A Literature review on the Identification of Variables for Measuring Hospital Efficiency in the Data Envelopment Analysis (DEA)

The selection of input and output variables usually pose a problem when carrying out efficiency assessment in hospitals. Data Envelopment Analysis (DEA) is an instrument that is used to calculate the efficiency of a hospital using some inputs and outputs. Therefore, this study aims to identify the most frequently used hospital inputs and outputs from an existing paper,, in order to assist the hospital management staffs in choosing the relevant variables that can represent available inputs, are easily accessible, and need improvement. It was conducted using keywords such as “hospital efficiency” and “DEA for hospital” to search for peer-reviewed journals in the PubMed and Open Knowledge Maps from the year 20142020. From, the 586 articles, 54 samples were obtained from the about 5-3504 hospitals which were analyzed from 23 countries. The results showed that, the five most used inputs were the number of beds, medical personnel, non-medical staff, medical technician staff and operational costs, while the most used outputs were number of inpatients, surgeries, emergency visits, outpatient service, and days of inpatients. These variables are often used for accessing the efficiency of hospitals in the DEA application.


INTRODUCTION
Resources of hospital are demanded to fulfil what patient wants. But in the reality, there are many hospital have not the same resources of each other so that makes inefficient resources of each hospital (Abdurachman et al., 2019). Efficiecy assesment in hospital are rarely conducted like the other sector because of resources setting and limited control of outputs (Shettian, 2017). Beside that, raising efficiency are needed especially for health care in a low or medium human development index countries. One of health care efficiency assessment problem is on methodological step (Vivekanantham et al., 2014). Efficiency is a condition when existing resources could make an usefull result. Hospital efficiency is about a hospital capacity to make a qualified result such as a well treated patient and have recovered discharged patient by using resources such as medical staff, non-medical staff, and finance. While unefficiency is a sign of low quality services which could affect a late treatment even an addition therapy (OECD, 2019). There are two type of efficiency, the first one is technical efficiency by combining or reducing input at certain level and economic efficiency by setting hospital finance (Samudro & Pratama, 2018).
There is a most used efficiency assessment method called Data Envelopment Analysis (DEA). A. Charnes, W. W. Cooper and Rhodes are the first who introduced DEA to public (1978) (Samudro & Pratama, 2018). DEA can be used in DEAP 2.1 (Tim Coelli Inc.) and to knowing its interpretation can be used SPSS (SPSS Inc., USA) and Frontier Analyst fourth version (Banxia Software Ltd, UK). There are some important term form DEA (Soares et al., 2017): Decision-Making Unit (DMU) is a main unit which efficiency is analyzed. In the case of hospital efficiency assessment, the DMU is hospital; Input is an available resources in the DMU; Output is an impact or result of the process of running the DMU; The efficiency score is a calculated value as a result of an efficiency assessment. The value often on a scale of 0 to 1, with means 0 is the minimum and 1 is the maximum value of efficiency.
The proper use of DEA can be used as a reference for considering DMU resources, as long as the used data could represent the DMU process and could be compared with othe DMU (Kang & Kaipornsak, 2014). Lack of information about relevant factors from variables makes it difficult to calculate hospital efficiency, therefore it is important to consider the selection of appropriate and effective inputs and outputs (Hsiao et al., 2018) and even become a source of hospital evaluation (Omrani et al., 2018) . This study aims to identify the most used input and ouput in calculating hospital efficiency using DEA. This study purposes to guide hospital management staff to find the relevant hospital input and output so that the efficiency assessment will be easier, right on target representing the available resources and it can be seen which part which need more attention to evaluate the hospital. This study also describe the form of each variable that can be generated in DEA.

METHOD
This study conducted a literature review method of several articles with inclusion criteria of search keywords such as "hospital efficiency" and "DEA for hospitals". Selected articles are published articles from peer-reviewed journals from the literature database PubMed and Open Knowledge Maps. The articles that appear are being reviewed from the title which states the elements of the keywords, the language used is English, the year the article was published around 2014-2020, the purpose of the article is to calculate hospital efficiency, the calculation method using DEA application and mentioning the use of input and output for calculation. The exclusion criteria for articles to be analyzed were articles obtained other than the specified keywords and articles that calculated the efficiency of the part of hospital unit. The articles reviewed were not limited to the type of hospital, city or country of origin, the combination of the DEA model used, and the type of efficiency that was calculated. After the relevant articles selected, the variables were collected and calculated by the stake method to see their frequency of used. The results of the literature review will be presented in a table that contains the name of the author of the article, the number of DMU used in the calculation, and the input and output mentioned. The five most used input and five output variables from the relevant article will be discussed further in the results and discussion section.

RESULT AND DISCUSSION
From the search results through the literature database based on keywords and year, the total number of searches was 586 articles. The articles are then reviewed according to the appropriate title and language getting 69 articles. Furthermore, the articles were examined according to their objectives, the method used, the DMU used and the input and output variables mentioned so that there were 51 articles which most relevant to be analyzed in this study. Of the 54 relevant articles, it was found that the number of DMUs was calculated starting from the smallest number DMUs was 5 to the largest number was 3,504 DMUs. The DMUs that are calculated by the DEA in the relevant article come from various types of hospitals such as public hospitals, private hospitals, university hospitals, regional hospitals, veteran hospitals, institutions, and ministry-bound hospitals. The relevant article calculates the DMU of many countries such as Germany, China, Iran, Canada, Brazil, United States, Turkey, Uganda, Bohemia, Greece, Italy, Ethiopia, Taiwan, Norway, Spain, Bangladesh, Poland, Japan, Portugal, South Korea, Saudi Arabia, Malaysia, and Palestine. Technical efficiency, economic efficiency, scale efficiency, managerial efficiency and operational efficiency are the aims in calculating the DEA of the relevant articles. The additional approaches or combinations of DEA calculations used in relevant articles are vary such as the use of Tobit regression, the Malmquist index, integrated K-means clustering, dynamic network DEA, bootstrap DEA, fuzzy DEA, slack-based DEA, window-based, two-level DEA, and the four-tier DEA. Several variables from the results of the review on the application of DEA in hospitals are more clearly shown in Table 1 From Table 1, there are many terms included in the input and output variables. The terms and how many times it has been used shown in Table 2. In Table 2, it shown that five most used input to assess hospital efficiency in DEA application are the number of beds, the number of medical personnel, the number of non-medical staff, operational cost, and the number of medical technicians.

(1). The Number of Beds
The number of beds which can be included for hospital efficiency assessment were suitable and available to use. The number of beds often considered as the capital of the hospital (Omrani et al., 2018). The number of beds in this case are chronic care beds and special care beds (Soares et al., 2017). An effective bed allocation planning, such as considering the number of beds by the size of the hospital could have an impact on calculating efficiency and have a role for hospital management  restriction on access and optimum use of resources is the main challenge of development in all organizations. Therefore, the aim of this study was to determine the technical efficiency and its factors, influencing hospitals of Tehran. Methods: This research was a descriptive-analytical and retrospective study conducted in 2014-2015. Fifty two hospitals with public, private, and social security ownership type were selected for this study. The required data was collected by a researcher-made check list in 3 sections of background data, inputs and outputs. The data was analyzed by DEAP 1.0.2, and STA-TA-13 technique. Results: Seventeen (31/48.

(2). The Number of Medical Personnel
Human resources have the most important role in the health service system. The number of doc- tors who are counted are doctors who work full time including dentists and Chinese medicine doctors. The other medical personnel who are counted are nurses who work in hospital and nurses who work in patient home (Soares et al., 2017)  (

3). The Number of Non-medical Staff
Non-medical personnel in this case were a staff who did not perform medical treatment on patients in their work. The number of non-medical personnel included in the calculation are the num-ber of full-time staff or equivalent, social workers, researchers, non-professional workers (Soares et al., 2017), full-time management staff (Hsiao et al, 2018), and logistics staff (Xu et al., 2015).

(4). Operational Cost
Total hospital expenditure counted as a part of the hospital's economic investment (Li et al., 2017). The expenses referred to the total of costs spent on purchasing goods and services to support hospital services (Miguel et al., 2019)as compared with traditional management. Specifically, we compare traditionally managed public hospitals, public hospitals managed by a private finance initiative (PFI. The expenditure of goods and services commonly referred as hospital operational costs (Fuentes et al., 2019). Operational costs often included in the productivity analysis which can show good comparisons in terms of units and time (Anthun et al., 2017(Anthun et al., )1999(Anthun et al., -2014. This period was characterized by a large ownership reform with subsequent hospital reorganizations and mergers. We describe how technological change, technical productivity, scale efficiency and the estimated optimal size of hospitals have evolved during this period. Material and methods Hospital admissions were grouped into diagnosis-related groups using a fixed-grouper logic. Four composite outputs were defined and inputs were measured as operating costs. Productivity and efficiency were estimated with bootstrapped data envelopment analyses. Results Mean productivity increased by 24.6% points from 1999 to 2014, an average annual change of 1.5%. There was a substantial growth in productivity and hospital size following the ownership reform. After the reform (2003-2014. Expenses incurred by hospitals are usually in the term of cost allocations for medical services (such as payroll, capital, and equipment depreciation costs) as well as nonmedical supplies (Büchner et al., 2014). In a study in China, large hospital expenditures affected by policy reforms did not lead to raised hospital operational efficiency (Jiang et al., 2016). Hospital operational costs used in calculating efficiency can be in several units of currency per year.

(5). The Number of Medical Technicians
Medical technician personnel referred to medical personnel other than doctors, nurses, and not including hospital administrative staff (Lin et al., 2019). Medical technician including clinical social workers, psychologists, hearing and speech therapists, and respiratory therapists (Hsiao et al., 2018); pharmacists, pharmacist assistants, dietitians, physiotherapists, occupational therapists, and radiology technicians (Kalhor et al., 2016;Soares et al., 2017); clinical laboratory technicians and medical imaging technicians (Cheng et al., 2016).
Beside of inputs, there were five most used outputs to assess hospital efficiency in DEA application are the number of inpatients, the number of outpatient services, the number of surgeries, days of inpatient, and the number of emergency visit.

(1). The Number of Inpatients
Inpatient is a patient who are treated and need more treatment which requires a day or night of stay or more in the hospital (Bateman et al., 2007). Inpatient could come from referrals from other health facilities and or referrals from other unit within a hospital. In terms of efficiency, the number of inpatients is usually expressed by the number of patients per year.

(2). The Number of Outpatient Services
Outpatients are patient who are hospitalized but do not require treatment that requires the patient to stay overnight (Bateman et al., 2007). Outpatients usually only receive pre-admission assessment or diagnostic procedures until consultation and can leave afterwards. In calculating efficiency, outpatients were expressed by the number of patients per poly in one year (Soares et al., 2017). As an output variable for calculating hospital efficiency, the number of outpatients often combined with the number of emergency patients (Li & Dong, 2015;Cheng et al., 2015;Narcı et al., 2015;Cheng et al., 2016;Wang et al., 2017;Zheng et al., 2018;Liu et al., 2019;Jing et al., 2020).

(2). The Number of Surgeries
The number of operations are the number of treatments for a disease of disorder by means of procedures that require some actions such as cutting, removing, or manipulating tissues, organs or parts (Bateman et al., 2007). In efficiency calculations, the number of surgeries usually expressed per year.

(3). Days of Inpatient
Days of inpatient is the cumulative length of stay of hospitalized patient or in emergency department (Lin et al., 2019); including length of stay in general care, acute care, intensive care, dan chronic care (Kalhor et al., 2016). Days of inpatient also referred as the specific duration of patient admission and utilization of clinical and non-clinical inputs such as treatment, pharmacy, paramedical support services, and administrative services (Sultan & Crispim, 2018). Realized that inpatient services have different features and consume more resources that outpatients, the use of term "days of inpatient" is considered more medically homogenous than the term "number of patients hospitalized" and can provide a more significant output . The use of days of inpatient widely used in the form of the Average Lentgh of Stay (ALoS) (Fuentes et al., 2019;Pirani et al., 2018;Giancotti et al., 2018;Jia & Yuan, 2017;Kalhor et al., 2016). But in other hand, the varying length of days the hospitalized can be considered a distortion of ALoS calculation because the level of use can be higher or lower within patient (Flokou et al., 2017). In the calculation of efficiency, days of inpatient can be expressed by the number of days the patient was treated per year.

(4). The Number of Emergency Visit
The number of emergency visit is the number of the arrival of patients in a condition that urgently requires prompt treatment and care (Bateman et al., 2007). In calculating efficiency, the number of visits by emergency patients is counted in one year (Soares et al., 2017)

CONCLUSION
Each of the five most used input and output variables for the calculation of hospital efficiency can be applied in the Data Envelopment Analysis (DEA). The hospital input variables that are often used in the DEA application include the number of beds, the number of medical personnel, the number of non-medical personnel staff, hospital expenses, and the number of medical technician personnel. While the hospital output variables that are often used include the number of inpatients, the number of outpatient services, the number of operations, days of inpatient and the number of emergency department visits.