Hospital Eciency Measurement in the West of Iran: Data Envelopment Analysis and Tobit Approach

Objective The optimal hospital performance and optimal use of resources are among the goals of healthcare policymakers. This study aimed to assess the association between hospital size and hospital area population with technical eciency in public hospitals . Methods In this descriptive-analytical study, the statistical population consisted of 15 public hospitals in the west of Iran. First, the data envelopment analysis (DEA) method was used to evaluate technical eciency. Data inputs included staff and beds, and data outputs consisted of the number of surgeries, the number of patients, and the average length of stay. Then, according to the public ownership of all hospitals, their educational and therapeutic activities, as well as their size and population were considered as the environmental factor affecting eciency. Thus, Tobit regression was applied to measure their effects on eciency.


Introduction
Health has a signi cant impact on the infrastructure of different parts of society based on sustainable social, economic, political, and cultural development [1]. The promotion of health is a moral obligation, including the social and economic categories. Thus, every health treatment service planning should be part of the pervasive attitude of healthcare policy to make part of the integrated plan of sustainable development [2]. Most of the world's countries have faced rising health treatment section expenses during the recent decade [3]. This problem has occurred due to the combination of factors associated with demand, including demographic and epidemiological changes, the developed technology, and the lack of available information for health treatment services' customers and consumers related to factors affecting supply. Moreover, the previous research shows that at least some parts of the rising expenses result from the ine cient use of sources [4]. Similar to major organizations, hospitals play a critical role in providing health treatment services, resulting in the recovery facilitation of the physical and mental health of the patient in society in a speci c way. It also leads to training specialists in the health treatment section, performing medical research, and improving the health of society. Therefore, this organization has a particular sensitivity and importance regarding economic infrastructures and its severe vulnerability against currency rate uctuations and commodity markets, particularly in developing countries [5]. This institution is the most extensive and most costly operating unit of the health treatment system in Iran [6].
The portion of hospital expenses is estimated at least 40% of total health expenses in 2015. This statistic is out of the total expenses of health treatment based on the national health accounts of Iran (4).
Considering that the health change plan was implemented in May 2014 with particular effects on hospitals, the portion of health expenses has increased out of gross domestic incomes, and that of the hospitals has risen through this statistic more than ever [7]. Despite many expenses spent on hospitals, many differences exist between the available and required resources in this section. The rise in demand, the rapid growth of health expenses to incomes in developing countries, economic crises, and the government budget lack are many problems for hospitals. Therefore, hospitals sustain heavy pressure to control and decrease expenses. These conditions double the necessity of creating additional probable resources and using the possible resources with resource allocation patterns and increasing e ciency in this section [8].
There is a pressing need concerning the optimal use of scarce sources and improvement of e ciency for providing health treatment cares. Accordingly, some measures are taken into account to prevent or decrease the waste of resources allocated to the health treatment system, helping in providing services as better as possible, developing availability, and improving hospital service quality [9]. Therefore, the use of scienti c and applied methods is necessary for assessing the function and activities of the hospital and the optimal use of physical and human resources. Thus, one can enjoy economic tools and analyses, which provide a logical and speci c framework for analyzing vital health care subjects. Although the mere assessment of health treatment services seems unnecessary, due to their human and humanitarian nature, it is highly bene cial to use assessment in the measurement, e ciency, and optimal use of resources [10].
In the economic literature, e ciency is the minimum use of inputs for a certain level of output. In other words, it is the increasing of outputs with a certain level of inputs. Inputs are the same as manufacturing factors such as energy, initial materials, capital, and labour force in the manufacturing process of commodities and services for generating outputs (i.e., commodities or services in the organization). E ciency is an appropriate criterion for measuring the acquirement of the best output by limited inputs.
Further, it is a new approach to peoples' work and life [11]. The ratio analysis can be used in most e ciency studies. This method has limitations due to its use in the measurement of e ciency between one input and one output and the association of the studied subject for creating a relation between one input and some outputs or some inputs and some outputs. It is noteworthy that more advanced methods should be used since a hospital is an organization that encounters some inputs and outputs [12]. Extensive studies have focused on assessing the hospital, including Mahfoozpour et al. [13], Kiadaliri et al. [14], Rezaei et al. [15,16], Mosadeghrad et al. [17], Hatam et al. [18], Goudarzi et al. [19] in Iran as well as Mujasi [20], Cheng, [21], and Ali. [22] in Uganda, China, and Ethiopia, respectively. Therefore, there is now a great interest in data envelopment analysis as a dynamic, capable, and progressive method for measuring e ciency and productivity. It is mainly applied in government units and the private sector, in which their valuable information is unavailable or unreliable.
Data envelopment analysis determines whether the considered decision-making units consider the e ciency line. It is non-parameter linear planning that estimates the frontier production function. The difference between this study and previous studies is Tobit regression, which can measure the effect of environmental factors on the e ciency level. The environment in this context is the factor that can affect rm e ciency although it is not part of the applied inputs. Furthermore, the assumption is that it is not under management control. Environment variables are ownership, the number of customers, and the rm position and size. Thus, if a dependent variable of a critical limit, Tobit regression or censored regression, will apply to review linear relationships [23]. Considering the above-mentioned explanations, the current research sought to evaluate the technical e ciency of the public hospitals of Hamedan County with data envelopment analysis and Tobit regression in 2018.

Data collection
The population of this descriptive study includes all public hospitals (N = 15) in the west of Iran. Due to ethical considerations, the name of the hospital is speci ed in alphabetical order in this study .Data collection tools for the theoretical framework of the research are scienti c and library documentation. Given that data are collected from hospitals by standard tables of the Ministry of Health and Medical Education, there is no need to determine validity and reliability. Some reports were used to collect data consisting of data in 2018 such as general particularities of the hospital, the number of xed and active beds, all patients (outpatients and inpatients), the number of staffs (i.e., physicians, nurses, and other staff), the number of surgeries (i.e., emergency, outpatient, and standard), and the length of stay.

Statistical analyses
Data envelopment analysis was used to analyze data and assess the e ciency level by Deap 2.1, assuming variables return to scale, which was of input-based type. The mathematical relation of data envelopment analysis is as follows: where m, s, and n are the number of inputs, the number of outputs, and the number of units, respectively. The existence of a free variable with a w signal is the difference of this relation with the constant returns to scale. Therefore, the variable w signal determines returns to scale for every unit. The type of returns to scale represents a decrease, the scale to scale is xed, and the type of returns to scale increases if w < 0, w = 0, and w > 0, respectively [24]. Scale e ciency and management e ciency are obtained in this relation in addition to technical e ciency. Technical e ciency shows the level of the rm's capability to maximize the production level concerning resources and production factors. Further, the scale e ciency of a unit is obtained from the ratio of the observed e ciency of that unit to the optimal e cient scale.
Moreover, many variable returns (VRS) to scale technical e ciency studies are divided into "scale e ciency" and "net technical e ciency" (net technical e ciency is also called management e ciency).
The mentioned e ciencies are between 0 and 1, and the closer to 1 and 0 indicate more and less e ciency, respectively [24]. Tobit regression was estimated to measure the effect of environmental factors on e ciency with Stata15. Hospital ownership, type of activity, the population covered by the hospital, and the size of the hospital are environmental factors. In this research, the ownership and the type of activity are determined as well. All hospitals have public ownership. Additionally, they are the subsets of the Ministry of Health and Medical Education, including educational and therapeutic activities.
Thus, the hospital size and hospital populations were independent variables, and the obtained technical e ciency was a dependent variable. Therefore, the dependent variable for hospitals with more and less than 180 beds was calculated as one and zero according to the previous study, respectively [20]. Furthermore, hospitals with a covered population of more and less than 170000 were scored as zero and one, respectively, according to the population dispersal in the west of Iran.

Technical e ciency, management e ciency, and scale e ciency
According to technical e ciency, the results concerning the e ciency and rankings of the hospitals are presented in Table 1. The name of the hospitals was encoded with English letters according to their e ciencies. Assuming variable returns to scale, the average technical e ciency, the average management e ciency, and the average scale e ciency of the hospitals were calculated as 0.933, 0.951, and 0.977, respectively. The calculated values by data envelopment analysis are presented as numbers 0-1. Further, 40% of them were six hospitals with a lack of maximum technical e ciency. The minimum technical e ciency was 0.544, which was related to hospital O. Moreover, the scale e ciency of 60 and 40% of nine and six hospitals was 1 and less than 1, respectively. Furthermore, 73.3 and 26.7% of 11 and 4 hospitals had management e ciency of 1 and less than 1, respectively. In total, six and four hospitals were ine cient in technical e ciency and management e ciency, respectively. The excess of the related hospitals is speci ed by the number of active beds and staff based on management e ciency. Excess inputs are shown in Figure 2.
According to the vertical axis representing the excess input, the most and least excess inputs of the number of staff belonged to hospitals M and O, respectively. Further, the most and least excess inputs of the number of active beds were related to hospitals M and O, respectively.

Tobit regression as environmental factors
Hospital ownership, type of activity, the population covered by the hospital, and hospital size are not under management control. However, the public ownership of all hospitals and their educational and therapeutic activities were speci ed in this research. Thus, the size of the hospital and its population were considered as the environmental factors affecting e ciency. Moreover, Tobit regression was employed to assess their effect on e ciency. Furthermore, the T-test was applied to demonstrate the signi cance of coe cients. The results are provided in Table 2. The computed values by Tobit regression are presented as the odds ratio (a 95% con dence interval).

Discussion
According to the very signi cance of hospitals in providing health treatment services, as well as the health management system of every country, data envelopment analysis can be a huge step by providing the possibility for comparing, ranking, and patterning capability. Thus, it will pave the way for improving the functions of hospitals, particularly in the health treatment section. Based on the limitations of data envelopment analysis, the total considered organizations should be more than or equal to 3 times the inputs and outputs. Therefore, due to technical limitations, there is no possibility to choose more than ve variables owing to the number of hospitals [24]. In the current study, the input-based and variable returns to scale method was applied since hospital outputs are not much in management control. This research assessed the e ciency of the hospitals and introduced ine cient units. Furthermore, the amount of the required resources in ine cient hospitals was estimated to achieve border e ciency. The results revealed that using the capacity of the existing hospitals and possible inputs can be a more usable solution compared to establishing new hospitals. The average technical e ciency, management e ciency, and scale e ciency of the considered hospitals were 0.933, 0.951, and 0.977, respectively. According to the results of data envelopment analysis and while assuming variable returns to scale, there was e ciency promotion without any increase in expenses. The ndings of a study by Kiadliri [14] on technical e ciency assessment of the hospitals in the west of Iran showed that hospitals decrease their use of inputs, resulting in decreasing the number of expenses and wastes by improving the function and increasing e ciency in hospitals. The results further represented that 60% of hospitals have constant returns to scale. In other words, more than half of the hospitals operate at the most returns to the production scale, and the number of inputs and outputs is at the optimal level. Mehraban and Raghfar [25] reported similar results as well. Further, Mujasi [20] and Ali et al. [22] indicated the effect of environmental factors on e ciency using Tobit regression. On the other hand, the initial and optimal values in hospitals with technical e ciency less than 1 are different. The initial values must be improved to the optimal values to achieve optimal e ciency. Therefore, the number of staff excess inputs in N, M, L, and O hospitals was 50, 88, 51, 41, and the number of excess inputs of the number of active beds was 15, 22, 17, 14, respectively.
Thus, hospitals must decrease their excess inputs to achieve maximum e ciency. Furthermore, the Tobit test results concerning environment variables in the studied method suggested that the size of the hospital and the population have a signi cant effect on e ciency. Therefore, the size of the hospital and the population of the location of the hospital will affect e ciency, which is out of management control.

Conclusion
In general, six hospitals were ine cient in technical e ciency. Ine ciency was also observed in ve and four hospitals in terms of scale e ciency and management e ciency, respectively. The size and population of the hospital as environmental factors have signi cant effects on hospital e ciency. Hospitals with the e ciency of less than one had different initial and optimal values, and there was also excess input. Therefore, the mentioned hospitals should decrease the initial values of their inputs to achieve maximum e ciency. According to the limitation of data envelopment analysis in this research, there was no possibility of choosing more than ve variables due to the limited number of public hospitals in the west of Iran.

Availability of data and material
The data that support the ndings of this study are available from the corresponding author, [AF], upon reasonable request. Figure 1 Excess inputs in ine cient hospitals