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

RESEARCH ARTICLE Open Access Measuring the efficiency of Palestinian public hospitals during 2010–2015: an application of a two-stage DEA method Wasim I. M. Sultan 1,2* and José Crispim 1 Abstract Background: While health needs and expenditure in the Occupied Palestinian Territories (OPT) are growing, the international donations are declining and the economic situation is worsening. The purpose of this paper is twofold, to evaluate the productive efficiency of public hospitals in West Bank and to study contextual factors contributing to efficiency differences. Methods: This study examined technical efficiency among 11 public hospitals in West Bank from 2010 through 2015 targeting a total of 66 observations. Nationally representative data were extracted from the official annual health reports. We applied input-oriented Data Envelopment Analysis (DEA) models to estimate efficiency scores. To elaborate further on performance, we used Tobit regression to identify contextual factors whose impact on inefficient performance is statistically significant. Results: Despite the increase in efficiency mean scores by 4% from 2010 to 2015, findings show potential savings of 14.5% of resource consumption without reducing the volume of the provided services. The significant Tobit model showed four predictors explaining the inefficient performance of a hospital (p< 0.01) are: bed occupancy rate (BOR); the outpatient-inpatient ratio (OPIPR); hospital’s size (SIZE); and the availability of primary healthcare centers within the hospital’s catchment area (PRC). There is a strong effect of OPIPR on efficiency differences between hospitals: A one unit increase in OPIPR will lead a decrease of 19.7% in the predicted inefficiency level holding all other factors constant. Conclusion: To date, no previous studies have examined the efficiency of public hospitals in the OPT. Our work identified their efficiency levels for potential improvements and the determinants of efficient performance. Based on the measurement of efficiency, the generated information may guide hospitals’managers, policymakers, and international donors improving the performance of the main national healthcare provider. The scope of this study is limited to public hospitals in West Bank. For a better understanding of the Palestinian market, further research on private hospitals and hospitals in Gaza Strip will be useful. Keywords: Public hospitals, Efficiency, 2-DEA, Tobit regression, West Bank Background The healthcare system in the Occupied Palestinian Territories (OPT) is influenced by the ambiguous political environment within which it is enacting [1]. The OPT (West Bank, East Jerusalem, and Gaza Strip) is a country in chronic conflict and economic emergency [2]. The never-ending conflict between the Palestinians and the Israelis seemed to come to an end when the Middle East peace process was settled, particularly, after the Madrid conference in 1991, then the Oslo Accords in 1993 and the establishment of the Palestinian Authority (PA) in 1994. Henceforth, building the capacity of the Palestinian public healthcare sector evolved [3], and had undergone several reforms. Reforms were heavily subsidized by international donations [4], as efforts made by the international community to resolve the conflict in Palestine-Israel through economic encouragements [5]. Despite the noticeable progress in rebuilding the institutions of the yet to be “The State of Palestine,”ground * Correspondence: [email protected] 1 School of Economics and Management, University of Minho, 4710-057 Braga, Portugal 2 P.O. Box 198, Hebron, Palestine © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Sultan and Crispim BMC Health Services Research (2018) 18:381 https://doi.org/10.1186/s12913-018-3228-1 reality suggests otherwise. The situation is remaining complicated and problematic as witnessed by more isolation and more restrictions on movement between West Bank (WB) and Gaza Strip (GS) and between cities within WB. The Palestinians are not allowed to travel freely between the OPT regions [1]. To date, the Israelis control over water, electricity, borders, and transport amongst other infrastructural matters, while, the Palestinians have limited control over their own affairs. This unique context has implications on the priority settings and the process of health policy implementation [6]. Therefore, in practice, the integration of health policies and health delivery operations is not just a matter of combining the two. The Palestinian Ministry of Health is the leading healthcare provider including hospital care and bears the most substantial burden to meet the constant growth in the demand for healthcare services. On average, health expenditure recorded consistent annual growth rate of 7%. The total health expenditure increased from $400 million in the year 2000 to $1400 million in the year 2015; the latter accounted for 10.7% of the country’sGrossDomestic Product (GDP). The public reimbursement schemes represent 62.5% of the total health expenditures [7]. Hospitals, with 6006 beds, are the main healthcare providers to serve 4.48 million people living in WB and GS. Forty-two percent of the total expenditure is spent on hospital care (i.e., 4.5% of the country’s GDP) [8]. Because hospitals make up a large portion of healthcare expenditure, hospitals are a potentially large source of cost savings. Therefore, the analysis of this study was intended to capture potential gains in the efficiency of public hospitals that may have a substantial contribution to large potential cost-savings of the country’s healthcare expenditure [9–11]. Moreover, the applied governmental health insurance scheme covers most of the Palestinians, by which they are entitled to public services, had increased the burden on public hospitals. Therefore, public hospitals (61.1% of all the hospital beds) are crowded and functioning at high bed occupancy rates or even over occupied [2]. To cater to the increasing health demand on healthcare services, the Palestinian Ministry of Health (PMoH) allocates about 40% of its budget to purchase hospital services from other referral hospitals within the country or abroad such as hospitals in Jordan [12]. Recently, the World Health Organization (WHO) report indicated that the decline in donors’support and the unique political situation of the Palestinians have serious effects on the scope and quality of health conditions [13]. The purpose of this work is twofold, analyzing the efficiency of the public hospitals in West Bank; and evaluating the environmental factors affecting their productivity. Keeping in mind that the hospital technical efficiency requires the use of minimum input to produce a given level of output [10] and that the ability of a hospital to transform inputs into outputs is influenced by its managerial efficiency as well as the external operating environment [14,15]. The scope of our work is limited to public hospitals in West Bank. Hospitals in Gaza Strip are excluded in this work due to many limitations: (1) The geographical separation between West Bank and Gaza, the Palestinians are not allowed to travel across them; (2) The 2008 and 2014 wars against Gaza makes the context of hospital operations incomparable; (3) The Palestinian internal conflict since 2006 escalated with the split of Palestinian Authority into one government in WB and another in GS, hence, the operational data of hospitals in GS is unreliable. Therefore, the main scope of this papers is to examine the technical efficiency of 11 public hospitals out of 13 public hospitals working in West Bank during 2010–2015 (i.e., 66 observations). We conducted secondary research to find studies evaluating the performance of healthcare providers in Palestine; to date, there are no previous studies concerning the topic. The existing relevant literature describes the transitional context and the complications within the country’s healthcare system in Palestine [2–4,6,16–19]. Hence, improving performance among the Palestinian public hospitals by performance measurement is a straightforward need. The generated information will provide valuable insights to hospital managers who make operational decisions and to policymakers and international donors who may influence the external operating environment by regulations, subsidies or by other policy measures. Data Envelopment Analysis (DEA) is a universal methodology in healthcare evaluation and widely used non-parametric methodology to evaluate performance [20–22]. Since the advent of DEA by Charnes et al. [23], more than 10 thousand studies had been published which estimated the performance of different kinds of entities and production activities including the healthcare sector [24]. Recent DEA studies extend the analysis to investigate variations in hospital performance over years and to identify contextual drivers of efficient practices [25]. Due to the lack of data in developing countries, few empirical works applied the data-based methodology of DEA models [26]. To date, no studies have examined the performance of public hospitals in Palestine for potential improvements. Therefore, this work addresses a DEA literature gap by analyzing the efficiency of the public hospitals and identifying contextual drivers of inefficient performance in a developing country, namely, Palestine. In response to this need, our endeavor goes to achieve the following research objectives: (1) evaluate how Palestinian public hospitals utilize resources while caring for their patients from 2010 to 2015; and (2) explore environmental effects associated with the efficient use of hospital resources. Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 2 of 17 We apply two-stage data envelopment analysis (2-DEA) where the efficient frontier and the hospital level efficiency score are estimated with DEA model in the first stage, and the efficiency estimates are regressed on contextual factors in the second stage [15,27]. In stage 1, we calculate the efficiency with which physical inputs produce output. In stage 2, we apply Tobit regression which is commonly used to relate efficiency scores to factors expected to influence efficiency while these factors are not under the control of hospital managers [14,28,29]. Empirical context The whole area of the OPTs is 6170 km 2 of which 5800 km 2 is the area of WB, and 365 km 2 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 2illustrates the sample characteristics and relevant market attributes during 2015. Production model and variables 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 1shows 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 Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 3 of 17 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 Table 1 Distribution of hospital beds and primary healthcare centers in OPTs in 2016 Hospitalization Type of hospitalization Regions Public a Others b By region Hospital beds General WB 1414 (32.2%) 1222 (28%) 2636 (60.2%) GS 1328 (30.2%) 421 (9.6%) 1749 (39.8%) 4385 (73%) Specialized WB 180 (15.7%) 437 (38.2%) 617 (53.9%) GS 293 (25.6%) 234 (20.5%) 527 (46.1%) 1144 (19%) Rehabilitation WB 0.0 141 (76.2%) 141 (76.2%) GS 0.0 44 (23.8%) 44 (23.8%) 185 (3.1%) Maternity WB 0.0 213 (72.9%) 213 (72.9%) GS 43 (14.7%) 36 (12.4%) 79 (27.1%) 292 (4.9%) Total by region WB 1594 (44.2%) 2013 (55.8%) 3607 (60%) GS 1664 (69.4%) 735 (30.6%) 2399 (40%) Total beds 3258 (54.3%) 2748 (45.7%) 6006 (100%) 6006 (100%) Public Primary Care Centers (PHCs) WB 422 (69.4%) 186 (30.6%) 608 (80.0%) GS 49 (32.2%) 103 (67.8%) 152 (20.0%) Total PHC 471 (62.0%) 289 (38.0%) 760 (100%) Public a , hospitals or PHCs are owned and administered by the Palestinian Ministry of Health Others b , hospitals or PHCs are not owned nor administered by the Palestinian Ministry of Health Table 2 Selected characteristics of the operating public hospitals in West Bank (2015) Governorate Market characteristics Public hospital characteristics PHC/10000 Beds/10000 % public beds Public hospitals Beds Occupancy rate Hosp. Hebron 2.22 9.0 48.9 Abu al Hasan 36 101.3 P01 Salfit 4.08 7.1 100.0 Yasser Arafat 50 71.9 P02 Jericho 3.85 10.4 56.4 Jericho 54 71.7 P03 Nablus 1.84 16.9 40.8 Watani 55 86.0 P04 Qalqilya 3.51 10.9 47.9 D. Nazal 58 95.0 P05 Tulkarm 2.36 9.3 69.1 Thabit Thabit 117 71.5 P06 Bethlehem 2.04 27.3 22.2 Al Hussein 131 79.4 P07 Jenin 2.09 7.1 73.8 Khaleel S. 163 90.1 P08 Nablus 1.84 16.9 40.8 Rafedia 200 87.6 P09 Ramallah 2.18 12.2 56.1 Med. Complex 238 97.6 P10 Hebron 2.22 9.0 48.9 Alia 275 120.4 P11 Tubas –5.7 –The Turkish 37 63.1 P12 a PHC Primary Health Care Centers a Hospital P12 is excluded, available data is limited to 2014 and 2015 Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 4 of 17 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 Fig. 1 Conceptual production structure of hospitals Table 3 Potential contextual factors Variable Definition Measurement Mean a SD BOR Bed occupancy rate The proportion of occupied beds in a year = Inpatient days / (number of beds a 365). 83.1% 1.65% OPIPR Outpatient –inpatient ratio Total outpatient visits divided by total inpatient days. 1.23 0.06 ALOS The average length of stay Total inpatient days divided by the number of admissions. 2.18 0.05 ADHR The ratio of administrative to health employees. The number of administrative FTEs divided by the total health FTEs including doctors in each observed hospital. 0.36 0.01 SIZE Hospital size (dummy) (1) For large hospitals > 130 beds, (0) otherwise. 0.36 0.06 LOC Hospital location (dummy) (1) for North Governorate and (0) for South Governorate. 0.6 0.06 REFP The proportion of refugees living in the governorate. The percentage of refugees living in camps of all the governate population where the observed hospital operates. 8% 0.8% HPFP Number of hospital beds per 10,000 inhabitants The number of all the available hospital beds per 10,000 in the governorate where the public hospital operates. 12 0.711 PRC The available primary care centers per 10,000 inhabitants The number of primary centers per 10,000 inhabitants in the governorate where the public hospital operates. 2.7 0.1 PPHB The percentage of public hospital beds. The percentage of the available public hospital beds in a governorate to the total available number of beds. 59.3% 2.8% a Mean and SD Values used six-year data of the predictors from 2010 to 2015 Data Source: Palestinian annual health reports 2010–2015 Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 5 of 17 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 3displays the ten proposed environmental factors. Two-stage data envelopment analysis (2-DEA) 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’sideas,Charnesetal.[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. Methods This work addresses the productive efficiency of the Palestinian public hospitals from 2010 to 2015. We extracted the relevant operational data from the published Annual Health Reports by the Palestinian Ministry of Health (PMoH). To achieve our research objectives, we organized the analysis around two key steps: (1) Using a six-year data of the Palestinian public hospitals, we employ the basic DEA-CCR and the DEA-BCC models to analyze the overall efficiency, pure technical efficiency and scale efficiency; (2) we regress the DEA-CCR scores of 66 observations of the first step on ten potential contextual factors. We apply Tobit regression to find the factors whose impact on efficiency is statistically significant. Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 6 of 17 Sample and data 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 4illustrates the year-specific means and standard deviations of the included input-output measures. Estimation of productive efficiency 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: θ o¼Minθoð1Þ Subject to, Xp¼11 p¼01λpxip ≤θxio i¼1;2;3;4 Xp¼11 p¼01λpyrp ≥yro r¼1;2;3 λp≥0p¼1;2::; 11 Where: θ o = the efficiency score of hospital “0”under evaluation. Table 4 Distribution of input-output measures, means and standard deviations, N=11 Year Input measures Output measures Hospital beds (X1) Doctors FTEs (X2) Health FTEs (X3) Administrative FTEs (X4) Inpatient days (Y1) Outpatient visits (Y2) Emergency care (Y3) 2010 107 55 164 74 32,152 38,111 56,082 (20) (8) (28) (9) (6667) (7702) (7452) 2011 106 46 170 75 32,101 35,085 56,872 (19) (8) (29) (9) (6728) (7491) (7915) 2012 111 47 174 75 36,015 41,305 65,094 (21) (7) (29) (8) (7914) (8430) (9461) 2013 119 44 179 75 37,719 40,983 66,301 (23) (6) (27) (7) (8678) (8117) (11292) 2014 123 46 195 77 39,908 41,737 69,016 (25) (6) (32) (8) (9837) (8652) (11284) 2015 125 49 194 74 42,692 46,017 68,425 (25) (7) (32) (8) (10588) (8994) (10272) FTEs Full-Time Employees. Health FTEs, medical personnel other than doctors, such as nurses, laboratory technicians, and radiology technicians Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 7 of 17 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: Xp¼11 p¼01λp¼1:0ð2Þ 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): CCRscore ¼BCCscore Scale efficiency TE ¼PTE SE ð3Þ Reproducing the graph of Banker et al., [62], Fig. 2illustrates 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]. Fig. 2 Illustration of SE derived from the CCR scores and the BCC scores. Reproduced from Banker et al. [62] Sultan and Crispim BMC Health Services Research (2018) 18:381 Page 8 of 17 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]. Evaluating the impact of contextual factors on efficiency 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: (1) The frontier separation approach: can be implemented only for categorical factors and requires a priori selection of the most important contextual factor [74]. (2) The all-in-one approach: Single-stage DEA estimation of the effects of contextual factors had been developed by Banker & Morey [76]. The procedure includes the external operating environment variables directly in the linear programming problem along with the traditional inputs and outputs. However, this approach requires that the external variable is classified as an input or an output in advance. Camanho et al. [77] propose a model that distinguishes between the influence of internal nondiscretionary factors and external nondiscretionary factors to estimate inefficiency. (3) The two-stage approach: The typical two-stage approach follows a first stage DEA estimation of efficiency based on inputs and outputs, then a second stage regression analysis seeking to explain variation in first stage efficiency scores concerning environmental factors. Some studies apply Ordinary Least Squares (OLS) regression to estimate the significant influence of contextual factors in the second stage; others use a Tobit regression model [78]. Ray [31,79] was the first to apply the twostage DEA model where the estimated efficiency scores in the first stage are regressed on contextual variables in the second stage. 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]andregressthe 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. 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