Measuring the efficiency of Palestinian public hospitals during 2010–2015: an application of a two-stage DEA method

The whole area of the OPTs is 6170 km² of which 5800 km² is the area of WB, and 365 km² is the area of GS. The Palestinian healthcare system comprises five main providers of healthcare services: (1) The Palestinian Ministry of Health (PMoH) and represents the public sector; this sector comprises primary healthcare centers and public hospitals. These hospitals are owned and administered by the Palestinian Ministry of Health. They are general hospitals that provide primary and secondary healthcare services, however; no public hospital provides tertiary services. (2) The United Nations Relief and Works Agency for Palestine Refugees (UNRWA); (3) Non-Governmental Organizations (NGOs); (4) Palestinian Military Medical Services (PMMS); and (5) Private for-profit organizations. According to the Palestinian Central Bureau of Statistics (PCBS), these providers manage80 hospitals with a capacity of 6006 hospital beds to serve 4.88 million people living in OPT, of which 2.97 million are living in WB, and 1.91 million are living in GS. The median age of the Palestinians is 19.8 years, and 39.4% of the population is under 15 years old. The age group (0–4 years) is 15% while for the age group over 65 years constitute only 2.9% of the population [12, 30].

There are 50 hospitals are operating in WB including East Jerusalem (60.1% of total beds), and 30 hospitals are operating in GS (39.9% of all the beds). 73% of all the hospital beds are general beds, 19% are specialized beds, 3.1% rehabilitation are beds and 4.9% are maternity beds (Table 1).

In West Bank, public hospitals are distributed in 11 administrative areas (governorates). They are Jenin, Tubas, Tulkarm, Nablus, Qalqillya, Salfit, Ramallah, Jericho, Bethlehem, Hebron, and East Jerusalem. However, due to political reasons, there is no Palestinian public hospital in East Jerusalem. Therefore, the included hospitals in this study are 13 public hospitals with a capacity of 1594 beds working in WB. To have a homogeneous sample of general hospitals, we excluded two hospitals from the analysis: a new hospital with 37 beds was established in 2014 (P12 in Table 2), data is not available from 2010 to 2013; the other hospital is psychiatric with 180 beds. As a result, we analyze the efficiency of 11 public hospitals (P01-P11 in Table 2) from 2010 to 2015 (66 observations). Table 2 illustrates the sample characteristics and relevant market attributes during 2015.

The ability of a hospital to transform inputs into outputs is influenced by its managerial efficiency (practices) and external operating environment (operational conditions) [15]. Therefore, relating the measures of inefficiency to the surrounding contextual factors provides a better understanding of efficiency differences and determines the key performance drivers across hospitals [31]. The OPT has a fragmented landscape of healthcare providers including hospitals which evolved across different regimes [1, 4]. However, the geopolitical setting of the OPT poses challenges to healthcare delivery and access, therefore, it is believed that environmental factors touch the production of healthcare services and should be included in our analysis. Figure 1 shows the relationships between input-output measures and contextual factors.

Different input and output sets had been used in the DEA literature to analyze the efficiency of hospitals [32, 33]. The basic principle, to identify variables, is to have a clear understanding of the “process” being evaluated among peer hospitals [34]. The investigated hospitals are all general hospitals; they are designed to provide primary and secondary health services, they don’t provide tertiary health services. Therefore, we included input-output measures that make a practical sense for the Palestinian public hospital settings. We used output measures that represent the level of public health benefits achieved in respect of three functional areas; admissions, outpatient visits, and emergency services. Since the other activities within the hospital (e.g., laboratory tests, deliveries, surgical operations, radiology activities) are highly correlated with the three measures, we did not include them in the set of outputs [35].

We included three output measures, they are: (1) inpatient services as measured by the total number of annual care days rather than a number of cases to account for case-mix adjustment [36]; (2) outpatient services as measured by the total number of annual visits [33]; and (3) the emergency services as measured by the total annual number of cases served without admission [37].

Inpatient days represent the total annual duration of patient admissions and the utilization of clinical and nonclinical inputs, such as nursing care, pharmaceutical items, paramedical support services, and administrative services. Outpatient visits represent the utilization of the outpatient clinics and the dedicated clinical and administrative resources to these clinics. In Palestine, the emergency departments and the ambulance services are vital outputs and represent the utilization of a considerable amount of resources in the public hospitals. The reasons behind the imperative role of emergency services are: (1) the hospital emergency departments become the first choice for patients seeking treatment because family practice model is absent in Palestine; (2) the primary healthcare centers work only for 6 hours a day, and 5 days a week, they provide a minor role of emergency and ambulance services; and (3) the majority of the population is covered by the government health insurance scheme by which they are entitled to the emergency departments in public hospitals [2].

In line with other DEA literature [38‐40], we included four input measures. They characterize the employed labor and capital. Labour input measures comprise three groups of personnel, the doctors, the healthcare full-time employees FTEs (e.g., Nurses, technicians, and other employees in para-medical departments), and the administrative FTEs [41]. Capital input measure was represented by the number of hospital beds [42]. Data on other resources, such as drugs, laboratory tests, or instruments were not available for the included hospitals.

As for the impact of the environment on the productivity of the public hospitals in West Bank, we considered ten factors (Table 3). These factors are organized into three sets: (1) Factors had been previously studied by other researchers such as the bed occupancy rate (BOR) and the average length of stay (ALOS). (2) Factors represent some proposed market settings in Palestine such as the percentage of public hospital beds (PPHB) and the availability of primary healthcare centers in the governorate where the included hospital serves (PRC). (3) Factors concerning the unique context of WB such as the percentage of refugees living in the governorate (REFP) where the included public hospital serves.

As for the first set, six factors are included. (1) The bed occupancy rate (BOR) is related to return to scale within hospital operations and capacity utilization, the higher the BOR, the higher constant return to scale and scale efficiency [40]. From economic point view, higher occupancy rate has a lower cost per case [43]. (2) The ratio of outpatient visits to inpatient days (OPIPR) shows to what extent hospital managers make a better combination of the two services that could make better use of available resources. (3) The average length of stay (ALOS) is the average days spent in a hospital from the time of admission to the time of discharge. It represents the intensity and efficiency by which individual patients are treated [22]. (4) The ratio of administrative employees to health employees including doctors (ADHR) may affect the way of doing clinical and nonclinical processes during hospitalization, accordingly may influence efficiency [39]. (5) The size (SIZE) of the hospital and the applied processes to patient treatment may differ as for their size and affect the level of resource utilization; a large hospital may suffer diseconomies of scale [44]. (6) Although all the investigated hospitals are public and don’t compete, it was felt that the market characteristics of each region may impact efficiency [33]. The proposed factors influence patients’ choices and may influence hospital efficiency. Due to differences in demographic and socioeconomic factors, we considered the location of the hospital (LOC) as a dummy variable to indicate whether the hospital is North to Jerusalem or South to Jerusalem where different social lifestyles apply.

As for the second set of environmental factors, two concentration indicators as a proxy for provider distribution were included: (7) The available number of primary health centers per 10,000 citizens in each governorate (PRC). (8) The percentage of public hospital beds (PPHB) to the overall providers’ beds in a certain governorate [45].

As for the third set of environmental factors, additional two factors are included. They apply to the unique context of Palestine. (9) Since the Palestinians’ loss of their land and homes in 1948, tens of thousands of Palestinians were displaced to live in refugee camps in West Bank cities; this factor was thought to influence efficiency; the way how refugees are living and working may influence the efficiency of the working hospital in that governorate. Therefore, the percentage of refugees living in every governorate (REFP) was considered. (10) The Palestinian healthcare system comprises fragmented healthcare providers evolved through different regimes, the number of available hospital beds per 10,000 inhabitants in a given administrative area was considered It represents the supply side of hospital services in a governorate (HBFP). Table 3 displays the ten proposed environmental factors.

The problem of measuring productive efficiency was best described, 60 years ago, by Farrell [46]. To solve the problem, Farrell introduced an activity analysis approach that combines the measurement of multiple inputs into a single measure of efficiency which he regarded as “technical efficiency.” Technical inefficiency is the amount of waste that can be eliminated without worsening any input or output. Building on Farrell’s ideas, Charnes et al. [23] introduced a powerful nonparametric methodology to assess the relative efficiencies of multi-input and multi-output production units such as hospitals which had been titled Data Envelopment Analysis [47]. These production units are denoted as decision-making units (DMUs) in the DEA literature.

The first published DEA work in healthcare context was in 1983 and investigated nursing services [48]. In 1984 the second published study investigated the medical and surgical departments in seven hospitals [49]. Among the empirical studies using DEA, hospitals received the most research attention [50]. The goals of hospital services are multiple and complex. Hospitals produce multiple outputs (e.g., inpatient care, surgeries, outpatient care, emergency) and absorb multiple inputs (e.g., clinical and non-clinical staff, beds, equipment, and supplies).

Based on a review of 317 published studies on frontier measurement of the efficiency of the healthcare delivery from1983 to 2006, Hollingsworth [51] found that 75% of the works applied the DEA, and other DEA–based methods. Empirical applications of DEA included performance examinations of different healthcare markets ranging from primary healthcare level [20, 52] to home healthcare agencies [53] and hospitals [54]. And from practice behavior at provider group level was also examined [55, 56] to the overall healthcare system and country level [45, 57].

The two-stage DEA is commonly used in productive efficiency analysis to estimate the impact of environmental factors and practices on performance. Because the DEA efficiency estimates of the first stage represent censored data, the second stage of analysis applies Tobit regression [28, 33]. Tobit regression applies the Maximum Likelihood Estimator (MLE) to find the model’s parameters [58]. The second stage generates additional information on managerial performance if we filter the impact of the component associated with the contextual factors. Further, the second stage analysis informs policymakers who may influence the operating environment [14, 15].

Many studies used the DEA efficiency score in the second stage analysis to evaluate the influence of operating environment on efficiency. Chowdhury & Zelenyuk [42] applied DEA and truncated regression model to explore the determinants of the hospital efficiency in Ontario/Canada. Their findings identified occupancy rate, outpatient-inpatient ratio, location, teaching status, and case-mix index as determinants of efficient practices. A study examined the hospitals in Ghana used DEA and Tobit regression, efficiency was determined by region and ownership [59]. Finally, Samut & Cafrı [45] analyzed the healthcare systems in 29 OECD countries during 2000–2010 and applied Malmquist Index and Tobit regression procedures, The authors, identified education, income, and market factors as determinants of hospital efficiency.

Despite the extensive body of DEA literature examining the performance of healthcare sector at all levels, due to the scarcity of data, few empirical studies were conducted in developing countries. Most DEA works were applied in the developed countries, mainly the US and Europe [60]. Particularly, in Arabic Speaking Countries, two previous studies employed the DEA and investigated the efficiency of hospitals in Jordan and Sultanate of Oman [38, 61]. Aimed at Palestine, to date, no studies have examined the efficiency of Palestinian hospitals or the influencing contextual factors. The performance measurement systems are already absent within the country’s healthcare organizations.

The study used data from 11 public hospitals operating in West Bank from 2010 to 2015 targeting a total of 66 observations. The sample excluded two public hospitals from the analysis. One psychiatric hospital in Bethlehem (180 beds) does not meet the homogeneity assumption of DEA method. Another newly established hospital in 2014 (37 beds) was also excluded because efficiency judgment of a new hospital could be biased in the early stages of managerial experience. We obtained ethical approval from the Palestinian Ministry of Health (PMoH) to carry out the research.

The investigated hospitals (1377 beds) are owned and administered by the Palestinian Ministry of Health. They are general hospitals and their resources are assigned from the ministry based on requests from their managers. Their patients are coved by a governmental insurance scheme by which patients are entitled to public hospitals. Then, patients are treated within the public hospital under two conditions; the availability of the required clinical services and the availability of unoccupied hospital bed, otherwise, the patient is transferred to other provider and financially covered by the applied insurance scheme. Hospital managers are asked to manage the given demand while managing the hospitals’ resources accordingly.

Public hospitals in WB are geographically distributed across ten governorates (see Table 2); one public hospital serves one governate. Hebron and Nablus are two exceptions where two hospitals serve in each governorate. Data on four input measures and three output measures have been extracted from the Annual Statistical Healthcare Reports published by the PMoH. Table 4 illustrates the year-specific means and standard deviations of the included input-output measures.

We employ two milestones DEA models, namely the CCR [23] and the BCC [62]. The letters in “CCR” and “BCC” stand for the initials of the developers’ last names. These two models have become standards in the literature of performance measurement under the assumptions of constant and variable returns to scale respectively [63]. Because public hospitals serve the public demand as given and must manage their resources accordingly, therefore, they target input minimizing rather than output maximization which recommends using the input-oriented DEA models [35, 64‐66]. We address the potential input savings and constructs input-oriented frontiers guided by the space of managers’ control.

First, we applied a DEA-CCR model which assumes a Constant Returns to Scale (CRS) within hospital operations and doesn’t account for the scale effects; then, we applied the DEA-BCC model which was developed in 1984 to satisfy scale effects in efficiency analysis. The mathematical formulation CCR dual linear programming model to estimate relative efficiencies of 11 hospitals is written as the following linear problem:

Subject to,

Where:

θ_o = the efficiency score of hospital “0” under evaluation.

x_ip = the quantity of input “i” utilized by the “p^th” hospital.

y_rp = the quantity of output “r” produced by the “p^th” hospital.

λ = weights obtained from the dual version of the linear programming.

The radial distance to frontier provides a technical efficiency measure for hospitals under assessment. The DEA-BCC input-oriented model requires an additional set of convexity constraint for the dual linear programming algorithm (Eq. 1), the sum of lambdas to be one and written as Eq. 2:

The sum of lambdas yielded from the CCR model provides information whether the hospital is operating under increasing or decreasing returns to scale [67, 68]. While the CCR efficient hospitals are operating at the most productive scale size and the sum of lambdas is one, the inefficient hospitals are operating under Decreasing Returns to Scale (DRS) when ∑λ > 1 and may benefit from economies of scale. Other inefficient hospitals are operating under Increasing Returns to Scale (IRS) when ∑λ < 1 and may suffer diseconomies of scale that may explain a state of weak control among large hospitals.

Since the BCC model always envelops the data more closely than the CCR model (input-oriented frontiers). Inefficient hospitals measure the shorter distance to the BCC frontier than the CCR frontier [69]. The analysis of the two models distinguishes three types of efficiencies that help managers to capture the components of inefficient operations [70, 71]. They are global technical efficiency (TE) as given by CCR score, pure technical efficiency (PTE) as given by the BCC score, and scale efficiency (SE) reflects the portion of inefficiency attributed to the given scale of operations (Eq. 3):

Reproducing the graph of Banker et al., [62], Fig. 2 illustrates the application of the CCR and BCC scores regarding the three components of efficiency related to the proposed production possibility set for the input-output mix (X, Y). Group of Hospitals “H1 to H6 and Hx” were used for demonstration purpose. The inefficiency component of hospital Hx as given by the ratio AB/AD is attributed to the scale of its operations. Moreover, it is distinguished from the pure technical inefficiency as given by the ratio AC/AD.

Because it is important to have a sufficient number of observations we employed the DEA framework presented by Boussofiane et al. [71]. The method allows us to capture the actual variations of each hospital through simultaneous estimation of efficiency of all the 66 observations (N = 66). This method strengthens the discriminatory power of DEA as sufficient number of DMUs are analyzed [34].

DEA is a relative measurement method, a change in the efficiency score in the following year of the tested hospital does not necessarily mean a change in its performance only; changes in the performance of the others may influence the relative position of that hospital. If we carry out an independent analysis for each year, we cannot certainly attribute the changes in the efficiency score of a focal hospital to actual performance change of that hospital. But, simultaneous inclusion of 66 observations in the model allows for addressing the variations of a hospital across two successive years with certainty [72].

Contextual factors which could influence the efficiency of a hospital (e.g., government regulations, geopolitical context, ..) are not under the control of the manager and can be accommodated in a DEA analysis [73]. The impact of environment on production was first considered by Charnes et al. [74]. The authors disentangled program efficiency from management efficiency by reference to empirical observations obtained from school programs.

Fried et al. [75] reviewed previous approaches to incorporating the external operating environment into a non-parametric measure of technical efficiency. Three categories classified by the applied method in the DEA literature are:

Despite a large number of useful applications of the two-stage DEA method [29, 45, 80], it has been criticized and different examinations of the statistical consistency of the method provided contrast conclusions that call for further testing [15]. Banker & Natarajan [14] show by simulation that the two-DEA estimator for the contextual variables is statistically consistent when OLS or Maximum Likelihood Estimator (MLE) is applied in the second stage. This method requires the contextual factors to be independent of the input variables, but the contextual factors may be correlated with each other. Hoff [28] concluded that Tobit regression is sufficient to represent the second stage DEA models when compared with alternative methods or with the OLS. McDonald [27] came to a similar conclusion as Hoff, but he advocated not using Tobit regression.

Kieschnick & McCullough [81] recommended using parametric regression rather than using quasi-MLE unless the sample size is large enough to justify the argument underlying the quasi-MLE. Simar & Wilson [82] had sharply criticized the two-DEA method for lack of a coherent data generating process (DGP) and for the bias and serial correlation of the DEA efficiency estimates. They argue that the conventional methods of statistical inference are invalid in the second stage regression. Then, the authors propose the use of a bootstrap method to correct for the small sample bias and serial correlation of the DEA efficiency estimates. Later, Daraio, et al. [83] tested the assumptions required for two-stage estimation and rejected them in the non-parametric setting.

We follow Banker & Natarajan [14] and regress the DEA-CCR estimates of 66 observations during 2010–2015 on ten potential contextual factors. We run Tobit regression models to identify which environmental factors have a significant influence on the productive efficiency of Palestinian hospitals. The regression model has a censored structure because the dependent variable yielded from DEA-CCR model is limited between zero and one, while the independent variables that correspond to one can be observed. Then, Tobit regression which takes the censored structure into account is suggested. The model supposes that there is a latent dependent variable Y_p^*, this unobserved variable linearly depends on the independent variables X_p via a set of parameters βs. There is a normally distributed error term ε_p to capture random influences on the relation. The observed value of the dependent variable Yp (Eq. 4) is defined to equal the “latent variable” whenever the latent variable is above zero, and to equal “zero” otherwise, where:

The CCR-DEA scores are right censored data, following the literature, the efficiency scores are transformed to become left-censored data of inefficiency scores the used Eq. 5 as suggested by Jon A Chilingerian [29, 33, 40]:

To estimate the regression coefficients (βs), we applied the Maximum Likelihood Estimation (MLE) method in Tobit regression [45, 84]. Regression coefficients are interpreted in the same manner as the ordinary least-squares OLS regression. The only difference is the interpretation of the factor signs. Specifically, negative sign means better efficiency and positive sign means more inefficiency [33]. The initially estimated general model (Eq. 6) included all the proposed predictors:

We tested six Tobit regression models and selected the model with the highest value of the Log Likelihood (55.47 in model 6) to interpret our results (Table 5).

We analyzed the efficiency 11 public hospitals operating in West Bank from 2010 to 2015. They utilize 1377 beds which make up 97.4% of the total public hospital beds in West Bank. It is worth noting the uneven spread of care providers across the governorates. (1) The distribution of public hospital beds per 10,000 citizens varies largely between seven beds and 27 beds. (2) The distribution of the primary healthcare centers per 10,000 citizens varies across governorates from 1.84 centers to 4.08 centers (3) The percentage of public hospital beds to the overall beds vary across governorates from 22 to 100% (see Table 2). The uneven distribution of providers is a remnant of previous political regimes in which the public sector evolved in West Bank [4]. Surprisingly, hospital P11 in Hebron governorate works at 120.4% occupancy rate. This hospital may show efficient scores, but it is reasonable to question the quality of care provided.

Figure 3 illustrates year-specific variations in means of the outputs produced during the study period. Since the year 2012, there is a consistent increase in emergency services that contributed significantly to the variations in the provided hospital services. However, input levels had slightly increased during the study periods, growth in the average number of health FTEs (e.g., nurses, laboratory technicians, radiology technicians) is noticed in Fig. 4.

To make results more tangible for inefficient hospitals, we started analyzing the year 2015 to shape opportunities for potential improvements. Table 6 summarizes the individual efficiency scores for 11 hospitals in 2015. As estimated by the CCR model, under the Constant Returns to Scale (CRS) frontier, average efficiency was 0.86; scores ranged from 67 to 100%. As a result, the Palestinian public hospitals have the potential to reduce 14% of their inputs while producing the same levels of services.

Three efficient hospitals P01, P04, and P011 constructed the best practices CCR frontier. These hospitals were efficient in the overall sense in both pure technical and scale efficiency. Hence, hospitals P01, P04, and P011 are operating under CRS. As for the other inefficient hospitals (Table 6), the sum of the optimal lambdas of the CCR model classifies each hospital as either operating under Increasing Returns to Scale (IRS) or Decreasing Returns to Scale (DRS). If Σλ > 1, then DRS prevail and if Σλ < 1, then IRS prevail [67, 68].

As estimated by the DEA-BCC model, under variable returns to scale approach, five hospitals P01, P02, P04, P10, and P11were pure technically efficient. The others, P03, P05, P06, P07, P08, and P09 suffer pure technical inefficiency and can individually reduce their inputs by (1- BCC score) without reducing the levels of the provided outputs. Hospital P06 is scale efficient, and its inefficient performance is attributed to technical inefficiency as illustrated by the BCC score 85% implying a potential savings of 15% of inputs producing the same level of outputs.

Scale efficiency measures show hospitals P01, P04, and P11 as efficient and working under constant returns to scale. Four hospitals P02, P03, P05, and P07 were operating under increasing returns to scale. Their average scale efficiency is 82.2% and could theoretically increase their size by 17.3% to achieve optimal scale. Hospitals P08, P09, and P10 were operating under decreasing returns to scale implying that their service outputs increase by a smaller proportion compared to an increase in inputs. Their average scale efficiency is 91.4% and appears to be higher than the average for increasing returns to scale hospitals. Thus the effect on scale efficiency due to the size of the hospital is stronger on small hospitals than on large ones. Managers of large hospitals P08, P09, and P10 are weakly controlling their service operations. Better adaptation to new technologies will help them improve their scale efficiency [41, 85].

Table 7 summarizes year-specific efficiency estimated by the DEA-CCR and the DEA-BCC frontiers of 66 observations. During the whole study period, the average CCR efficiency score was 85.29% in the overall sense of technical efficiency. To become efficient, the public hospitals in Palestine could save 15% of their resources to produce the given level of the observed outputs. The average pure technical efficiency as given by the BCC e scores was 93.7%, managerial practices could enhance performance by 6.3%. The average scale efficiency was 91%, resource allocation can enhance scale efficiency. Savings will have a significant impact on hospital operations and on reducing the volume of purchased hospital services and save public money.

During 2011, hospitals show the best performance level as given by average pure technical efficiency of 90.5% (see Fig. 5). The years 2010 and 2014 show relatively poor performance as given by the average efficiencies of 81.8 and 81.6% respectively. Hospitals, in the general sense, gave the idea as improving their performance during the study period. More specifically, there was 4% increase in the average efficiency scores in 2015 compared with 2010.

We included the 66 observations from the years 2010 to 2015 in simultaneous CCR estimates (see Additional files 1 and 2). The resulting cross-sectional data is right-censored then transformed to left censored inefficiency scores. Then, we regressed the inefficiency scores on the proposed contextual factors in Table 3. To get more robust results, we tested six Tobit models using Stata 14 to examine the significance and to estimate the parameters. We started with four predictors to get a significant overall model, then included additional predictor in each model, model 6 showed four significant predictors. We run robust standard error procedure to avoid the heteroscedasticity; Table 5 presents the results of Tobit regressions.

The joint null hypothesis as H₀: β1 = β2 = β3 = β4 = β5 = β6 = β7 = β8 = β9 = β10 = 0 is rejected at the 1% level of significance when given at least one non-zero parameter in all the models. The final empirical regression model (Table 5) including the significant predictors at 10% significance level was (model 6):

When decomposing the overall efficiency into pure technical and scale efficiency components, it is worth noting five findings:

Four predictors were significant in explaining hospital inefficiency, they are: (1) the bed occupancy rate (BOR) at 1% significance level p <  0.01. (2) the outpatient visits to inpatient days ratio (OPIPR) at 1% significance level p <  0.01. (3) the hospital size (SIZE) at 10% significance level p <  0.1. (4) and the available number of primary healthcare per 10,000 citizens (PRC) living in the served governorate at 1% significance level p <  0.01.

The coefficients of BOR and OPIPR are negative implying that increasing these predictors by one unit will lead a decrease in the predicted hospital inefficiency by 0.0129 and by 0.197 respectively, holding all other variables in the model constant. The higher the hospital BOR or OPIPR, the lower the predicted inefficiency score with a substantial effect of OPIPR, a change of one unit in OPIPR will decrease inefficiency level by 19.7%. Our result was expected and goes consistently with the previous evidence [40, 42].

The coefficient of SIZE was positive implying that inefficiency and SIZE change in the same direction. Results indicate that predicted inefficiency for large hospitals is 0.0745 higher than for small hospital keeping all other predictors constant. As hospital capacity increases for more than 130 beds, hospital inefficiency is more likely to increase. Our results are inconsistent with previous evidence from Turkey [86].

The coefficient of PRC was positive implying that increasing the number of available primary centers per 10,000 by one unit in a governorate will lead an increase in the predicted inefficiency score by 1.327. The more available primary healthcare centers in the served region, the less efficient the hospital working there. This result may be explained as the more primary healthcare centers; healthcare seekers have more flexibility in choosing a provider and become less likely to go to a public hospital [87].