Performance Evaluation of the Combination of Medical Care and Old-age Service in Old-age Institutions in China: A Two-stage DEA Approach


 Background: In the context of China’s aging population, comprehensive medical care, convenient diagnosis, comprehensive medical care and elderly care services are increasingly needed. But China's medical care and elderly care service system is still immature. This study aims to build a performance evaluation index/criteria system for the combination of medical care and elderly care services and present an empirical approach to assess them.Methods: A two-stage DEA approach is taken: 1) establish a performance evaluation index system for the combination of medical care and elderly care services, 2) adopt a two-stage DEA to evaluate the performance of 30 pension institutions in China, and 3) Determine and identify important criteria to improve the efficiency of pension institutions. Results: The results show that the two-stage DEA accounted for a relatively high affiance of medical and nursing care services, but resource allocation still needs to be further optimized. Institutions with ineffective DEA need to reduce the five factors of operations, management, fixed assets, technology and services in the input dimension. In the output dimension, the service evaluation effect and safety management effect need to be improved. The performance of combined old-age care and medical care in old-age institutions can be improved in terms of investment in fixed assets, methods of capital subsidies, supervision and management, as well as standardized operations.Conclusions: This study establish a performance evaluation index system for the combination of medical care and elderly care services and present a two-stage DEA empirical approach to evaluate the performance of 30 pension institutions in China, which provides the method supports for decision-makers and researchers in performing evaluation of pension institutions in China, outlines the suggestions in improving them.


Background
The elderly population of 65 years and above in China accounts for 10.8% of the total population. The proportion of the elderly aged 65 and above has increased for 21 consecutive years. However, the supply for various old-age beds in China is currently tight, with 30 beds for every 1,000 elderly people. China's aging population accounts for about one-fth of the world's aging population, and it is the country with the largest aging population and the fastest growth rate in the world. Providing proper health care for the elderly population is the focus of attention from all walks of life. As a new type of old-age care model, the combination of medical and nursing care combines medical services with old-age care services. On the basis of providing traditional old-age care services, it provides professional medical and rehabilitation services for the elderly. Judging from China's current family development trend and the development trend of the elderly service industry, the combination of medical and nursing is an inevitable trend.
There are still many di culties in the implementation of the combination of medical and nursing. The main reasons are that China's current social reality of getting old before getting rich and the combination of medical and nursing services lacks an effective performance evaluation mechanism. The most important thing to evaluate the performance of pension services is to determine the evaluation content and formulate scienti c evaluation methods. Assessing the e ciency of a medical institution needs to consider the quality and quantity of services it provides rather than the resources it uses. In this multi-dimensional input/output environment, domestic and foreign researchers have used parametric statistics/metrics and non-parametric methods [2,3]. Among these methods, Data envelopment analysis (DEA) [4] is particularly popular in assessing the e ciency of health care units and has many applications in China, Europe, and other parts of the world [5][6][7]. [8] uses constant and variable returns to measure technical e ciency and distribution e ciency in 98 Greek hospitals. Due to the excessive concentration of human and nancial resources in large cities, suburban and rural hospitals are more e cient than large cities. [9] nds that Spanish hospitals are more e cient, while hospitals located in areas with low population-to-bed ratios are less e cient. [10] reviews researches on the assessment of primary health care providers, especially those using nonparametric technical data envelopment analysis. Most researches focus on structure and output, without considering the ultimate measure of performance. [11] studies balancing the e ciency of health services in remote areas of Greece with the fairness of access to services. [12] compares different specialization measures for hospital specialization and technology use e ciency, including two novel methods based on the number of patients rather than the proportion of patients. [13] uses two alternative conceptual models to evaluate the e ciency of public hospitals and regress the scores on explanatory variables related to hospital service performance to improve e ciency. [14] evaluates the production performance, e ciency and technological changes of 22 Greek public general hospitals. [15] combines differential methods and fuzzy preference programming methods for hospital performance evaluation. [16] proposes a worst-best method for hesitant fuzzy language with inconsistent repair to evaluate hospital performance. Considering the existence of complex information in the evaluation process of cognitive hospitals, [17] proposes a multi-criteria decision method with hesitant fuzzy linguistic information. [18] uses a two-stage method to evaluate hospital performance. In the rst stage, DEA is used to assess e ciency scores, and then truncated regression estimates are used to test the importance of explanatory variables. Based on the balanced scorecard and analytic hierarchy process, [19] designs a public hospital performance evaluation model. [20] proposes the integration of fuzzy set theory and SERVQUAL method to measure the service quality of four hospitals in India. [21] improves hospital operating performance from the perspective of mixed sustainability and resilience.
The current domestic and international researches on the performance evaluation of pension services have achieved certain results, but there are still de ciencies. Most of the evaluation research on elderly care services focuses on home-based elderly care services, government-purchased elderly care services, and institutional elderly care services. There is a lack of performance evaluation research on the combination of medical and elderly care services. In addition, most of the researches focus on the construction of the indicator system, and lack of empirical analysis. Therefore, this paper summarizes the current status of the research on the evaluation of integrated care and elderly care services, based on the system theory and the theory of relevant stakeholders, and combined with the use of a two-stage DEA evaluation method to evaluate the performance of integrated care and medical services in China. This study takes the elderly care service agency as an example to conduct an empirical analysis, and proposes ways to improve the combination of medical and nursing care. This research can make up for the de ciencies of existing research, and promote the development of integrated medical and nursing care services.

Methods
Two-stage DEA model Data envelopment analysis (DEA) is a non-parametric frontier analysis method especially suitable for complex systems with multiple inputs and multiple outputs. It uses mathematical programming models to evaluate the relative effectiveness of decision-making units (DMU). The traditional DEA model regards innovation activities as a black box. In order to deepen the analysis and analysis of the internal structure of the system, Kao establishes a two-stage DEA model with variable scale returns, which is suitable for comparison between enterprises of different sizes and is widely used in e ciency research. Therefore, this paper uses a two-stage DEA model to evaluate the e ciency of the combination of medical care and nursing.
In a two-stage DEA model, there are n decision-making units DMUs. In each DMU j (j = 1,2,...,n), the rst stage DEA has m input elements x ij (i = 1, 2,..., m) and d output elements z dj , d = 1,2 ,...,d. At the same time, the output element of the rst stage is regarded as the input element of the second stage, namely the intermediate element. The output factors of the second stage are y rj , r = 1, 2, ..., s. The two-stage model of the combination of medical care and elderly care service model is as follows:

Variable Selection
This study divides the operation process of the combination of medical and nursing into two stages. The rst stage is the operation effect stage and the second stage is the service evaluation effect stage. The de nition of the input and output indicators of the performance evaluation index system of integrated care and elderly care services takes into account the particularity of integrated care and elderly care services. In this paper, the performance level is measured from the two dimensions of effect and e ciency. In the e ciency-oriented medical and nursing performance evaluation, the DEA method is used for evaluation. Therefore, it is necessary to classify the theoretical indicator system for input and output, and integrate the resource input and service output dimensions in the initial theoretical indicator system into the input and output indicators.
Essentially, an organization will only produce output if it is operating, so the internal organizational operating dimension is divided into input indicators, as shown in Tables 2 and 3.
In the evaluation process, it is necessary to eliminate the correlation between the evaluation indicators and carry out dimensionality reduction. Based on the limited research time and the availability of data, this paper conducts factor analysis on the data of 30 medical and nursing-type old-age care service institutions, and reduces the evaluation index. In this paper, IBM SPSS software is used to reduce the dimensionality of the data. Before factor analysis, the reliability of the data of the survey scale is tested. The internal reliability value indicates whether each scale measures a single concept, that is, how the internal consistency is maintained between the items that make up the scale. If the intrinsic reliability coe cient is above 0.8, it can be considered that the scale has a high intrinsic consistency. The Cronbach coe cient of the data in this paper is 0.885, which proves that the survey scale designed in this paper has a high internal consistency. According to the results of factor analysis, the economic meaning of each public factor is de ned, and 19 indicators are re-divided into 7 indicators. Among them, the indicators of the input side are ve evaluation indicators: operational investment, management input, xed asset input, technical input, and service development; the indicators of the output side are the operating effect and service evaluation effect indicators. The performance-oriented evaluation index is determined by two evaluation dimensions: operation effect and service evaluation effect, so as to determine the performance evaluation index system of the combination of medical care and elderly care services. As shown in Table 4.

Results
This study estimates the changes in the overall e ciency E and staged e ciency indexes E 1 and E 2 of the combination of medical and nursing care of pension services in Qingdao of China. Using DEA to measure the service e ciency of 30 medical and nursing-type pension service institutions, we can obtain the results of the calculation, which are regarded as the comprehensive performance evaluation results as shown in Table 5 and Fig. 1. It can be seen from Table 5 that the comprehensive e ciency value of 20 of the 30 medical and nursing-type pension institutions is 1, which is regarded as effective for DEA. The other 10 are in weak DEA, that is, they have not reached the optimal value in terms of scale e ciency or pure technical e ciency. Among them, the lowest is institution 12, whose comprehensive e ciency is only 0.638. In the case of variable returns to scale, there are 24 companies with a pure technical e ciency value of 1, accounting for 80%. From the perspective of scale e ciency, 20 of them have effective e ciency, and 10 is ineffective e ciency.
This study divides the reasons for the low e ciency of the input and output of the combination of medical care and old-age care services into two types. The rst is the low scale e ciency, that is, the supply structure of pension services is unreasonable. The second is the low e ciency of pure technology, that is, the resource utilization rate of pension service institutions is not high, resulting in the input elements not being used most effectively. Therefore, it is necessary to further analyze the reasons for the ine ciency of the 10 DEA ineffective medical and elderly care services.
In these 10 DMUs with ineffective DEA, the pure medical e ciency of DMU22, DMU23, DMU26 and DMU30 is 1, and the scale e ciency value is less than 1, that is, the pure technology is effective but the scale is invalid. This means that the resource utilization technologies of these 4 DMUs match their service capabilities, and there is no problem that the input elements are not maximized. The reason for the ine ciency of its integrated medical and nursing services is that its supply structure is unreasonable and there is a problem of large or small operation scale. The remaining 6 DMU's pure technical e ciency value and scale e ciency value are not 1, indicating that the service resource utilization technology is not good. There are input factors that are not used effectively and the organization's service supply structure is unreasonable, and there are also problems of too large or too small an operation scale.
Performance score and ranking analysis is based on the super-e ciency CCR model. As can be seen from the foregoing, It can be seen from Table 6 that each DMU has a different super e ciency value, so that the e ciency values of all DMUs can be sorted. Figure 3 is the e ciency ranking of 30 institutions. technical e ciency and scale e ciency are all 1, and its super e ciency has reached 3.734. Among the 30 medical and nursing-type pension service institutions, its e ciency is the highest. It is easier for 10 DEA invalid institutions to choose DMU27 with the highest e ciency value to stimulate their own enthusiasm. The second is to choose an institution that is closer. If there is a large gap between the DEA invalid institution and the most e cient DMU27, other DMUs with an overall e ciency value of 1 can be selected as a benchmark according to the similarity or similar principle of the region. These backward institutions can take advantage of geographical advantages to gradually approach the optimal e ciency. If the amount of input is smaller and the amount of output is larger, it means that the utilization of medical care and elderly care services for the elderly care resources is higher and the input-output e ciency is higher. On the contrary, if the output is insu cient and the input is excessive, it means that there is a waste of resources and ine ciency of input and output in the   Regarding operational investment, the operational input redundancy rate of DMU10, DMU22, and DMU30 all exceeded 10%.
Among them, the highest redundancy rate of DMU30 is 14.38%, and the lowest redundancy rate of operation investment is DMU20 (6.95%).Regarding the investment in management elements, the operational input redundancy rate of DMU12, DMU20, and DMU22 all exceeded 10%, among which the highest was DMU12 (13.54%), and the lowest was DMU14 (8.25%).Regarding xed asset inputs, those with a redundancy rate of more than 10% are DMU12, DMU20, and DMU30. Among them, the xed asset investment rate of DMU20 and DMU30 is as high as 20%. The resource allocation level of these institutions is poor, and they only focus on the scale of investment, but not on the improvement of resource utilization technology. It is di cult to achieve comprehensive e ciency effectively. Regarding technology investment, there are still four pension service institutions whose technology investment redundancy rate is higher than 10%. Technical input represents the number of persons who have obtained professional quali cation certi cates, medical quali cations and training times. The higher redundancy rate in technology investment proves that although the investment in technical elements is relatively high, the best use effect has not been obtained. The investment in high-tech elements has not played a greater role. Regarding service development, the service deployment redundancy rate of DMU12, DMU14, and DMU20 is higher than 10%. Although more service projects have been carried out, they have not brought more output. Regarding output, only the service effect evaluation indicators have insu cient output, which is related to two aspects. On the one hand, the projection analysis in this paper is based on the super-e ciency DEA model from the input side, so the analysis is mainly from the input side. On the other hand, it may be related to the actual situation. Business performance is mainly related to the total number of occupants, the number of people receiving long-term medical care insurance, the number of disabled and semi-disabled, and operating income. Three of the four indicators are related to direct numbers. However, the number of elderly people admitted is an uncontrollable output, so pension service agencies cannot increase the output by increasing the number of elderly people admitted. For service evaluation, the main output shortages are DMU10, DMU12, DMU20, and DMU20 is as high as 20.35%. The output of them can be improved by improving the satisfaction of the elderly admitted and the effects of safety management. In summary, for an organization with a pure technical e ciency of less than 1 to achieve DEA effectiveness, it is necessary not only to reasonably adjust the organization`s service supply structure and operating scale, but also to improve its own resource utilization technology.

Discussion
Through the DEA comparison analysis of 30 pension institutions, the following research conclusions can be drawn: (1) The e ciency of the combination of medical care and elderly care services is relatively high, but the resource allocation still needs to be further optimized.
(2) Though the super-e ciency DEA evaluation Organizations are ranked a whole, the benchmarking organizations can be established to be further optimized and improved. From the analysis of the projection structure of input and output, we can know that the improvement path can be set from the input and output elements. (3) For the projection effect of input and output, the operational performance of each DMU is different, so the improvements of the indicators of each DMU are also different. (4) The Invalid DEA institutions need to reduce their input from ve elements: operational input, management element input, xed asset input, technical input and service development. The increase in output mainly depends on improving the service evaluation effect.
Based on the research results and the investigation on the combination of medical care and elderly care services, this study proposes the following countermeasures and suggestions.
Regarding the evaluation results, the average value of the xed asset input redundancy rate is the highest among the input indicators. Fixed assets mainly cover four variables: building area, number of beds, investment amount, and service facility con guration. From the analysis results, it can be seen that the main variables leading to investment redundancy are the building area and the number of beds, which are also consistent with the actual situation. Old-age service agencies generally have large construction land, but the occupancy rate is less than 50%. At present, the main index for the government to subsidize the construction of pension institutions is the number of beds. The availability of pension land makes the construction area of pension institutions generally larger. The subsidy policy orientation has, to a certain extent, made pension institutions blindly pursue the number of beds. The government can adjust policies appropriately to favor aspects related to the results of operations.
The pension service institutions have poor operating capabilities, and depend on government operating subsidies. However, from the evaluation data, it can be seen that the pension service institutions have redundant operational inputs. In order to increase the utilization rate of operating subsidy funds, the government needs to build a hierarchical classi cation of capital allocation mechanism. In addition, government subsidies have no obvious impact on service performance. The government fund subsidies should be transformed to play the incentive role. According to the actual operation level, service level, and service e ciency of the medical care and elderly care service organization, the organizations can be divided into different levels. The amount of subsidies should be linked to the assessment level to reduce subsidies for underutilized operating capital resources. In order to encourage institutions with high operating e ciency and high service evaluation, the government may encourage them with appropriate operating funds. This can ensure that the investment of operating capital is maximized, so as to better improve the operating e ciency of the combination of medical care and elderly care services. Relevant departments should be aware of the various nancial problems that arise in the process to improve the feasibility and practicality of subsidies.
From the analysis results, it can be seen that the medical care and elderly care service agencies have not made reasonable arrangements for the resources invested. In addition to the problems of the institutions' own operation and management, they also lack effective government supervision and management. Among the existing management systems in various regions, there is no management system and evaluation standard speci cally for pension institutions. As a result, the hardware facilities of the pension institutions and the con guration of service personnel have not reached the required standards. To a certain extent, this also puts the medical care and elderly care service institutions in a state of lack of supervision, which cannot guarantee that they will make reasonable plans and resources allocation during the operation process. In order to ensure the effective operation of medical care and elderly care service institutions, relevant government departments should establish a set of service operation speci cations and standards including management, service, facility construction and other indicators as soon as possible. Relevant government departments irregularly supervise and inspect the medical and nursing care service agencies, and rank the evaluation results. Increased operational e ciency and improved service standard will encourage pension institutions to improve facility con guration, improve management and service levels.
According to the super-e ciency analysis ranking, DEA-invalid pension service agencies can choose benchmark companies based on two principles: choose the rst-ranked pension service agency or choose an institution with a comprehensive e ciency value greater than 1 according to distance. The government should take the lead in evaluating the medical and nursing care service, and use the best-ranked institutions as industry benchmarks and formulate standards for various indicators in the operation of pension institutions. A perfect standardization system is conducive to the organization's own standardized operation and improvement of operation quality.

Conclusion
This study establishes a performance evaluation index/criteria system for the combination of medical care and elderly care services in China, and develops a two-stage DEA empirical approach to evaluate them for the rst time. A total of 30 pension institutions in China are adopted to comprehensive performance evaluation via using the proposed method. Additionally, we identi ed some potential issues/factors of which decision-makers should be aware after performing these methods. Our rigorous, quantitative analysis of the proposed method provides guidance for decision-makers/researchers/practitioners when facing a pension institution preference study.  Figure 1 Comparison of e ciency between two stages.

Figure 2
Histogram of 30 institutions' e ciency ranking. Service evaluation performance.