Analyzing the Efficiency of Moroccan Hospital Network Regions via DEA and Tobit Regression: Assessing DEAP 2.1 Software versus Generative AI ChatGPT 3.5

doi:10.21203/rs.3.rs-4369365/v1

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Analyzing the Efficiency of Moroccan Hospital Network Regions via DEA and Tobit Regression: Assessing DEAP 2.1 Software versus Generative AI ChatGPT 3.5

https://doi.org/10.21203/rs.3.rs-4369365/v1

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This study aims to assess the technical efficiency of hospital networks in each health directorate region in Morocco and analyze the impact of staff personnel health on inefficiency. The study uses Data Envelopment Analysis Programming (DEAP) software version 2.1 and generative Artificial Intelligent ChatGPT 3.5 to analyze 12 hospital network health directorate regions. Tobit regression was employed to analyze the impact of worker health and hospital activity on inefficiency. Results showed that the average technical efficiency was more inefficient in generative AI ChatGPT 3.5 than in DEAP software version 2.1. Hospital activity and nurse staffing significantly impacted inefficiency levels. The study concludes that inefficiency in hospital networks and staff personnel health pose challenges for managers in health directorate regions, emphasizing the need for New Public Management principles based on contractualization, accountability, and managerial practices.

Hospital network

Data Envelopment Analysis

Tobit regression

DEAP software

ChatGPT 3.5

Morocco and health directorate region

1.1 Background

Hospitals play a crucial role in achieving Sustainable Development Goals (SDG) 3, "Good Health and Well-Being," by providing essential healthcare services across various domains, including communicable diseases, non-communicable diseases, mental health, maternal, newborn, and child health, as well as contributing to the realisation of universal health coverage (UHC). They ensure access to skilled healthcare professionals and necessary medical interventions (UN, 2020; WHO, 2019, 2023).

Optimising hospital establishment efficiency, particularly in staffing and resource utilisation, is critical for achieving SDG 3 objectives such as quality healthcare services, universal health coverage, and individual well-being. Especially in countries with medium and low incomes, such as African nations, there is a notable lack of financing, disparities in access to healthcare, prolonged waiting times, inadequate patient care and healthcare services in hospitals, and a delay in using generative artificial intelligence (GAI) such as ChatGPT (Er-Rays & M’dioud, 2024).

Morocco, like African countries, consumes a significant health budget for hospital network (HN), approximately 60%. Thus, monitoring the technical efficiency of hospitals is crucial for several reasons, including maximise patient care, minimise costs, enhance staff satisfaction, adapt to changing demands, and make data-driven decisions to improve health outcomes and achieve SDG 3 targets. Efficient management of medical and nursing staff ensures timely and high-quality care; predicting failures leads to avoiding or mitigating human, economic, and material losses; reducing wait times; improving patient outcomes; and improving health management quality (En-Naaoui et al., 2024). This contributes to SDG 3 by promoting good health and well-being.

Key indicators linked to the SDG 2030 in Morocco, focusing on three main areas: good health and well-being, no poverty, and sero hunger (WB, 2023). In terms of good health and well-being, Morocco has made significant progress. The maternal mortality ratio, a crucial indicator of maternal health, stands at 72 per 100,000 live births as of 2020, reflecting improvements in maternal care and healthcare access. Additionally, the under-5 mortality rate, both overall and disaggregated by gender, has declined to 18 per 1,000 live births as of 2021, indicating advancements in child health and survival. Although relatively low at 26 births per 1,000 women aged 15–19 in 2021, the adolescent fertility rate indicates the need for ongoing efforts to ensure adolescents have access to reproductive healthcare and education (WB, 2023).

In terms of poverty, Morocco shows promising trends. The poverty headcount ratio at $2.15 a day, an important measure of extreme poverty, stood at 1.4% of the population in 2013, indicating a relatively low incidence of extreme poverty. Similarly, the poverty headcount ratio at the national poverty line was 4.8% in 2013, reflecting a relatively low overall poverty rate in the country. These figures suggest that Morocco has made strides in poverty reduction efforts, although continued efforts are necessary to address the remaining pockets of poverty and inequality (WB, 2023).

Morocco faces challenges in the realm of sero hunger, but also shows progress. The prevalence of stunting, which reflects chronic malnutrition in children under 5, remained at 14.2% in 2019, indicating that a significant portion of children experience growth faltering (WB, 2023). However, efforts to combat undernourishment have shown promise, with only 6% of the population experiencing it as of 2021. Moreover, the prevalence of stunting, disaggregated by gender, shows relatively balanced rates among male and female children. These findings underscore the importance of continued investments in nutrition programmes and food security initiatives to ensure all Moroccans have access to adequate nutrition and achieve optimal health outcomes.

1.2 Up to day

Measuring the performance of healthcare systems requires the development of a conceptual framework to model system components and identify key performance indicators (Smith, Mossialos, Papanicolas, & Leatherman, 2012). This process assists stakeholders in pinpointing the information required for effective evaluation and streamlines the selection of appropriate performance metrics (Vrijens et al., 2014).

In the late 1970s, William W. Cooper, Lawrence M. Seiford (Cooper et al., 2004), and Kaoru Tone developed Data Envelopment Analysis (DEA), a non-parametric method, to measure the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs (Debreu, 1951) and (Koopmans, 1951).

It compares DMUs' performance to a hypothetical best-practice frontier, allowing for the assessment of relative efficiency without explicit assumptions about the underlying production process or functional form. Various fields such as economics, operations research, management science, and healthcare widely apply DEA (Cooper et al., 2000a, 2000b, 2011a, 2011b; Seiford, 1996).

Many studies show that hospitals in African countries have a low score on technical efficiency. The low levels of technical efficiency in hospitals exacerbate resource scarcity and hinder efforts to provide accessible, high-quality healthcare services in many countries (Africa WHO, 2023; Arhin et al., 2023; Babalola et al., 2022; Ibrahim et al., 2019; M. Kirigia Joses, 2015; Musoke et al., 2023). The studies conducted in Morocco (Er Rays & Ait-Lemqeddem, 2020; Er-Rays, 2021a; Er-Rays, Ait-Lemqaddem, et al., 2024; Er-Rays, M’dioud, & Ait-Lemqaddem, 2024; Er-Rays, M’dioud, Ait-Lemqeddem, et al., 2024; Er-Rays & Ait Lemqeddem, 2020b; Er-Rays & M’Dioud, 2024), Benin (Asbu et al., 2003), Ethiopia (Ali et al., 2017), Burkina Faso (Marschall & Flessa, 2009), Botswana (Tlotlego et al., 2010), and Eritrea (J. M. Kirigia & Asbu, 2013). Additionally, research has been carried out in specific regions such as KwaSulu-Natal Province, South Africa (Babalola et al., 2022); Ghana (Vukey et al., 2023); northwestern Ethiopia (Lamesgen et al., 2022); and Uganda (Mujasi et al., 2016), Egypt (Habib & Shahwan, 2020).

For example, Asbu et al. conducted a study to assess the changes in productivity of sone hospitals in Benin over five years, using the Malmquist data envelopment analysis method. Through physical visits, they collected health inputs and utilisation data from the records of sampled hospitals (Asbu et al., 2003). Marschall et Flessa proposed a study to evaluate the relative efficiency of health centres in rural Burkina Faso and investigate reasons for inefficient performance. They used data envelope analysis (DEA) to account for the situation in that country and applied the Tobit model to identify the spatial effect of the catchment area on efficiency (Marschall & Flessa, 2009). Another study for Kirigia and Asbu (2013), whose used Tobit regression analysis to figure out how inefficient public secondary level community hospitals in Eritrea are in terms of technical and scale. They also figured out how much output and/or input reductions would have to happen for hospitals to become more efficient, and they found out how institutional and contextual/environmental variables affected hospital inefficiency (J. M. Kirigia & Asbu, 2013). As for Babalola and his colleagues used data from 38 public district hospitals in KwaSulu-Natal province from 2014/15 to 2016/17. They used both constant return to scale (CRS) and variable return to scale (VRS) models to determine the technical efficiency of the hospitals.

Among these studies is the use of data envelope analysis (DEA) as the primary method for assessing efficiency. DEA allows researchers to evaluate the relative efficiency of healthcare facilities by comparing their input-output relationships. Regarding input and output variables, there is variation among the studies based on the specific context and objectives. Inputs commonly include factors such as non-salary recurrent costs, salary costs, the number of beds, and health resources. Outputs typically consist of measures related to patient care, such as neonatal admissions, outpatient visits, referrals, bed occupancy rates, average length of stay, and bed turnover rates. The analysis's orientation also differs. Some studies adopt an output-oriented approach, focusing on maximising outputs given a set of inputs. Others may take an input-oriented approach, seeking to minimise inputs while maintaining a certain level of output. Additionally, some studies explore both technical and scale efficiency, while others focus on total factor productivity or assess changes in efficiency over time using methods like the Malmquist productivity index. Despite these differences, the common thread of utilising DEA for efficiency analysis, along with consideration of inputs, outputs, and analysis orientation, underscores the importance of this method in evaluating healthcare system performance across diverse contexts.

Generally, the majority of these studies concentrate on the first stage, assessing the efficacy of either hospital-provided curative care or primary healthcare settings' preventive care. However, there remains a notable gap in the research relating to the second stage of the analysis. This phase involves comprehensively evaluating hospitals while exploring the determinants of technical efficiency or inefficiency, often using panel data methodologies. Although this study focuses on the first and second stages of DEA analysis, it is critical to acknowledge the broader landscape of research in this area.

Each study in this area adapts its approach based on the available data and the researchers' perspectives regarding the selection of input and output variables. This customisation allows for a nuanced examination of hospital effectiveness, taking into account the unique characteristics and objectives of different studies.

Additionally, it is essential to recognise the critical link between the quality of patient care and population health outcomes. Improvements in patient safety and the efficiency of hospital healthcare delivery systems have contributed significantly to improvements in overall population health metrics. The observed increase in life expectancy and decrease in infant mortality rates demonstrate this positive impact, underscoring the interdependence between hospital system performance and broader public health outcomes.

1.3 Research Gaps

The study discusses the importance of understanding healthcare hospital system efficiency through various methodologies and analyses. However, gaps in research exist in Moroccan HN.

Moroccan HN suffers from many dysfunctional regional healthcare disparities. A minority of health directorate regions (HDR), including the administrative capital Rabat-Sale-Kénitra, the economic hub Casablanca-Settat, and the touristic Marrakech-Safi HDR, host the majority of healthcare hospitals. Despite the concentration of health care in these regions, the efficient use and distribution of resources remains elusive.

As far as we know, Morocco hasn't done any research that uses the Data Envelopment Analysis (DEA) method and its parts to look at the technical efficiency of hospital networks (HN) for each HDR, as estimated by DEAP Software version 2.1 and GAI ChatGPT 3.5.

1.4 The study's purpose

The goal of this study is to look into how well DEAP Software version 2.1 and GAI ChatGPT 3.5 can be used to make HNs more efficient in each HDR in Morocco. This will be done through scientific research in the areas of health economics, econometrics, accounting, and computer sciences. Additionally, it seeks to provide valuable insights and recommendations to academics and practitioners across various healthcare sectors, including hospitals.

1.5 Motivation

The objective of this analysis is to provide significant insights into the recent improvements and capabilities of HN efficiency, with a specific focus on its effectiveness in enhancing the operational efficiency of healthcare HNs. This study seeks to stimulate discovery and innovation in the realm of healthcare efficiency by providing researchers with current information about the possibilities of improving Moroccan hospital performance.

1.6 The study's contribution

This study contributes to exploring the integration GAI in monitoring of hospital efficiency and its potential applications in HN in each HDR in Morocco settings to improve efficiency. By examining existing literature, the research aims to identify gaps, challenges, and opportunities for leveraging technical efficiency to streamline workflows and improve HN outcomes and efficiency.

1.7 Brief country profile

Morocco, a country in North Africa and the Middle East, falls into the middle-income category, a lower segment. This economic position reflects both the challenges and opportunities the country faces. Despite its strategic geographical location and rich cultural heritage, Morocco faces obstacles such as unemployment, poverty, and socio-economic inequalities. However, the Moroccan government is implementing policies aimed at stimulating economic growth, diversifying productive sectors, and improving access to education and health services. These efforts aim to create an environment conducive to sustainable development and social inclusion in order to promote a more prosperous future for all Moroccan citisens.

Morocco's healthcare system has undergone several phases over the years, reflecting evolving priorities and challenges (Errami & Cargnello, 2016; Harfaoui et al., 2024).

From 1959 to 1980, the focus was on establishing the national health system, with infrastructure development, nationalisation of resources (Ministry of Health, 2013), and initiatives against epidemics being key. Notable milestones included the creation of medical faculties, vocational training schools, and delegating healthcare responsibilities to local authorities (Espace, 2015).

From 1981 to 1995, Morocco emphasised primary healthcare, extending services, strengthening basic health structures, developing health programmes, and adopting health promotion measures. Major restructuring efforts in 1994 laid the groundwork for hospital reform, including the creation of central directorates (Ministry of Health & WHO, 2016).

Between 1996 and 2010, Morocco embarked on significant healthcare reforms, focusing on regionalisation and financing. Morocco fostered partnerships to enhance regionalisation, hospital reform, and health insurance. We initiated major projects aimed at improving hospital management, care quality, and sector financing. Legislative changes, such as Law 65 − 00, facilitated the implementation of reforms, including the Basic Medical Coverage (BMC) reform (Er-Rays & Ait-Lemqeddem, 2021; Harfaoui et al., 2024; Hazimi, 2006; Ministry of Health, 2008; UNDP, 2016).

From 2011 to 2019, Morocco focused on developing the right to health in new constitution 2011 and further reforming the healthcare system. International commitments to SDG and programmes aimed at equitable access and quality improvement were prominent. The COVID-19 pandemic prompted mobilisation efforts and further healthcare system reforms (Constitution, 2017; La Loi Cadre N° 34 − 09 Relative Au Système de Santé Et À L’offre de Soins PDF | PDF, s. d.; IRES, 2022).

Morocco is undergoing a new phase of reform from 2020 to 2024, aiming for a more efficient and equitable healthcare system. Royal directives in 2020 called for a system overhaul, while legislative measures like Framework Law 09–21 (Official Bulletin No. 6975: Implementing Framework Law no. 09.21 on Social Protection (2021), 2021) and Reform 06.22 (Official Bulletin No. 7178: Promulgating Framework Law No. 06–22 Relating to the National Health System, 2023) facilitate social security coverage generalisation and system reorganisation.

In 2022, new reforms were implemented, including the reform aimed at improving the productivity of HNs for each region, namely: the National Health System, the creation of Territorial Health Groupings (Law No. 08–22 Relating to the Creation of Territorial Health Groups. (2023), 2023), the establishment of the Health Function (Law No. 09–22 Relating to Healthcare Employment. (2023), 2023), the creation of the Moroccan Agency for Medicines and Health Products (Law No. 10–22 Relating to the Creation of the Moroccan Agency for Medicines and Health Products, 2023), the creation of the Moroccan Blood Agency and its derivatives (Law No. 11–22 Relating to the Creation of the Moroccan Agency for Blood and Blood Products. (2023), 2023), the establishment of the High Authority for Health (Law No. 07.22 Establishing the High Authority for Health. (2023), 2023), and the complete revision of the responsibilities, functions, and organisation of the central administration. While the Ministry of Health and Social Protection reorganisation aims to improve system quality and efficiency, improvement of healthcare facilities, both hospitals and primary healthcare, generalisation of medical coverage, rehabilitation of healthcare provision, strengthening of the budget of the Ministry of Public Health and Health, digitisation of the healthcare system, consolidation of health programs and epidemiological surveillance, enhancement of access to medicines and healthcare products, and assessment of digital communication activities.

The funding, legal framework, and health segmentation determine the structure of the HN in Morocco.

Hospital funding is based on a combination of public resources from the state budget as well as private funding and health insurance.

With regard to the legal framework, health areas are defined by articles 17, 18, and 19 of Decree 2-14-562. They correspond to the regions' territories, as defined by the Kingdom's administrative division. Each health region consists of two or more health prefectures and provinces and is the field of intervention of the Regional Health Directorate under the Ministry of Health (Health Card - Situation of health care provision - Year 2022: Health care provision, 2022) (Er-Rays & Ait Lemqeddem, 2020b; Er-Rays & M’Dioud, 2024) .

In terms of hospital care, the HN's health facilities include different types of facilities, such as prefectural and provincial hospitals, regional hospitals, and interregional hospitals. Psychiatric hospitals include regional, oncology centres, hemodialysis centres, neighbourhood hospitals, day clinics, excellence centres, and reference centres. There are also specialised support structures for hospital facilities, such as the National and Regional Centre for Blood Transfusions and Haematology, the National Institute of Hygiene, the National Centre for Poisoning and Pharmacovigilance, and the National Centre for Radiation Protection (Health Card - Situation of health care provision - Year 2022: Health care provision, 2022).

In terms of public hospital infrastructure in 2022, there were 159 hospitals with 25,889 beds, 11 psychiatric hospitals with 1,512 beds, and 131 hemodialysis centres equipped with 2,739 dialysis devices (Health, 2022).

In analysing the production indicators of public hospitals in Morocco, several key metrics shed light on healthcare provision and resource utilisation (Table 4). With a total population of 37,140,944, the Ministry of Health and Social Protection's budget for 2022 stands at 23,542,550,000 Moroccan Dirham (DH), representing 7.14% of the total state budget. Despite this, the global budget, as a percentage of GDP, is 1.76%. Hospital capacity, both functional and existing, is significant, with 21,455 and 27,401 beds, respectively. Admissions totaled 1,043,904, with 4,289,970 hospitalisation days and 300,162 surgical interventions (Health, 2022). Outpatient consultations average 613 per physician, while caesarean section rates stand at 18%, with instrumental and non-instrumental low-path deliveries at 37.3% and 44.7%, respectively. The average occupancy rate is 60.8%, with a mean length of stay of 4.1 days and a turnover rate of 48.7%. Each physician performs an average of 154 surgical interventions (Health, 2022). These indicators collectively offer insight into the performance and efficiency of Morocco's public hospital system in delivering healthcare services to its population.

The organisation of this paper was as follows: the next section (Section 2) presents the method adopted to develop this model by presenting the DEA method and Tobit regression steps. Section 3 describes the results of testing these two stages in a Moroccan public HN. Section 4 provides a discussion of the results.

2.1 Study design

This study selected Moroccan HN for each HDR, which based on the administrative division's criteria. The HN includes local, provincial, regional, and academic facilities. The Ministry of Health, 2022, gathered data sets from a total of 12 hospitals within the network (Ministry of Health, 2022). The inputs include the number of hospitals in each HDR, as well as the number of doctors, specialist doctors, nurses, and midwives. The outputs consist of hospital activities, specialised consultations, public hospital laboratory activities, and surgical services (Tables 1).

Table 1

Justification of Inputs and Outputs variables
Variable		Justification
Inputs (Ministry of Health, 2022)
Hospital		The facility itself serves as a fundamental input to healthcare operations. Its physical infrastructure, equipment, and amenities significantly impact the delivery of care and overall efficiency. A well-equipped and maintained facility enhances the patient experience, facilitates smooth workflows, and supports healthcare staff in delivering quality services.
Physicians		• General Practitioners (GPs) are vital in primary healthcare, managing various medical conditions and influencing patient access. • Specialist doctors, with advanced expertise in specific fields, handle complex cases and contribute to multidisciplinary care teams. • Pharmacists ensure safe medication use, optimize therapeutic outcomes, and reduce errors. Dentists specialize in oral health, addressing conditions like tooth decay and gum disease. Their involvement in healthcare enhances overall patient care quality and efficiency.
Nursing Staff	• Nurses provide direct patient care, administer treatments, and monitor patient status, ensuring timely and compassionate care. • Midwives specialize in maternal and newborn care, promoting healthy pregnancies and reducing complications. • Other healthcare professionals, including allied health professionals, medical assistants, and administrative personnel, contribute to patient care, clinical operations, and facility management, recognizing the multidisciplinary nature of healthcare delivery.
Populations in each province (HCP, 2018; Health, 2022)		A healthcare facility directly influences its service demands, resource requirements, and operational dynamics based on the population it serves. Understanding population demographics, health needs, and geographic distribution is essential for effective healthcare planning, resource allocation, and service provision. Population data informs decisions related to facility location, staffing levels, service expansion, and community outreach initiatives, ultimately enhancing healthcare access, equity, and efficiency.
Outputs (Ministry of Health, 2022)
Hospital activity		The metric for assessing resource allocation efficiency in a healthcare facility includes functional bed capacity, hospitalization days, admissions, rotation interval, average occupancy rate, turnover rate, and average length of stay. These metrics help evaluate the efficiency of patient care processes, ensuring timely access to care, efficient resource utilization, and effective treatment plans. Shorter stays indicate streamlined processes and higher technical efficiency.
Specialised Consultations		Total Number of Doctors: The availability of doctors who can provide specialised care influences the facility's ability to effectively meet patient needs. Higher numbers of specialists can enhance the range and quality of services offered. The total number of External Specialist Consultations reflects the demand for specialised medical services. Efficient facilities can quickly accommodate these consultations, ensuring timely access to specialised care. External Specialist Consultations per Doctor: This metric assesses the efficiency of specialist utilisation. Higher consultation rates per doctor suggest effective referral systems and optimised resource allocation.
The study focuses on public hospital laboratory activities		Exams performed: These represent the range of laboratory tests conducted by the facility (bacteriology, parasitology, immunoserology, haematology and transfusion, food hygiene, biochemicals, and biology (biochemistry)). Comprehensive testing capabilities contribute to accurate diagnoses and effective treatment plans. The total number of samples Tracking the volume of samples processed provides insights into the workload and efficiency of laboratory operations. Efficient facilities can handle a higher volume of samples without compromising accuracy or turnaround time.
Surgical Services (Ministry of Health, 2022)		Total Number of Surgical Interventions: This metric reflects the volume of surgical procedures performed by the facility. A higher number of surgeries may indicate a higher demand for services or more efficient surgical processes. Number of Surgical Interventions per Doctor: Evaluating the productivity of surgical staff helps assess resource utilisation and patient care outcomes. Higher intervention rates per doctor suggest efficient surgical workflows and effective resource allocation.

2.2 Dataset

This study utilized the dataset from Morocco's Ministry of Health and Social Protection (Health, 2022) to ascertain the efficiency of the HN in each HDR. The 12 HN comprise 159 hospitals, totaling 25,889 beds, distributed across 12 HDR (Health, 2022).

2.3 First Stage

DEAP software for calculating DEA: CRS versus VRS

Measure efficiency use two frontier methodologies, stochastic frontier analysis (SFA) and data envelopment analysis (DEA). In 1957, Farrell laid the groundwork for efficiency measurement methodology and principles (Farrell, 1957). Establishing the best-practice production frontier (isoquant) and assessing each decision-making unit (DMU) against it is a fundamental aspect of evaluating efficiency. Aigner, Lovell, and Schmidt introduced the Stochastic Frontier Analysis (SFA) method in 1977 (Aigner et al., 1977) and Meeusen and Van den Broeck (1977) (Meeusen & Van Den Broeck, 1977). Charnes et al. introduced the Data Envelopment Analysis (DEA) method (Charnes et al., 1978), utilising distinct techniques to envelop data, such as statistical or mathematical programming (Linh Pham Thuy, 2011).

There has been a long-standing discussion on measuring technological efficiency in health facilities, but there has been no agreement on the optimal approach for quantifying frontier efficiency in hospitals. This study used the DEA approach to evaluate the effectiveness of Morocco's HN for two specific purposes. DEA is most appropriate in low-income nations with inadequate health sector information, namely, lacking data on hospital input and output pricing. Additionally, DEA is less reliant on extensive data compared to econometric approaches. It does not necessitate a large sample sise, information on input and output prices, or the conversion of physical units into a single unit of measurement. Nevertheless, it is susceptible to outliers and measurement errors.

DEA is a mathematical programming-based technique used to evaluate the relative performance of organisations. While not-for-profit organisations have been its primary application, DEA can also successfully compete with techniques such as cost-benefit analysis and multi-criteria decision-making in other contexts. Charnes et al. introduced DEA in 1978, drawing its roots from earlier works (Farrell, 1957) and (Koopmans, 1951). Even in the original constant returns to scale (CRS) models, which assume proportionality, DEA, often presented as a non-parametric technique, relies on the assumption of linearity. DEA identifies both efficient and inefficient units within a specific context, allowing for comparisons among units while considering various factors. The technique also identifies "peer groups" of efficient units that serve as role models for inefficient units, helping to identify best practices.

Constant Returns to Scale (CRS) Model:

The CRS model assumes that the production process exhibits constant returns to scale (Cooper et al., 2000b, 2007). To put it another way, scaling up or down the inputs proportionately does not affect the output. This model facilitates efficiency assessment by allowing peer group comparisons and identifying efficient and inefficient units within a specific context. Additionally, it facilitates benchmarking, where efficient units serve as role models for others, guiding best practices and resource allocation. Lastly, the CRS model considers sensitivity to input proportions, although this assumption of proportionality may not hold in scenarios with varying input mixes.

Variable Returns to Scale (VRS) Model:

The VRS model relaxes the assumption of constant returns to scale, allowing for variations in efficiency due to different scaling factors (Banker et al., 1984). This model offers flexibility in scaling, accommodating nonlinear input-output relationships and providing a more realistic assessment of efficiency. Additionally, VRS facilitates the customisation of efficiency frontiers, where each Decision Making Unit (DMU) seeks an optimal weight bundle to maximise its CRS-efficiency score under VRS. Furthermore, it has the ability to handle extreme cases in heterogeneous environments where units operate at different scales.

Inputs Orientation

The paper discusses using an input-oriented DEA framework to analyse HN efficiency. It highlights the growing demand for health services, which requires accurate estimation. The approach is more appropriate for this context because it focuses on optimising resource use to meet uncertain demand (Ozcan, 2014). Managers in public hospitals typically have more control over inputs than outputs, making the input-oriented approach more suitable. The paper also emphasises the policy goals and obligations of public hospitals, which often involve meeting population healthcare needs while managing costs effectively. The input-oriented approach supports these goals by emphasising efficient resource utilisation to meet demand, potentially reducing costs or limiting input use. The study aims to provide insights into the efficiency of public hospitals in utilising resources to deliver healthcare services, offering valuable information for policymakers, hospital administrators, and healthcare management and planning stakeholders.

The mathematical formulas

The mathematical formulas for CRS and VRS with orientation towards Inputs in DEA can be expressed as follows, using DEAP version 4.1 (DEAP) (T. Coelli, 1996; T. J. Coelli, 1995; Cooper et al., 2011b; Ozcan, 2014):

1. CRS Model with Orientation Input (Charnes et al., 1978; T. Coelli, 1996):

Efficiency Score (CRS)=∑k = 1mµk⋅yik∑j = 1nλj⋅xij

Where:

xij represents the amount of input i used by Decision Making Unit (DMU) j.

yik represents the amount of output k produced by DMU j.

λj and µk are the weights assigned to inputs and outputs, respectively, obtained from the DEA optimisation process.

2. VRS Model with Orientation Input (Charnes et al., 1978; T. Coelli, 1996):

Efficiency Score (VRS)=∑k = 1mµk⋅yik∑j = 1nλj⋅xij

Where:

xij represents the amount of input i used by Decision Making Unit (DMU) j.

yik represents the amount of output k produced by DMU j.

λj and µk are the weights assigned to inputs and outputs, respectively, obtained from the DEA optimisation process.

These formulas represent the ratio of weighted sums of inputs to weighted sums of outputs for each DMU, indicating their relative efficiency in utilising inputs to generate outputs under the CRS and VRS assumptions.

CHATGPT

To calculate efficiency scores using GAI ChatGPT, we used Open AI ChatGPT 3.5, which consists of several steps. Here's a simplified explanation of the process (Er-Rays & M’dioud, 2024):

Define Inputs and Outputs: First, you need to identify the inputs and outputs for each unit or entity you want to evaluate. Inputs are the resources or factors used in the production process, while outputs are the results or products generated from these inputs.

Normalise Data: Normalise the data to ensure comparability. This step involves scaling the inputs and outputs to a common scale, typically between 0 and 1. Normalisation helps to remove biases caused by differences in the scale of variables.

Choose the DEA Model: Decide on the type of DEA model to use based on the nature of your data and the research question. Common DEA models include CCR (Charnes, Cooper, and Rhodes) model and BCC (Banker, Charnes, and Cooper) model.

Formulate the DEA Linear Programming Problem: Formulate the DEA problem as a linear programming problem, where the objective is to maximise the efficiency score subject to certain constraints. The ratio of weighted outputs to weighted inputs measures efficiency in DEA.

Solve the Linear Programming Problem: Using appropriate optimisation techniques, solve the linear programming problem. The solution provides the efficiency scores for each unit, indicating how efficiently they utilise resources to generate outputs.

Interpret Results: Interpret the DEA analysis's efficiency scores. Units with efficiency scores of 1 are considered efficient, while scores less than 1 indicate inefficiency. Analyse the results to identify factors contributing to inefficiency and opportunities for improvement.

GAI like ChatGPT can assist in various stages of this process, including data preprocessing, model selection, problem formulation, and result interpretation. However, the actual calculation of efficiency scores typically requires specialised software or programming tools designed for DEA analysis.

2.4 Second Stage Tobit model

Hoff explored that second-stage DEA often encounters Tobit regression, which assesses the relationship between exogenous factors (non-physical inputs) and DEA efficiency scores. It is, however, not obvious that Tobit is the only, or optimal, approach to modelling DEA scores (Haldrup, 1998; Hoff, 2007). In exploring the relationship between DEA efficiency scores and hospital characteristics, the aim is to uncover how various factors influence the efficiency (or inefficiency) of hospitals.

This analysis delves into understanding which specific attributes or variables contribute to better or worse performance according to DEA assessments. By employing the censored Tobit model, which accounts for the lower-bound censoring of the dependent variable at sero, this study aims to provide a comprehensive understanding of the determinants of hospital efficiency. Changing DEA scores to inefficiency scores also makes it easier to understand the results, pointing out the things that make hospital operations less efficient (Er-Rays, 2021b; Er-Rays & Ait Lemqeddem, 2020a; Hoff, 2007; Linna & Häkkinen, 1999; Tobin, 1958; Zere, 2000). This approach facilitates actionable insights that can inform strategies for improving hospital performance and resource allocation in healthcare systems.

Inefficiency score = 1 / (DEA score − 1)

The model is structured as follows:

yi=βiXi+ui

Where:

yi represents the observed inefficiency score for hospital i.

βi is a vector of unknown parameters with dimensions K×l.

Xi is a vector of explanatory variables with dimensions ×1.

ui follows a normal distribution with mean 0 and variance.

The observed inefficiency score yi takes on the value of the predicted inefficiency score yi∗ if yi∗>0, and 0 if yi∗≤0.

Thus, the empirical regression model can be expressed as:

INEFF = α0+β1HOP + β2DOC + β3NURS +ϵi

where:

INEFF denotes the inefficiency score.

α0 is the intercept.

HOP, DOC and NURS represent the explanatory variables.

ϵi is the error term.

3.1 Descriptive statistics for the study variables

The correlation matrix reveals strong positive correlations between various variables, such as hospital activity, specialised consultations, public hospital laboratory activities, surgical services, hospitals, doctors, nurses, and the population in each region. Hospital activity is positively associated with all other variables, while specialised consultations and public hospital laboratory activities have strong positive correlations with hospital activity, specialised consultations, and nurse staffing. Surgical services exhibit strong positive correlations with hospital activity, specialised consultations, public hospital laboratory activities, hospitals, doctors, nurses, and the population in each region. Hospital sise is positively associated with various activities and staffing levels, while doctors and nurses have strong positive correlations, indicating a strong association between the number of doctors and nurses in hospitals. Population sise in each region is positively associated with hospital activities and staffing levels, as evidenced by the strong positive correlations between hospital activity, specialised consultations, public hospital laboratory activities, surgical services, hospitals, doctors, nurses, and population in each region. Overall, the correlation matrix provides valuable insights into the relationships between various variables in healthcare (Table 2).

Table 2

correlation
	Hospital activity	Specialised consultations	Public hospital laboratory activities	Surgical services	Hospital	Doctors	Nurse	Population each region
Hospital activity	1
Specialised consultations	0,96	1,00
Public hospital laboratory activities	0,83	0,74	1,00
Surgical services	0,83	0,74	1,00	1,00
Hospital	0,94	0,94	0,69	0,69	1,00
Doctors	0,89	0,95	0,56	0,56	0,90	1,00
Nurse	0,97	0,98	0,83	0,83	0,94	0,91	1,00
Population each region	0,96	0,97	0,71	0,71	0,95	0,93	0,94	1,00

This research included all Moroccan hospitals, with the exception of one for which the data are incomplete. The collected data covers the year 2022. Table 2 summarises the descriptive statistics for input and output variables used in all HN. The dataset reveals significant variability in healthcare provision across different regions and hospitals in Morocco. The average hospital activity is 75,427, with a wide range from 1,362 to 634,016. The mean number of specialised consultations is 49,371, with a similar level of variability. The average activities of public hospital laboratories are 408,168, with a significant standard deviation of 831,227. The average number of surgical services is 4,030, with a range of 36 to 35,633. The dataset comprises four hospitals on average, with a standard deviation of 4, reflecting variability in the number of hospitals across provinces. The mean total number of doctors and nurses is 129 and 320, respectively, with considerable variability. The mean population per province is 518,992, with a wide range from 44,112 to 3,613,337. These descriptive statistics highlight the diversity and heterogeneity of healthcare provision across different regions and hospitals in Morocco. Further analysis, such as correlation or regression analysis, could explore relationships between these variables and identify factors influencing hospital performance and healthcare outcomes.

Table 3

descriptive statistics of inputs and outputs variables (N = 12)
	Hospital activity	Specialised consultations	Public hospital laboratory activities	Surgical services	Hospital	Doctors	Nurse	Population each region
Mean	446277	284788	2512151	2512151	28	916	2101	3095079
Standard Error	92226	66141	625770	625770	5	243	451	648113
Median	430945	228554	2223482	2223482	27	664	1775	2854550
Standard Dev	319479	229119	2167731	2167731	16	842	1563	2245130
Minimum	23203	18418	98901	98901	3	58	242	194066
Maximum	929225	772090	8232607	8232607	56	2659	4891	7641949
Sum	5355329	3417457	30145810	30145810	331	10989	25213	37140944

3.2 DEA: First Stage

Figure 1 presents the estimated CRS and VRS technical efficiency and scale efficiency for each HN. The average CRS technical efficiency score was 0.474, the VRS technical efficiency score was 0.644, and the scale efficiency was 0.745. Overall, 11 (92%) of the regions had a CRS technical efficiency score of less than 1, while the Laâyoune-Sakia El Hamra HDR demonstrated the highest level of efficiency with a score of 1. On the other hand, 09 (75%) VRS were technically efficient with less than a score of 1, while Rabat-Salé-Kénitra, Laâyoune-Sakia El Hamra, and Eddakhla-Oued Eddahab HDRs were efficient, and 25% of the HN had a technical efficiency score of 1. The majority of HN exhibited both models of technical efficiency scores, with 9 HN for CRS and 7 HN for VRS being less than 0.6.

The technical efficiency analysis using GAI ChatGPT revealed that the mean CRS efficiency across regions is approximately 0,730, while the mean VRS efficiency is about 0,581. Among the regions, Béni Mellal-Khénifra, Laâyoune-Sakia El Hamra, and Eddakhla-Oued Eddahab attained maximum efficiency scores of 1 for both CRS and VRS models. This equates to 20% of the total regions achieving perfect efficiency. These findings highlight variations in efficiency levels across regions, with some demonstrating higher efficiency than others.

Significant disparities emerge when comparing technological efficiency between DEA Software and GAI ChatGPT. In terms of DEA software, the average CRS technical efficiency score for all regions was 0.474. This metric deemed only 92% of hospitals to be technically efficient. Conversely, the average VRS technical efficiency score stood at 0.644, with 75% of hospitals achieving technical efficiency. The Laâyoune-Sakia El Hamra HDR stands out, with perfect efficiency scores of 1 for both CRS and VRS models, whereas other regions showed varying levels of efficiency. However, the analysis of the data using GAI ChatGPT revealed a slight increase in the mean CRS efficiency to approximately 0.6914, while the mean VRS efficiency was around 0.5461, indicating a 26.4% difference. This discrepancy suggests a 31% higher efficiency for CRS and a 17% lower efficiency for VRS compared to DEA Software. Furthermore, using this method, Béni Mellal-Khénifra, Laâyoune-Sakia El Hamra, and Eddakhla-Oued Eddahab HDRs achieved flawless efficiency scores. These findings underscore the variability in efficiency levels among regions and the potential for different outcomes using diverse analytical methods.

3.3 Tobit regression: Second Stage

The study uses Tobit regression analysis the factors effect on inefficiency of HN (DEAP version 2.1) using STATA 18 software (Table 4). The model is statistically significant, indicating that at least one of the coefficients is non-sero. The model explains approximately 55% of the variation in inefficiency. The coefficients for hospital activity and nurse are statistically significant at 0.05, suggesting that an increase in hospital activity and nurse are associated with higher inefficiency. The coefficients for "doctors staff" and "population" are not statistically significant, indicating no significant relationship between these variables and inefficiency. The intercept (_cons) is -0.3519811, which is not statistically significant, indicating that there is no evidence for a non-zero inefficiency when all independent variables are zero.

The statistically significant coefficient for hospital activity suggests that this factor may be an important driver of inefficiency in the studied system. However, the non-significant coefficients for doctors, staff, and population suggest that these variables may not significantly impact inefficiency. The negative and significant coefficient for nursing staff implies that increasing the number of nursing staff may lead to a decrease in inefficiency, which could have implications for resource allocation and staffing decisions within healthcare facilities. The non-significant intercept suggests that there are likely other unobserved factors contributing to inefficiency in the system. This analysis sheds light on the factors driving inefficiency in the system under study, but additional research may be necessary to comprehend the intricate dynamics and enhance the accuracy of the model.

Table 4

Tobit regression of VRS (DEAP software)
Number of obs = 12
LR chi2(4) = 16.46		Prob > chi2 = 0.0025			Log likelihood = -6.7323622			Pseudo 0.5500
Innefeciency VRSTE	Coef.		Std. Err.	t		P>\|t\|	[95% Conf. Interval]
Hospital activity	.0772036		.0304739	2.53		0.035	.0069308		.0772036
Doctors staff	.0007434		.0005524	1.35		0.215	− .0005304		.0020171
Nurses staff	− .0012601		.0004183	-3.01		0.017	− .0022247		− .0002955
Population	2.84e-07		2.41e-07	1.18		0.274	-2.73e-07		8.40e-07
_cons	− .3519811		.3687832	-0.95		0.368	-1.202397		.4984344
/sigma	.4406304		.1053366				.1977237		.6835371

3 left-censored observations at ineficienc ~ 1 < = 0 (9 uncensored observations and 0 right-censored observations).

The Tobit regression analysis the factors effect on inefficiency (GAI ChatGPT 3.5) (Table 5) provides valuable insights into the factors influencing inefficiency in the studied system. The model is highly statistically significant, explaining approximately 72.3% of the variation in inefficiency. The coefficients for doctors are not statistically significant, suggesting no significant relationship between this variable and inefficiency. However, an increase in hospital activity and nursing staff is associated with lower inefficiency, which is statistically significant at 0.05.

When all independent variables are zero, the intercept (_cons) is -0.732358 with a standard error of 0.5422317, indicating that there is no evidence to suggest a non-zero inefficiency. There are four left-censored observations, indicating that the model may not fully capture the range of inefficiency values present in the dataset. Like what the DEAP software model found, the statistically significant coefficients for hospital activity and nurses suggest that these factors may be a big reason why the system being studied isn't working as well as it could. The non-significant coefficients for doctors and population suggest that these variables may not significantly impact inefficiency in this context, possibly due to variations in the dataset or modelling techniques.

The negative and significant coefficient for nurses implies that increasing the number of nursing staff may lead to a decrease in inefficiency, consistent with the DEAP software and ChatGPT 3.5 model's findings. This analysis provides valuable insights into the factors influencing inefficiency in the studied system, with implications for healthcare management and resource allocation, as well as personal stuff. We need further research to validate the findings and address any limitations in the modelling approach.

Table 5

Tobit regression of VRS (ChatGPT 3.5)
Number of obs = 12
LR chi2(4) = 28.64		Prob > chi2 = 0.0000			Log likelihood = -5.4861643			Pseudo R2 = 0.7230
Inefficiency VRS ChatGPT 3.5	Coef.		Std. Err.	t		P>\|t\|	[95% Conf. Interval]
hospital activity	0.1032411		0 .0359893	2.87		0.021	0.0202496	0.1862326
Doctors	0.0008436		0.0010562	0.80		0.448	-0.001592	0.0032792
Nurses	− .0028168		0.0009482	-2.97		0.018	-0.0050033	-0.0006303
Population	1.33e-06		2.82e-07	4.73		0.001	6.84e-07	1.99e-06
_cons	-0.732358		.5422317	-1.35		0.214	-1.982747	0.5180306
/sigma	.4516999		0.1103767				0.1971708	0.7062289

4 left-censored observations at ineficienc ~ A < = 0 (8 uncensored observations and 0 right-censored observations).

The study's findings show that the majority of HN within each HDR were more inefficient when using GAI ChatGPT compared to DEAP version 2.1. This difference between the two methods suggests:

On the one hand, GAI ChatGPT 3.5 as a method to calculate technical efficiency provides valuable insights into technical efficiency for AI developers and managers. It can analyse vast amounts of data, providing data-driven insights that help identify areas for improvement. It can also handle complex technical efficiency problems, offering solutions based on a variety of factors. GAI provides real-time feedback on technical processes, enabling immediate adjustments. Managers and developers can adapt their approach to measuring efficiency by customising AI models to specific contexts. GAI solutions can scale effortlessly to handle large datasets and diverse technical processes, making them suitable for organisations of all sises and complexities. AI-powered solutions enable more informed decision-making, leading to better resource allocation and performance optimisation. Overall, GAI ChatGPT 3.5, is a powerful tool for measuring technical efficiency in AI development, allowing organisations to streamline processes and achieve greater success.

On other hand, technical efficiency using DEAP 2.1 software, the results of this study align with previous research conducted in several African countries (Africa WHO, 2023; Arhin et al., 2023; Babalola et al., 2022; Ibrahim et al., 2019; M. Kirigia Joses, 2015; Musoke et al., 2023), which demonstrate the extensive occurrence of technological inefficiency. For exemple, in Morocco (Er Rays & Ait-Lemqeddem, 2020; Er-Rays, 2021a; Er-Rays, Ait-Lemqaddem, et al., 2024; Er-Rays, M’dioud, & Ait-Lemqaddem, 2024; Er-Rays, M’dioud, Ait-Lemqeddem, et al., 2024; Er-Rays & Ait Lemqeddem, 2020b; Er-Rays & M’Dioud, 2024). For instance, studies in countries (see section Up to day) like Morocco, Benin, Ethiopia, Burkina Faso, and Eritrea have highlighted challenges in productivity growth and technical efficiency among healthcare hospital.

For example, the study conducted by Asbu et al. in Benin found that only 43.5% of hospitals experienced productivity growth over a five-year period, indicating significant challenges in productivity management strategies (Asbu et al., 2003). Similarly, Ali et al.'s study in Eastern Ethiopia revealed that a majority of hospitals were technically inefficient, with decreasing efficiency trends over time (Asbu et al., 2003). The study of Kirigia et Asbu in Eritrea also underscored the importance of efficiency analyses in improving hospital performance, suggesting potential strategies for enhancing efficiency through resource allocation and optimisation. Marschall et Flessa showed that 14 health centres in rural Burkina Faso were relatively efficient, with DEA projections suggesting that inefficient units were too big to be efficient (Marschall & Flessa, 2009). Furthermore, studies in specific regions, such as KwaSulu-Natal province in South Africa and regional hospitals in Ghana, have identified factors that influence technical efficiency, such as catchment population, staff allocation, and expenditure patterns. These findings emphasise the need for tailored policy interventions to address inefficiencies and promote better healthcare delivery. Habib et Shahwan identified 17 hospitals as inefficient due to a decline in technical efficiency. Common factors affecting efficiency include software programme value, operational expenses, and employee number. The number of physicians also significantly impacts the hospital's financial efficiency. A sensitivity analysis was conducted for model validation (Habib & Shahwan, 2020). Kirigia et Asbu showed that the average constant returns to scale technical efficiency score was 90.3%, the variable returns to scale technical efficiency score was 96.9%, and average scale efficiency score was 93.3%. To make hospitals more efficient, the researchers could have increased outputs by 20,611 outpatient visits and 1,806 hospital discharges, or they could have transferred excess doctors, nurses, midwives, laboratory technicians, and beds to primary care facilities. The Tobit regression analysis revealed a negative sign for OPDIPD (outpatient visits as a proportion of inpatient days) and a positive sign for ALOS (average length of stay) (J. M. Kirigia & Asbu, 2013). Babalola et al showed that a significant proportion of the hospitals were technically inefficient. Factors influencing technical efficiency included catchment population, inpatient treatment per medical and nursing personnel, and expenditure per patient day equivalent. These findings highlight the need for improved efficiency in healthcare systems (Babalola et al., 2022). Lamesgen et al. found that 80% of primary hospitals were pure technical efficient, while 46.67% were scale efficient for neonatal health services in three sones of Northwest Ethiopia. The mean pure technical and scale efficiency scores were 0.948 ± 0.113 and 0.887 ± 0.143, respectively. The study found that the total catchment population, incentive packages for clinical staff, and the educational status of the manager positively influenced the technical efficiency of hospitals (Lamesgen et al., 2022).

Enhancing the performance of Moroccan HN is vital to ensuring efficient healthcare delivery and optimal resource utilisation. Health manager makers in health directorate areas need precise data on the efficiency of hospitals' resource utilisation in order to make well-informed judgements. This study demonstrated the use of DEA techniques in each regional health directorate's HN. It used both the DEAP Version 2.1 software and the advanced GAI ChatGPT 3.5 to analyse efficiency differences among HN based on readily available data.

The study's findings offer empirical data on the technical efficiency of the sampled HN. Additionally, the findings emphasise the need for specific modifications in input and output factors in order to enhance the efficiency of hospitals that are currently inefficient. The comparison between DEAP V 2.1 and GAI ChatGPT 3.5 highlights disparities in their ability to recognise inefficiencies and the variables related to them.

The DEAP version 2.1 and ChatGPT 3.5 analyses identify the hospital activity (HOP) and the stuff nurse (NURS) as statistically significant in terms of inefficiency. This suggests that internal issues inside the hospital activity (HOP) and the stuff nurse (NURS) had a substantial impact on determining the levels of efficiency. We link the number of hospital activities (HOP) and the number of nurses (NURS) to reduced inefficiency, underscoring the significance of human resource management in improving hospital performance.

These conflicting findings underscore the importance of employing multiple analytical methods to gain a comprehensive understanding of HN effectiveness. Health policymakers and researchers can enhance their decision-making and improve healthcare delivery by leveraging both traditional DEA approaches and modern AI technology. This enables better-informed decisions and future research, as well as tailored interventions such as engaging with managers and healthcare staff, reducing regional health disparities, and enhancing the quality of care.

First, applying the principles of New Public Management (NPM) (Errami & Cargnello, 2016; Er-Rays et al., 2022b) to the public HN can be beneficial. This approach, based on contractualisation, accountability, and managerial practices, involves collaboration between the central administration, hospital directors, and managers of medical, paramedical, and administrative departments. These stakeholders would establish a contract to ensure alignment of goals and responsibilities.

Secondly, to reshape the relationship between healthcare institutions and citisens, particularly in nursing and medical services, adopting a Citisen Relationship Management (CiRM) strategy and embracing digital transformation in the health system is advisable. Moroccan hospitals could benefit from developing digital transition strategies (Er-Rays et al., 2022a), such as leveraging GAI ChatGPT with a focus on the national level. This would help harness collective awareness and sustain momentum through an ambitious and integrated health strategy.

Thirdly, optimising resource allocation, utilising GAI to improve healthcare accessibility for marginalised patients in remote areas, and analysing hospital performance at the regional level are essential steps in this process. Furthermore, these findings emphasise the dynamic nature of healthcare efficiency, highlighting the need for ongoing monitoring and adjustment to ensure continuous improvement in HN performance.

This study represented a relative research endeavour that can serve as a foundation for scholarly discussions regarding the merits and demerits of healthcare provision in hospitals. The primary challenge lies in reconciling organisational constraints, such as human resource management (including enhancing the productivity of medical services), waiting lists, and access to services, with patient preferences and the quality of healthcare. These observations emphasise the need for further research by expanding the list of input and output variables from an objectivist perspective. Therefore, it is imperative to explore several scientific research questions, such as: how to implement this model of care delivery in the field and develop GAI to enhance the performance of HNs in each HDR?

This study presents certain limitations, both in theoretical and methodological terms, in the choice of variables and the study.

Firstly, the theoretical limitations of our work can be classified into two categories: firstly, because of practical considerations, we have not been able to take fully into account the contingency factors that may influence the content and usefulness of DEA methods. These factors include, for example, psychological aspects of the personalities of managers, doctors, nurses, and patients; the decision-making style of the management of each institution; and the influence of the culture or history of the health care hospital and patients. Unfortunately, these elements have not been taken into account in our research model. Secondly, our research approach did not take account of inter-factor relationships within the variable "diversity of use of indicators." An inter-factor study could enrich our model by analysing the relationship between financial and non-financial indicators to determine how DEA operational measures predict and anticipate the HN's performance.

As for methodological, firstly, the limitations on the choice of variables, inputs, and outputs generally cover the whole range of healthcare hospitals in Morocco. As a result, studying the hospital's performance is considered difficult and requires technical indicators that health institutions do not have.

Secondly, the sise of the sample—12 HN for each HDR—links, on the one hand, to the methodological limit. Although these observations may be considered large enough for a management sciences researcher, a statistician will find them relatively limited, which limits the possibility of generalising the results. To overcome this limit, it would be of great interest to conduct similar research on a larger sample. However, the chosen data collection method, based on an outdated period like 2022, presents another methodological limitation due to the absence of recent and up-to-date technical data. Although we have identified all information to limit perceptual bias and interviewed managers and management controllers for validation, this restriction of data collection to only critical perceptual data raises the risk of a deviation between reality and perception.

Finally, with regard to the study's limitations, it determined the levels of inefficiency of HNs' activities without methodologically explaining the real factors leading to this ineffectiveness. It is difficult to understand why such inefficiencies exist because there is a lack of information and data on the technical functioning of health facilities. In this context, every approach has strengths and weaknesses.

CRS: Constant Returns Scale, DEA: Data Envelopment Analysis, DEAP: Data Envelopment Analysis Programming, DMU: Decision Making Unit, ET: Technical Efficiency VRS: Variable Returns Scale, SDG: Sustainable Development Goals, HDR: Health directorate region, GAI: Generative Artificial Intelligence, HN: Hospital networks.

Author Contribution

The authors involved in the literature review, data analysis, interpretation of the results, and drafting of the manuscript. This author read and approved the final manuscript.

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Analyzing the Efficiency of Moroccan Hospital Network Regions via DEA and Tobit Regression: Assessing DEAP 2.1 Software versus Generative AI ChatGPT 3.5

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Version 1

Abstract

Figures

1 Introduction

1.2 Up to day

1.3 Research Gaps

1.4 The study's purpose

1.5 Motivation

1.6 The study's contribution

1.7 Brief country profile

2 Method

2.1 Study design

2.2 Dataset

2.3 First Stage

2.4 Second Stage Tobit model

3 Results

3.1 Descriptive statistics for the study variables

3.2 DEA: First Stage

3.3 Tobit regression: Second Stage

4 Discussion

5 Conclusion and recommendations

6 Limitation of the study

Abbreviations

Declarations

Author Contribution

References

Additional Declarations

Status:

Version 1