for greater efficiency. The PTE of PHC institutions in the northeast region remains the lowest, indicating that the levels of medical technology and management are the lowest. Third, compared to PTE, the SE values for the four regions are small in the third stage, and most of them are in a state of increasing returns to scale. This result indicates that the PHC institutions in the four regions have not yet reached an efficient scale and therefore have the potential to increase their investment scale. The SE of PHC institutions in the northeast region no longer lags significantly compared with that in other regions without considering environmental factors and random noise.

Figure 8 displays scatter plots based on the PTE and SE scores of PHC institutions in the first and third stages. Thirty-one provinces are classified into four categories based on the average scores of PTE and SE: high-high, low–high, low-low, and high-low categories. The two red lines in the scatter plots represent the average PTE and SE scores of PHC institutions.

The high-high category is composed of provinces with relatively high PTE and SE values of PHC institutions. The results of classification in the first stage show that nine provinces, i.e., ZJ, CQ, YN, SH, HEN, JX, HEB, HB, and GX, are in this category. When accounting for the effects of environmental factors and random noise, the PTE and SE values of PHC institutions in ZJ, CQ, YN, HEN, JX, HEB, and HB remain relatively high. The PTE values of PHC institutions in ZJ and GD are greater than 1 in the two stages. However, because they have SE values of less than 1, the PHC institutions in these two provinces do not reach the efficient state, implying that the PHC institutions in these two provinces can enhance their efficiency by increasing their SE. GD, SC, HN, and SD change from the low–high category to the high-high category, showing that the values of SE are significantly improved in a homogeneous environment.

The low–high category contains provinces with relatively high PTE values but low SE values. NX, QH, TB, and TJ are classified in this category, with or without considering the impact of environmental factors and random disturbances. This result implies that these four provinces can enhance the efficiency of their PHC institutions by improving SE. HAN, which originally belonged to the low-low category, is classified into the low–high category in the third stage, showing that the PTE of its PHC institutions is improved. However, the PHC institutions in this province still need to improve their SE. GS changes from the high-low category to the low–high category, indicating that the PTE of its PHC institutions is higher than that of some other provinces in a homogeneous environment. However, these institutions still need to improve their SE.

The low-low category consists of provinces whose PHC institutions have relatively low levels of both SE and PTE. JL falls into the low-low category in the first and third stages, indicating that among all provinces, the PTE and SE of PHC institutions in this province are relatively backward, which is probably related to the economic development level and inadequate policy support. HLJ, SX, LN, SAX, IM, and XJ change from the high-low category to the low-low category, indicating that the PTE and SE values of PHC institutions in these five provinces are relatively low. SH and BJ change from the high-high category and the low–high category, respectively, to the low-low category. As cities at the forefront of China's economic development, SH and BJ have a relatively privileged environment with a concentration of high-quality health care resources, advanced medical technology and quality management, resulting in their relatively high PTE values in the first stage. However, their PHC institutions do not outperform PHC institutions in other provinces in a homogeneous environment. All these provinces in the low-low category should focus on increasing both PTE and SE.

The high-low category includes provinces with relatively high SE values but relatively low PTE values. Whether or not the effects of environmental factors and random noise are considered, GZ, FJ, and JS remain in the high-low category, implying that low PTE is the main reason limiting the improvement in TE in these three provinces. GX changes from the high-high category to the high-low category. That is, in a homogeneous environment, PHC institutions in GX fall behind PHC institutions in other provinces in terms of PTE. Therefore, future efforts to improve the efficiency of PHC institutions in these provinces should be directed mainly toward improving medical technology and management.