Decomposing Health System Inefficiency: A Cross-National Two-Stage Network Analysis of 30 Nations and the German Case

Decomposing Health System Inefficiency: A Cross-National Two-Stage Network Analysis of 30 Nations and the German Case | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Decomposing Health System Inefficiency: A Cross-National Two-Stage Network Analysis of 30 Nations and the German Case Ingrid Franz, Mirella Cacace, Eva Maria Bitzer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9246265/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Background In the context of demographic ageing, rising healthcare expenditure, and persistent health outcome differences, improving the efficiency of healthcare systems has become a key policy priority across many high-income countries. While previous cross-country studies often assess overall system efficiency, they provide limited insight into where inefficiencies arise within the healthcare production process. This study therefore examines healthcare system efficiency across two functional stages - resource generation and service delivery - and investigates whether structural country characteristics are associated with efficiency patterns. Methods A two-stage Network Data Envelopment Analysis (NDEA) was applied to assess the efficiency of 30 national healthcare systems using cross-sectional data for 2022. Stage 1 represents resource generation and includes healthcare expenditure, hospital beds, general practitioner density, and digital health infrastructure. The intermediate output, avoidable hospitalisations, enters Stage 2 (service delivery), which additionally incorporates bed-days and doctor consultations. System outcomes are captured by treatable mortality and self-assessed health status . Countries were subsequently grouped according to contextual similarity using hierarchical clustering. Exploratory associations between efficiency scores and structural factors were examined using fractional logit regression models and non-parametric tests. Results Average overall efficiency across countries was 0.75, with mean stage-1 efficiency (0.85) exceeding stage-2 efficiency (0.65), indicating that efficiency losses predominantly occur in the transformation of healthcare services into health outcomes. Considerable cross-country variation was observed. Germany ranks among the lowest-performing systems within the sample, primarily due to comparatively weak second-stage efficiency. Cluster analysis revealed structural differences between country groups; however, efficiency differences across clusters were not statistically robust. In contrast, healthcare system type showed significant associations with efficiency, with social health insurance systems displaying lower stage-2 efficiency compared to national health service systems. Conclusions The findings suggest that inefficiencies in healthcare systems primarily arise in service delivery rather than in resource generation. Institutional system characteristics appear more closely related to efficiency variation than socioeconomic context. Differences in care coordination may be associated with variation in the translation of healthcare services into health outcomes. The two-stage NDEA approach helps identify where efficiency losses occur and provides a more detailed understanding of how resources are translated into health outcomes. Health system efficiency Two-stage Network DEA Cross-country comparison Structural clustering Efficiency determinants Germany’s health care efficiency Figures Figure 1 Figure 2 Background In view of an ageing population and labour shortages, improving the efficiency of healthcare systems has become a key policy priority across Europe. Despite increasing healthcare expenditure, significant differences in health outcomes persist, even among countries with comparable economic development and health spending [ 1 ]. These persistent outcome differentials suggest that higher spending alone does not necessarily translate into better health outcomes and point to differences in efficiency with which healthcare systems transform resources into health outcomes. From a policy perspective, understanding the sources of inefficiencies within healthcare systems is crucial to contain costs, allocate resources more effectively, and maintain high-quality care under increasing fiscal and demographic pressure. A growing body of literature has examined healthcare system efficiency using cross-country comparisons, often applying data envelopment analysis (DEA) or related approaches [ 2 ] as a single production process. While these studies provide important insights into efficiency, their aggregated perspective limits their ability to identify where inefficiencies arise within the healthcare system and may therefore offer limited guidance for policy interventions. To address this limitation, we apply a two-stage network DEA (NDEA) framework that distinguishing between resource generation and service delivery. This structure follows the analytical framework for healthcare system performance, proposed by Papanicolas et al. [ 3 ], which conceptualises health outcomes as the result of interconnected production stages [ 4 ]. Building on this perspective, we test whether inefficiency primarily occurs in the transformation from service delivery to outcomes rather than in resource generation. This expectation is consistent with evidence that bottlenecks often occur in care coordination and the translation of service volume into health gains. Within this approach, efficiency is conceptualised as input-oriented technical efficiency, which is achieved when resources are allocated such that inputs are minimised for a given level of outputs [ 5 ]. Resource generation is proxied by health expenditure and structural capacity (workforce, beds, digital infrastructure), while service delivery is measured by consultations and bed-days; outcomes are captured by treatable mortality and self-assessed health. Cross-country comparisons are particularly informative when socio-economic and institutional contexts are explicitly considered [ 6 ]. We therefore complement the two-stage efficiency assessment by analysing patterns across clusters of countries that share similar demographic, economic and regulatory contexts, and by comparing established health system types. We subsequently examine how these contextual factors are associated with stage-specific efficiency differences and discuss related policy implications. Although the empirical strategy relies on a cross-country comparison, particular attention is devoted to the German healthcare system in order to contextualise the results within one of Europe’s largest social health insurance systems. This study addresses three research questions: (1) How efficient are healthcare systems in transforming resources into services and outcomes across two functional stages (resource generation and service delivery)? (2) Do countries sharing similar socio-economic and regulatory contexts exhibit comparable stage-specific efficiency profiles? (3) Which contextual factors are associated with stage-specific efficiency differences? Review of the literature Efficiency measurement in health economics frequently relies on DEA to benchmark health systems across countries or regions [ 7 ]. Early contributions predominantly used single-stage “black-box” models, which treat national health systems as unified production units mapping aggregate inputs, such as total health expenditure or health workforce, onto outcome indicators like life expectancy [ 8 ]. While this literature documented substantial cross-country variation in efficiency levels (e.g. [ 2 ]) and highlighted that higher spending does not automatically translate into better outcomes [ 4 ], it offers only limited insight into where inefficiencies arise within the system. More recent studies therefore apply network or multi-stage DEA frameworks to distinguish conceptually different subprocesses within healthcare (e.g. [ 8 ], [ 4 ], [ 9 ], [ 10 ]). Kujawska (2021) [ 10 ], for example, applies a NDEA to European countries by modelling a “lifestyle” component alongside a healthcare component, and shows that efficiency scores can differ markedly between these subprocesses within the same country. Other contributions apply NDEA to specific areas, such as prevention-to-treatment chains or to distinct performance domains (e.g. disease-specific care pathways) (e.g. [ 9 ]). Taken together, this literature illustrates that NDEA offers a flexible framework for opening the “black box” of health systems and attributing inefficiencies to specific stages of the production process. However, many existing network structures are organised around specific determinants (e.g. lifestyle factors) or broad domains (public health vs. medical care) rather than around core health system functions. This reduces policy interpretability because inefficiencies cannot be directly linked to functional levers that policymakers commonly address. Contemporary health system performance frameworks, building on work by the WHO and related approaches, distinguish between resource generation (e.g. health workforce) and service delivery, assuming that resources primarily contribute to health outcomes through the function of service delivery [ 3 ]. As mentioned earlier, we develop a two-stage NDEA model for national health systems that separates (i) resource generation from (ii) service delivery in order to bridge this gap. This structure aligns with the health system performance framework proposed by Papanicolas et al. (2022) [ 3 ] and allows for a stage-specific efficiency assessment. Previous cross-country efficiency studies have often incorporated contextual variables directly into second-stage regressions (e.g. [ 11 ], [ 2 ]). However, structural and socioeconomic characteristics such as income distribution, demographic composition, or institutional system type do not constitute healthcare production inputs in a strict sense. Including them directly in the DEA model would risk conflating production technology with environmental conditions. By contrast, cluster analysis allows grouping countries according to shared structural constellations (e.g. [ 12 ], [ 13 ]) without altering the underlying efficiency frontier. In this study, clustering therefore serves as a contextualisation strategy rather than as a component of the efficiency measurement itself. Methods The study comprises three analytical steps. First, the technical efficiency of national healthcare systems is assessed using a two-stage NDEA. Second, countries are clustered to identify structural similarities in socioeconomic and healthcare system characteristics. Finally, the relationship between structural characteristics and efficiency scores is examined using fractional regression models. Two-stage NDEA DEA is a widely used non-parametric method for cross-country efficiency analysis, derived from production theory and initially introduced by Charnes et al. [ 14 ]. As a non-parametric, linear programming technique, DEA evaluates the relative efficiency of decision-making units (DMUs) by comparing their ability to convert inputs (e.g., health expenditure, digital infrastructure) into outputs or outcomes. In this study, “outputs” refer to the immediate results of healthcare services, whereas “outcomes” capture their effects on patients’ and populations’ health status [ 15 ]. An empirical production frontier is defined by the most efficient country or countries within the sample. Countries located on the efficiency frontier receive an efficiency score of one, while countries below the frontier receive efficiency scores between zero and one [ 5 ]. DEA is well suited for analysing the efficiency of healthcare systems, as it does not require any prior assumptions about the functional form or parameterisation. Standard DEA models yield a single efficiency score for the healthcare system as a whole. In contrast, a two-stage NDEA model allows the estimation of both overall efficiency and stage-specific efficiencies, where outputs from one stage serve as inputs to subsequent stages. The NDEA is based on Färe and Grosskopf [ 16 , 17 ]. We opted for an input-oriented DEA model assuming constant returns to scale (CRS), treating scale as part of the production technology rather than as a factor to be controlled for [ 5 ]. The orientation is appropriate because healthcare systems typically have limited control over outputs and outcomes, whereas inputs can, at least potentially, be influenced by policy decisions. Several robustness checks were conducted, including alternative scale assumptions (CRS vs. VRS), alternative model orientation (input vs. output), and bootstrapped DEA models with 2,000 replications. Rank correlation tests were used to assess the stability of efficiency rankings. All DEA and NDEA analyses were conducted using “R” software (version 4.4.1). The number of variables included in the model was deliberately limited to maintain sufficient discriminatory power relative to the number of DMUs and to avoid the curse of dimensionality in DEA. Variable selection was guided by the literature on economic efficiency measurement in healthcare. In particular, we draw on the systematic reviews by Varabyova and Müller [ 18 ] and Mbau et al. [ 7 ] – updated by Dlouhý and Havlík [ 19 ]– for the selection of input and output/outcome variables. The selection of variables was undertaken in accordance with the conceptual framework developed by Papanicolas [ 3 ]. Guided by the health system performance framework and data availability, the overall concept of the two-stage NDEA model is illustrated in Fig. 1 . The framework distinguishes three core system functions, financing, resource generation, and service delivery, that ultimately shape the efficiency of service delivery in healthcare system performance [ 3 ]. These functions are encompassed by the ‘governance’ function, which in turn is broken down to four sub-functions: policy and vision, stakeholder voice, information and intelligence, legislation and regulation [ 20 ]. Governance is not explicitly included in the model for two reasons. First, no suitable cross-country indicator is available that captures governance or its sub-functions in a comparable way. Second, governance can be interpreted less as an input and more as a contextual determinant of system performance. As shown in Fig. 1 , the two-stage design disentangles the efficiency of ‘resource generation’ in the first stage from the efficiency of “service delivery” in the second stage. Source: own depiction In order to align our two-stage model with the three core functions of the framework, financing, resource generation, and service delivery, we combine the function of financing (healthcare expenditures) with the inputs of “resource generation”, i.e. the access to digital health infrastructure and the density of GPs and hospital beds per 1,000 population. This is justified insofar as all resource generation must be financed by healthcare expenditures, and conversely, all financial healthcare resources ultimately flow into resource generation and are used for the purchase of goods and services [ 21 , 22 ]. Figure 1 illustrates this graphically by depicting ‘healthcare expenditures’ somewhat apart from the other elements. The intermediate output at the first stage is the avoidable hospitalisation rate due to diabetes. Such admissions are largely avoidable and therefore commonly used as a marker of quality and access to primary care [ 1 , 23 ]. Lower avoidable hospitalisation rates are expected were digital health infrastructure and appropriate supply of primary care resources support effective disease management, while excessive hospital capacity may increase the risk of avoidable admissions [ 24 , 25 ]. As avoidable hospitalisations represent an undesirable output, the indicator was transformed accordingly so that lower rates indicate better performance. Comparable measures for other conditions were not consistently available across countries. At the second stage of our model, we used doctor visits and bed-days as inputs for “service delivery”. In addition, avoidable hospitalisation due to diabetes, the intermediate output at the first stage was also used as an input in the second stage. Thus, the first stage captures the efficiency of the resources generation in producing quality healthcare, whereas the second stage reflects patients’ use of, and thus access to, medical care, even if it cannot be ascertained whether use is always medically justified or not. The outcomes at the second stage were measured by two factors: treatable mortality and self-assessed health status (SAH). Treatable (or amenable) mortality is a well-established indicator of healthcare system performance, also reflecting the effectiveness of service delivery, while SAH is widely used as a patient-reported outcome measure [ 26 ]. Cluster Analysis Cluster analysis (CA) is a statistical technique used to group objects or cases into clusters based on their similarity, allowing for the identification of patterns or structures within complex datasets. A cluster can be defined as a group where the characteristics within the group are as similar as possible, while being as distinct as possible from other groups [ 27 ]. Given the combination of continuous and categorical variables and the unknown number of clusters, a hierarchical agglomerative clustering approach using Complete Linkage method and Gower’s dissimilarity measure was applied. In Complete Linkage, the distance between two clusters is defined as the largest distance between any pair of observations belonging to the two clusters, and clusters are merged stepwise such that this maximum inter-cluster distance is minimised at each step [ 27 ]. Agglomerative methods proceed step by step, with each unit initially representing a single cluster, and end with all objects being grouped together in one large cluster. The optimal number of clusters was determined using the Calinski–Harabasz criterion, the Duda–Hart stopping rule, and visual inspection of the dendrogram. Cluster robustness was assessed by varying country inclusion and applying alternative clustering methods. The countries were grouped based on six variables. In contrast to previous studies, which employed a range of indicators, including characteristics of the healthcare system and preventive measures [ 13 ], we used: (1) GDP per capita, (2) Gini coefficient, (3) percentage of the population aged 65 and older, (4) share of population living in rural areas, (5) a composite index of preventive health policies (alcohol, smoking, obesity), and (6) a typology of healthcare system models according to Böhm et al. [ 28 ] and [ 21 ]. These variables capture core socioeconomic and system-level factors. The resulting clusters provide a structural context for interpreting efficiency differences across countries and allow efficiency scores to be compared among systems with broadly similar socioeconomic and institutional characteristics. CA was conducted with STATA Version BE 19. Fractional Regression Analysis To examine whether institutional and socioeconomic characteristics are associated with efficiency differences, fractional regression models were estimated [ 29 ]. As DEA efficiency scores are bounded between zero and one, conventional linear regression models are inappropriate due to potential heteroskedasticity and the possibility of predicted values outside the admissible range. We therefore apply a fractional logit model with a logit link function, originally proposed by Papke and Wooldridge [ 29 ], which is specifically designed for proportion-type dependent variables constrained to the unit interval [ 30 ]. Separate models were estimated for overall efficiency as well as stage-1 and stage-2 efficiency scores. Robust standard errors were used to account for potential heteroskedasticity. Given the relatively small sample size and the cross-sectional design, the regression analysis is exploratory and aims to identify associations rather than causal relationships. Cluster analysis and health system typology capture partially overlapping but conceptually distinct structural dimensions. Data source Our analysis primarily relies on data from OECD Health Statistics (2025) [ 31 ]. Missing values were complemented using data from Eurostat (2025) [ 32 ], and one key variable was obtained from the European Commission (2023) [ 33 ]. A detailed overview of variables, data sources, and availability is provided in Table 1 . The final sample comprises 30 countries, predominantly located in Europe, with two additional cases from outside the region. Most countries are OECD members. Country inclusion was driven by the availability of complete and harmonised data for all DEA variables in 2022. Restricting the sample to countries with comparable data ensures internal consistency of the efficiency frontier and avoids distortions due to missing information. A detailed overview of the variables used in the DEA and their values for each country, including the respective data sources, is provided in the additional file 1. As two countries (Turkey and Israel) were identified as outliers in the CA, fractional regressions are based on 28 countries. Table 1 Variables and Data Sources for the 2-stage NDEA Stage Variable Name Role Description Unit Source 1 Healthcare Expenditures Input Public and mandatory health expenditure per capita, PPP adjusted and expressed in constant prices USD PPP per capita 1 1 Digital Health Infrastructure Index 4 Input Composite eHealth score capturing national digital health capacity across thematic layers (e.g., electronic records, interoperability, e-prescriptions, data exchange) Index score (0–100) 2 1 GP Density Input number of general practitioners per 1,000 population Per 1,000 population 1 1 Hospital Bed Density Input Number of hospital beds per 1,000 population Per 1,000 population 1 1–2 Avoidable Hospital Admissions 4 Intermediate output/ Input stage 2 number of avoidable hospital admissions related to diabetes per 100,000 population (undesirable output; transformed for DEA) Per 100,000 population 1 2 Bed-Days Input total number of inpatient hospital days per person in the population per year Days per population 1 2 Doc Consultations Input average number of physician consultations per capita per year Visits per capita 1 2 Treatable Mortality 4 Outcome Mortality from causes amenable to timely and effective healthcare Per 100,000 population 1, 3 2 Self-Assessed Health Status (SAH) Outcome Share of individuals in the lowest income quintile reporting “very good” or “excellent” health % of respondents 1, 3 Legend 1 OECD Health Statistics (2025) [ 31 ] 2 European Commission (2023) (Digital Health Infrastructure Index, composite score) [ 33 ] 3 Eurostat Database (2025) [ 32 ] 4 Values inverted for analysis Results Table 2 summarises descriptive statistics for the input, intermediate output, and outcome variables included in the two-stage NDEA model across the 30 countries. Considerable variation is observed across all variables, indicating substantial cross-country differences in resource endowment, service delivery patterns, and health outcomes. In terms of resource generation inputs, per capita health expenditure and hospital bed density display particularly wide dispersion. Germany records the highest values for both indicators within the sample. The intermediate output “avoidable hospitalisations” and service delivery indicators (bed-days and consultations) exhibit substantial heterogeneity. Germany again ranks among the countries with the highest bed-day intensity. In terms of final health outcomes, Germany performs below the sample mean for both outcome indicators. Table 2 Descriptive Statistics of DEA Variables Variable Mean SD Min Max Germany Healthcare Expenditures 2347.69 1013.67 724.83 4347.07 4347.07 Digital Health Infrastructure Index 80.67 16.71 11.00 100.00 87.00 GP Density 1.26 0.84 0.56 4.00 1.03 Hospital Bed Density 4.38 1.68 1.90 7.72 7.72 Avoidable Hospital Admissions 108.31 49.76 28.20 236.10 179.50 Bed-Days 0.81 0.22 0.40 1.50 1.50 Doc Consultation 6.55 2.54 2.30 12.00 9.60 Treatable Mortality 80.52 40.33 38.00 179.00 66.00 Self-Assessed Health Status (SAH) 58.17 15.60 25.10 98.10 51.70 Stage-specific efficiency Stage-specific efficiencies reveal notable differences between resource generation (stage 1) and service delivery (stage 2), as illustrated in Fig. 2 . The mean efficiency score for the first stage is 0.85, exceeding the mean efficiency at the second stage (0.65) and the overall efficiency score, suggesting greater performance losses in the transformation of services into health outcomes. For 20 of the 30 countries, stage-1 efficiency exceeds stage-2 efficiency, suggesting that efficiency losses predominantly occur in the second stage of the production process. Germany follows this general pattern. Its overall efficiency score lies below the sample mean and ranks 29th out of 30 countries. The efficiency gap is particularly pronounced in stage 2 (efficiency value 0.29), where Germany performs substantially weaker relative to most other countries under consideration. While the first stage has an average efficiency of 0.85, this drops to just 0.65 in the second stage. This illustrates how much more difficult it is to achieve an efficient outcome transformation. Caption: The figure plots stage-1 (resource generation) against stage-2 (service delivery) efficiency scores for all countries. The dashed 45-degree line indicates equal efficiency across stages. Most countries lie below the line, indicating lower efficiency in service delivery than in resource generation. Overall efficiency As illustrated in Table 3 , overall efficiency scores derived from the two-stage NDEA model range from 0.46 to 1, with a sample mean of 0.75. Iceland, Israel, and Sweden are located on the efficiency frontier and thus represent the most efficient systems within the sample. Fifteen countries exhibit overall efficiency scores above the sample mean. Germany’s overall efficiency score is 0.51, placing it among the lowest-performing systems. Robustness checks based on alternative network DEA specifications (CRS vs. VRS; input vs. output orientation; bootstrapped DEA models with 2,000 replications) broadly confirm the main pattern of higher stage-1 than stage-2 efficiency and the comparatively low relative position of Germany (see additional file 3). In addition, bootstrap inference for the overall DEA model with 2,000 replications shows that the relative position of Germany is robust to sampling variation. Spearman rank correlations across network DEA specifications are uniformly positive, ranging from 0.43 to 0.91 (median ρ = 0.78), indicating a broadly stable ordering of DMUs across alternative model assumptions (see additional file 4). The highest agreement is observed between input- and output-oriented specifications under CRS, suggesting that the choice of orientation has only a limited effect on the ranking. Correlations involving VRS specifications are more moderate, indicating that the rankings are somewhat sensitive to assumptions regarding returns to scale and suggesting that scale effects contribute to cross-country differences in efficiency. Table 3 Overall and Stage-Specific Efficiency Scores Country 1. Stage Efficiency 2. Stage Efficiency Overall Efficiency Rank overall Iceland 1.00 1.00 1.00 1 Israel 1.00 1.00 1.00 1 Sweden 1.00 1.00 1.00 1 Netherlands 0.90 1.00 0.95 4 Italy 0.95 0.92 0.93 5 Norway 0.78 1.00 0.89 6 Turkey 1.00 0.70 0.85 7 Portugal 0.83 0.84 0.83 8 United Kingdom 0.88 0.78 0.83 9 Denmark 1.00 0.66 0.83 10 Spain 0.90 0.76 0.83 11 Malta 0.63 1.00 0.82 12 Slovenia 0.97 0.62 0.79 13 Belgium 1.00 0.54 0.77 14 Finland 0.88 0.65 0.77 15 Romania 0.88 0.62 0.75 16 Estonia 1.00 0.44 0.72 17 Hungary 0.99 0.43 0.71 18 Ireland 0.77 0.62 0.70 19 Switzerland 0.57 0.78 0.67 20 Poland 0.89 0.39 0.64 21 Lithuania 1.00 0.24 0.62 22 Latvia 0.92 0.31 0.61 23 France 0.51 0.71 0.61 24 Croatia 0.86 0.34 0.60 25 Luxembourg 0.59 0.60 0.60 26 Czechia 0.80 0.38 0.59 27 Slovakia 0.59 0.46 0.52 28 Germany 0.72 0.29 0.51 29 Austria 0.53 0.39 0.46 30 mean 0.85 0.65 0.75 min 0.51 0.24 0.46 max 1.00 1.00 1.00 Cluster Analysis While the NDEA results reveal cross-country differences in efficiency, they do not account for structural similarities between health systems. To provide contextual orientation, a hierarchical cluster analysis based on socioeconomic and institutional characteristics was conducted. The analysis identifies five distinct clusters comprising four to eight countries each, as summarized in Table 4 . Two countries (Turkey and Israel) were found as outliers. Alternative cluster solutions (k = 4 and k = 6) yielded less interpretable group structures and lower cluster validity indices (refer to additional file 5a, 5b and 5c). The clusters differ primarily with respect to healthcare system type, economic development, demographic structure, rural population share, and the prevention index. Cluster A predominantly consist of social health insurance systems; Cluster B is mainly composed of state-organised healthcare systems with comparatively low rural population shares; Cluster C combines high prevention index values with etatist social health insurance systems; Cluster D is characterised by lower economic resources and the highest mean share of rural population; Cluster E includes countries with the highest level of economic development and the smallest proportion of elderly individuals in comparison with the other clusters. Table 4 Cluster Characteristics (mean values) Cluster N GDP per Capita (USD) Gini Coeff. Rural Population (%) Elderly Population (%) Prevention Index Pre-dominant Health System Types Stage 1 Efficiency Stage 2 Efficiency Overall Efficiency A 6 61886 0.31 18.17 21.01 47.13 Societal 0.78 0.52 0.65 B 8 58033 0.31 15.82 20.64 68.68 State 0.89 0.74 0.82 C 5 59452 0.27 18.60 20.08 73.54 Etatist 0.82 0.60 0.71 D 5 45263 0.28 47.02 20.30 61.36 Etatist 0.86 0.49 0.68 E 4 120954 0.27 30.39 15.90 68.88 Mixed 0.78 0.81 0.80 Legend: Cluster means for socioeconomic indicators and efficiency scores from the two-stage NDEA model are presented. Stage 1 captures resource generation efficiency; Stage 2 captures service delivery efficiency. Efficiency scores are bounded between 0 and 1. Health System Types are classified according to Böhm et al (2013), distinguishing systems by financing, provision, and regulation. “State” systems are tax-funded with public provision; “Societal” systems rely on social health insurance; “Etatist” systems combine social insurance with strong state control. Cluster E combines the types: “State”, “Societal” and “Etatist”. Country-level data are provided in the Appendix. To contextualise potential production differences, cluster-specific means of DEA input and outcome variables were compared (see additional file 6 for details including tests of differences ). Cluster A shows significantly higher bed density consultation frequency (p < 0,05) in comparison to Cluster B, whereas latter combines comparatively higher GP density and digital maturity. The mean values for health care expenditures, hospital beds, and consultations in Cluster C are comparatively higher than those in Cluster B, although the outcome measures lag behind those of Cluster B. Cluster D exhibits lowest average expenditure levels and highest treatable mortality in comparison to the other Clusters. Conversely, Cluster E exhibits the highest mean healthcare expenditures and the lowest treatable mortality rate, while concurrently demonstrating the highest rate of self-assessed health status. Despite observable mean differences, Kruskal–Wallis tests do not indicate statistically significant differences in overall efficiency across clusters (p = 0.17). However, fractional logit models suggest weak evidence of cluster differences for overall efficiency (Wald χ² = 8.46, p = 0.076) and stage-2 efficiency (Wald χ² = 9.26, p = 0.055), whereas no differences are observed for stage-1 efficiency (p = 0.63). Taken together, the results indicate that cluster membership is not robustly associated with stage-1 efficiency and only weakly associated with overall and stage-2 efficiency. Small cluster sizes likely contribute to limited statistical power. Across Clusters A to D, stage-1 efficiency exceeds stage-2 efficiency, whereas Cluster E exhibits a more balanced stage-specific pattern. Germany is assigned to Cluster A and mirrors the general pattern of comparatively lower second-stage efficiency within this group. However, its efficiency score ranks among the lowest within the cluster, indicating that structural similarity alone does not account for its comparatively weak performance. In contrast to the cluster results, health system type is significantly associated with efficiency levels. Fractional logit models indicate statistically significant differences across system types for stage-1 efficiency (Wald χ² = 15.59, p = 0.0036), stage-2 efficiency (Wald χ² = 16.10, p = 0.0029), and overall efficiency (Wald χ² = 30.71, p < 0.001). Marginal effects indicate that system types 3 (social health insurance systems) and 4 (etatist social health insurance systems) are associated with markedly lower expected stage-2 efficiency compared to type 1 (Δ = -0.39 and − 0.31, respectively). Non-parametric Kruskal–Wallis tests confirm significant differences for stage-2 efficiency (p = 0.034) and overall efficiency (p = 0.005). Exploratory fractional logit models examining individual structural indicators show limited and partly inconsistent associations. GDP per capita is negatively associated with stage-1 efficiency (p = 0.012), while rural population share displays a marginal negative association with stage-2 efficiency (p = 0.065). The prevention index is weakly positively related to overall efficiency (p = 0.089). No statistically significant associations are observed for income inequality or elderly population share. Given the small sample size and multiple exploratory tests, regression results are interpreted as exploratory and were not adjusted for multiple comparisons. Results should be interpreted with caution. Overall, structural clusters do not robustly explain systematic efficiency, although weak evidence suggests that some disparities may be related to cluster affiliation. In contrast, institutional system type appears more closely related to both overall and stage-specific efficiency. Associations with individual socioeconomic indicators remain weak and statistically fragile. Germany belongs to health system type 3 (social health insurance systems), which exhibits comparatively lower stage-2 efficiency. This aligns with Germany’s below-average second-stage efficiency observed in the NDEA results. Discussion Several frontier countries combine comparatively favourable health outcomes with less resource intensity than higher-spending systems. This suggests that countries with abundant resources do not necessarily have an efficiency advantage. Against this backdrop, the cluster analysis suggests that structural similarity alone does not robustly explain these efficiency differences. However, in all clusters except Cluster E, mean stage-1 efficiency exceeds stage-2 efficiency. This pattern suggests that performance losses predominantly occur in the transformation of healthcare services into health outcomes rather than in resource generation. Importantly, DEA measures relative technical efficiency conditional on observed inputs and outcomes and therefore does not imply that countries with lower efficiency scores are under-resourced. While care coordination and institutional design may play a role, the present analysis does not allow causal inferences regarding underlying mechanisms. Descriptively, Cluster B exhibits comparatively high overall and stage-specific efficiency score. Many systems in this cluster combine structural features typical of predominantly state-organised systems, including strong primary care orientation, gatekeeping arrangements, and comparatively advanced digital infrastructure. However, these observations should be interpreted cautiously given the absence of statistically significant cluster-level differences. Previous studies suggest that gatekeeping may reduce specialist utilisation and contribute to cost control (e.g., [ 34 ], [ 35 ], [ 36 ]). However, the present study does not directly test these mechanisms, and any interpretation linking institutional coordination structures to efficiency outcomes therefore remains tentative. Cluster E, which comprises countries with high GDP levels and relatively younger populations, demonstrates a comparatively balanced stage-efficiency pattern. While these countries may benefit from favourable socioeconomic conditions, the regression analysis does not provide robust evidence that GDP systematically improves efficiency advantages. Unobserved contextual factors may nevertheless contribute to this pattern. Within Cluster A, several structurally similar countries achieve higher stage-2 efficiency levels, suggesting that Germany’s comparatively weak performance cannot be attributed solely to shared institutional characteristics. Importantly, DEA measures relative technical efficiency conditional on observed inputs and outcomes and therefore does not imply that Germany is under-resourced. Germany’s comparatively weak outcome transformation may be related to service delivery patterns, including high hospital bed density, high inpatient utilisation, and comparatively high rates of avoidable hospitalisations in international comparison [ 37 ]. Prior research has also identified ambulatory care-sensitive conditions as an area of potential efficiency gains in Germany (e.g. [ 38 ]). Because digital maturity enters the first stage of the DEA model as a proxy for structural capacity, its relevance for efficiency depends not only on availability but also on whether it is effectively integrated into care coordination and service delivery. While some digitally advanced countries exhibit favourable efficiency levels, the overall pattern does not reveal a systematic or statistically robust association between digital capacity and efficiency outcomes. In Germany, recent investments in digital infrastructure do not appear to coincide with stronger stage-2 efficiency in the present cross-sectional comparison, suggesting that resource expansion alone is insufficient to improve outcome performance. To further examine whether structural characteristics are systematically associated with efficiency differences, fractional regression models were estimated. These models complement the descriptive cluster analysis by assessing whether the observed patterns are also reflected in multivariable associations. In contrast to the cluster results, health system type is significantly associated with both overall and stage-specific efficiency. Specifically, social health insurance systems (type 3) and etatist social health insurance systems (type 4) exhibited lower efficiency levels compared to national health service systems (type 1), particularly in stage 2. This pattern is consistent with the broader finding that institutional arrangements appear to matter more for outcome transformation than for resource generation. Associations with individual socioeconomic indicators were weaker and less consistent. GDP per capita showed a weak negative association with stage-1 efficiency, while rural population share showed a marginal negative relationship with stage-2 efficiency. No robust associations were observed for income inequality or elderly population share. Given the limited sample size, these regression findings should be interpreted as exploratory rather than confirmatory. Several limitations should be considered. First, both data availability and methodological constraints affect the analysis. International data sets such as OECD Health Statistics offer substantial advantages for cross-country comparisons but may lack harmonised information for very recent developments, such as digitalisation. Second, DEA requires careful variable selection and is sensitive to the sample size, variable specification, and modelling choices. Given the relatively small sample size, the statistical significance of the results is limited. Although the sample covers a wide range of countries with comparable data availability, the results should therefore be interpreted as indicative patterns rather than precise parameter estimates. Third, the analysis is based on a cross-sectional design and therefore captures efficiency patterns at a single point in time. Temporal dynamics in health system performance or potential lagged effects between resource investments and health outcomes cannot be assessed within this framework. Longitudinal analyses could provide additional insights into how efficiency evolves over time. Fourth, the specification of the NDEA model relies on a single intermediate indicator—avoidable hospital admissions related to diabetes—as a proxy for primary care effectiveness. Although this measure is widely used as an indicator of ambulatory care performance, it captures only one dimension of the care process but represents a widely used proxy for primary care effectiveness in international comparisons [ 23 , 24 ]. Data limitations prevented the inclusion of comparable indicators for other conditions. Finally, one of the outcome indicators, self-assessed health status (SAH), refers specifically to individuals in the lowest income quintile. While this choice allows consideration of population groups potentially most affected by health system performance, it may also reflect broader socioeconomic conditions beyond healthcare delivery alone. Conclusion This study assessed the relative efficiency of 30 healthcare systems using a two-stage NDEA framework that distinguishes resource generation from service delivery. The results reveal substantial cross-country variation, with an average overall efficiency level of 0.75 and pronounced efficiency losses in the second stage of the production process. Germany ranks among the lowest-performing systems, primarily due to comparatively weak efficiency in transforming healthcare services into health outcomes. While socioeconomic clusters do not explain systematic efficiency differences, institutional system type appears more closely associated with variation in efficiency, particularly in stage 2. The two-stage network approach allows inefficiencies in resource generation to be distinguished from those in service delivery, thereby providing more policy-relevant insights than traditional one-stage DEA models. These findings suggest that enhancing coordination mechanisms, such as gatekeeping and primary care integration, could yield efficiency gains in outcome transformation, especially in hospital-centric systems like Germany, where high inpatient utilisation persists despite structural expansions [ 37 ]. Similarly, digital maturity requires effective integration into care processes to improve outcomes beyond mere availability. Given the cross-sectional design and limited sample size, results should be interpreted cautiously. Efficiency scores reflect relative performance within the sample and remain sensitive to modelling assumptions and variable selection. Future research could extend these findings using longitudinal data or quasi-experimental approaches to examine temporal dynamics and causal mechanisms underlying stage-specific inefficiencies. Abbreviations DEA Data Envelopment Analysis NDEA Network Data Envelopment Analysis DMU Decision Making Unit OECD Organisation for Economic Co-operation and Development SHARE The Survey of Health, Ageing and Retirement in Europe CA Cluster Analysis WHO World Health Organisation VRS Variable returns to scale CRS Constant returns to scale SAH Self-Assessed Health GP General practitioner Doc (consultations) Doctor consultations SD Standard deviation GDP Gross Domestic Product Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials The data used in this study are derived from publicly available sources, including databases from the OECD (OECD Health Statistics) and the European Commission (Eurostat). The compiled dataset used in this study is provided as additional file 1 and additional file 2. Competing interests The authors declare that they have no competing interests. Funding This article is part of the first author's doctorate in the doctoral college Health Services Research: Health Equity . This is supported by the federal state of Baden-Württemberg, Germany, through state graduate funding. Authors' contributions IF conceived the study, drafted the manuscript, performed the data analysis, and serves as the corresponding author. MC contributed to the conceptual development of the study, critically revised the manuscript, and reviewed the data analysis. EB contributed to the conceptual development and reviewed the manuscript. All authors read and approved the final manuscript. Acknowledgements Not applicable References OECD. Rethinking Health System Performance Assessment: A Renewed Framework. 1st ed. Paris: Organization for Economic Cooperation & Development; 2024. Hollingworth B. The measurement of efficiency and productivity of health care delivery. Health Econ. 2008;17:1107–28. 10.1002/hec.1391 . Papanicolas I, Rajan D, Karanikolos M, Soucat A, Figueras J, editors. Health system performance assessment: a framework for policy analysis. Geneva: World Health Organization; 2022. Gavurova B, Kocisova K, Sopko J. Health system efficiency in OECD countries: dynamic network DEA approach. Health Econ Rev. 2021;11:40. 10.1186/s13561-021-00337-9 . Jacobs R, Smith PC, Street A. Measuring efficiency in health care: Analytic techniques and health policy. 3rd ed. Cambridge [etc.]: Cambridge University Press; 2011. Cacace M, Ettelt S, Mays N, Nolte E. Assessing quality in cross-country comparisons of health systems and policies: towards a set of generic quality criteria. Health Policy. 2013;112:156–62. 10.1016/j.healthpol.2013.03.020 . Mbau R, Musiega A, Nyawira L, Tsofa B, Mulwa A, Molyneux S, et al. Analysing the Efficiency of Health Systems: A Systematic Review of the Literature. Appl Health Econ Health Policy. 2023;21:205–24. 10.1007/s40258-022-00785-2 . Ozcan YA. Health care benchmarking and performance evaluation: An assessment using Data Envelopment Analysis (DEA). 2nd ed. New York, NY: Springer; 2014. Pereira MA, Dinis DC, Ferreira DC, Figueira JR, Marques RC. A network Data Envelopment Analysis to estimate nations’ efficiency in the fight against SARS-CoV-2. Expert Syst Appl. 2022;210:118362. 10.1016/j.eswa.2022.118362 . Kujawska J. Health System Efficiency in European Countries: Network Data Envelopment Analysis Approach. EUROPEAN RESEARCH STUDIES JOURNAL. 2021;XXIV:1095–117. 10.35808/ersj/2176 Simar L, Wilson P. Estimation and inference in two-stage, semi-parametric models of production processes. J Econ. 2007;136:31–64. Böhm K, Tesch-Römer C, Ziese T, editors. Gesundheit und Krankheit im Alter. Berlin: RKI; 2009. Reibling N, Ariaans M, Wendt C. Worlds of Healthcare: A Healthcare System Typology of OECD Countries. Health Policy. 2019;123:611–20. 10.1016/j.healthpol.2019.05.001 . Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. Eur J Oper Res. 1978;2:429–44. 10.1016/0377-2217(78)90138-8 . Herwartz H, Schley K. Improving health care service provision by adapting to regional diversity: An efficiency analysis for the case of Germany. Health Policy. 2018;122:293–300. 10.1016/j.healthpol.2018.01.004 . Färe R, Grosskopf S. Productivity and intermediate products: A frontier approach. Econ Lett. 1996;50:65–70. 10.1016/0165-1765(95)00729-6 . Färe R, Grosskopf S, Network DEA, Socio-Economic. Plann Sci. 2000;34:35–49. 10.1016/S0038-0121(99)00012-9 . Varabyova Y, Müller J-M. The efficiency of health care production in OECD countries: A systematic review and meta-analysis of cross-country comparisons. Health Policy. 2016;120:252–63. 10.1016/j.healthpol.2015.12.005 . Dlouhý M, Havlík P. Efficiency evaluation of 28 health systems by MCDA and DEA. Health Econ Rev. 2024;14:59. 10.1186/s13561-024-00538-y . Rajan D, Koch K, Rohrer K, Soucat A. Governance. In: Papanicolas I, editor. Health System Performance Assessment: A Framework for Policy Analysis. 1st ed. Geneva: World Health Organization; 2022. pp. 43–69. Rothgang H, Cacace M, Frisina L, Grimmeisen S, Schmid A, Wendt C. The State and healthcare: Comparing OECD Countries. Palgrave Macmillan; 2010. [Place of publication not identified]. Cylus J, Sallaku J, Jowett M. Financing. In: Papanicolas I, editor. Health System Performance Assessment: A Framework for Policy Analysis. 1st ed. Geneva: World Health Organization; 2022. pp. 131–56. OECD. Health at a Glance 2023. 2023rd ed. OECD Publishing; 2023. Rosano A. The relationship between avoidable hospitalisation and primary care; 2014. Müller D, Akmatov MK, von Stillfried DG. Lower ambulatory care availability and greater hospital capacity are associated with higher hospital case volumes. Res Health Serv Reg. 2025;4:7. 10.1007/s43999-025-00066-0 . Bitzer E. Die Perspektive der Patientinnen und Patienten - Lebensqualität und Zufriedenheit. Public Health, Gesundheit und Gesundheitswesen. 4th ed. Deutschland: Elsevier; 2023. pp. 521–8. Everitt B, Landau S, Leese M. Cluster analysis. 4th ed. London, New York: Arnold; Oxford University; 2001. Böhm K, Schmid A, Götze R, Landwehr C, Rothgang H. Five types of OECD healthcare systems: Empirical results of a deductive classification. Health Policy. 2013;113:258–69. 10.1016/j.healthpol.2013.09.003 . Papke LE, Wooldridge JM. Econometric Methods for Fractional Response Variables With an Application to 401 (K) Plan Participation Rates. J Appl Econom. 1996;11:619–32. Ramalho EA, Ramalho JJ, Murteira JM, ALTERNATIVE ESTIMATING AND TESTING EMPIRICAL STRATEGIES FOR FRACTIONAL, REGRESSION MODELS. J Economic Surveys. 2011;25:19–68. 10.1111/J.1467-6419.2009.00602.X . OECD Health Statistics. OECD Health Statistics; 2025. Eurostat. Eurostat Database; 2025. European Commission, Capgemini Invent. 2024 digital decade ehealth indicator study: Final report. Luxembourg: Publications Office; 2024. Velasco Garrido M, Zentner A, Busse R. The effects of gatekeeping: a systematic review of the literature. Scand J Prim Health Care. 2011;29:28–38. 10.3109/02813432.2010.537015 . Dusheiko M, Gravelle H, Jacobs R, Smith P. The effect of financial incentives on gatekeeping doctors: Evidence from a natural experiment. J Health Econ. 2006;25:449–78. 10.1016/j.jhealeco.2005.08.001 . Sripa P, Hayhoe B, Garg P, Majeed A, Greenfield G. Impact of GP gatekeeping on quality of care, and health outcomes, use, and expenditure: a systematic review. Br J Gen Pract. 2019;69:e294–303. 10.3399/bjgp19X702209 . Cacace M, Böcken J, Edquist K, Klenk T, Martinez-Jimenez M, Preusker U, et al. Coping with COVID-19: the role of hospital care structures and capacity expansion in five countries. Health Econ Policy Law. 2023;18:186–203. 10.1017/S1744133122000275 . Sundmacher L, Schüttig W. Krankenhausaufenthalte infolge ambulant-sensitiver Diagnosen in Deutschland. In: Klauber J, Geraedts M, Wasem J, editors. Krankenhaus-Report 2016: Schwerpunkt: Ambulant im Krankenhaus. Stuttgart: Schattauer GmbH Verlag für Medizin und Naturwissenschaften; 2016. pp. 149–60. Additional Declarations No competing interests reported. Supplementary Files AdditionalFilesManuscriptFranz.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 13 May, 2026 Reviews received at journal 11 May, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers agreed at journal 14 Apr, 2026 Reviewers invited by journal 14 Apr, 2026 Editor invited by journal 01 Apr, 2026 Editor assigned by journal 31 Mar, 2026 Submission checks completed at journal 31 Mar, 2026 First submitted to journal 27 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9246265","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624280562,"identity":"7a625c7d-2fdb-413e-afd5-99adea43a064","order_by":0,"name":"Ingrid Franz","email":"data:image/png;base64,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","orcid":"","institution":"University of Education Freiburg","correspondingAuthor":true,"prefix":"","firstName":"Ingrid","middleName":"","lastName":"Franz","suffix":""},{"id":624280563,"identity":"a3c443b8-a9e2-463e-913e-92c1f610f15a","order_by":1,"name":"Mirella Cacace","email":"","orcid":"","institution":"Catholic University of Applied Sciences Freiburg","correspondingAuthor":false,"prefix":"","firstName":"Mirella","middleName":"","lastName":"Cacace","suffix":""},{"id":624280564,"identity":"5b8c8d41-0d76-480b-9735-31151d44a808","order_by":2,"name":"Eva Maria Bitzer","email":"","orcid":"","institution":"University of Education Freiburg","correspondingAuthor":false,"prefix":"","firstName":"Eva","middleName":"Maria","lastName":"Bitzer","suffix":""}],"badges":[],"createdAt":"2026-03-27 15:10:53","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9246265/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9246265/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107705701,"identity":"4631e190-cac4-4917-aa7d-394a5952ea9a","added_by":"auto","created_at":"2026-04-24 09:14:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":96723,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTwo-Stage NDEA Model\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSource: own depiction\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-9246265/v1/5ebbb94170b3bfbd6171e677.png"},{"id":107500384,"identity":"7bfd4f60-4441-481d-915e-b0ea134fd54b","added_by":"auto","created_at":"2026-04-22 05:46:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":73656,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStage-Specific Efficiency in Healthcare Systems: Resource Generation vs Service Delivery\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-9246265/v1/3a627746e8c673d12beb92ab.png"},{"id":107709016,"identity":"3587cc71-e843-42fd-8e76-17a901969ca7","added_by":"auto","created_at":"2026-04-24 09:34:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":627852,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9246265/v1/eea729bc-c0bd-4dfe-95ce-42dfc2f74479.pdf"},{"id":107500382,"identity":"ea7d2e01-7706-44da-a75b-b87bac8d0430","added_by":"auto","created_at":"2026-04-22 05:46:37","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":5855396,"visible":true,"origin":"","legend":"","description":"","filename":"AdditionalFilesManuscriptFranz.docx","url":"https://assets-eu.researchsquare.com/files/rs-9246265/v1/56e451a319c0c333e74f657a.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Decomposing Health System Inefficiency: A Cross-National Two-Stage Network Analysis of 30 Nations and the German Case","fulltext":[{"header":"Background","content":"\u003cp\u003eIn view of an ageing population and labour shortages, improving the efficiency of healthcare systems has become a key policy priority across Europe. Despite increasing healthcare expenditure, significant differences in health outcomes persist, even among countries with comparable economic development and health spending [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. These persistent outcome differentials suggest that higher spending alone does not necessarily translate into better health outcomes and point to differences in efficiency with which healthcare systems transform resources into health outcomes. From a policy perspective, understanding the sources of inefficiencies within healthcare systems is crucial to contain costs, allocate resources more effectively, and maintain high-quality care under increasing fiscal and demographic pressure.\u003c/p\u003e \u003cp\u003eA growing body of literature has examined healthcare system efficiency using cross-country comparisons, often applying data envelopment analysis (DEA) or related approaches [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] as a single production process. While these studies provide important insights into efficiency, their aggregated perspective limits their ability to identify where inefficiencies arise within the healthcare system and may therefore offer limited guidance for policy interventions. To address this limitation, we apply a two-stage network DEA (NDEA) framework that distinguishing between resource generation and service delivery. This structure follows the analytical framework for healthcare system performance, proposed by Papanicolas et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], which conceptualises health outcomes as the result of interconnected production stages [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Building on this perspective, we test whether inefficiency primarily occurs in the transformation from service delivery to outcomes rather than in resource generation. This expectation is consistent with evidence that bottlenecks often occur in care coordination and the translation of service volume into health gains.\u003c/p\u003e \u003cp\u003eWithin this approach, efficiency is conceptualised as input-oriented technical efficiency, which is achieved when resources are allocated such that inputs are minimised for a given level of outputs [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Resource generation is proxied by health expenditure and structural capacity (workforce, beds, digital infrastructure), while service delivery is measured by consultations and bed-days; outcomes are captured by treatable mortality and self-assessed health.\u003c/p\u003e \u003cp\u003eCross-country comparisons are particularly informative when socio-economic and institutional contexts are explicitly considered [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. We therefore complement the two-stage efficiency assessment by analysing patterns across clusters of countries that share similar demographic, economic and regulatory contexts, and by comparing established health system types. We subsequently examine how these contextual factors are associated with stage-specific efficiency differences and discuss related policy implications. Although the empirical strategy relies on a cross-country comparison, particular attention is devoted to the German healthcare system in order to contextualise the results within one of Europe\u0026rsquo;s largest social health insurance systems.\u003c/p\u003e \u003cp\u003eThis study addresses three research questions:\u003c/p\u003e \u003cp\u003e(1) How efficient are healthcare systems in transforming resources into services and outcomes across two functional stages (resource generation and service delivery)?\u003c/p\u003e \u003cp\u003e(2) Do countries sharing similar socio-economic and regulatory contexts exhibit comparable stage-specific efficiency profiles?\u003c/p\u003e \u003cp\u003e(3) Which contextual factors are associated with stage-specific efficiency differences?\u003c/p\u003e"},{"header":"Review of the literature","content":"\u003cp\u003eEfficiency measurement in health economics frequently relies on DEA to benchmark health systems across countries or regions [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Early contributions predominantly used single-stage \u0026ldquo;black-box\u0026rdquo; models, which treat national health systems as unified production units mapping aggregate inputs, such as total health expenditure or health workforce, onto outcome indicators like life expectancy [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. While this literature documented substantial cross-country variation in efficiency levels (e.g. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]) and highlighted that higher spending does not automatically translate into better outcomes [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], it offers only limited insight into where inefficiencies arise within the system. More recent studies therefore apply network or multi-stage DEA frameworks to distinguish conceptually different subprocesses within healthcare (e.g. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]).\u003c/p\u003e \u003cp\u003eKujawska (2021) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], for example, applies a NDEA to European countries by modelling a \u0026ldquo;lifestyle\u0026rdquo; component alongside a healthcare component, and shows that efficiency scores can differ markedly between these subprocesses within the same country. Other contributions apply NDEA to specific areas, such as prevention-to-treatment chains or to distinct performance domains (e.g. disease-specific care pathways) (e.g. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]). Taken together, this literature illustrates that NDEA offers a flexible framework for opening the \u0026ldquo;black box\u0026rdquo; of health systems and attributing inefficiencies to specific stages of the production process.\u003c/p\u003e \u003cp\u003eHowever, many existing network structures are organised around specific determinants (e.g. lifestyle factors) or broad domains (public health vs. medical care) rather than around core health system functions. This reduces policy interpretability because inefficiencies cannot be directly linked to functional levers that policymakers commonly address. Contemporary health system performance frameworks, building on work by the WHO and related approaches, distinguish between resource generation (e.g. health workforce) and service delivery, assuming that resources primarily contribute to health outcomes through the function of service delivery [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs mentioned earlier, we develop a two-stage NDEA model for national health systems that separates (i) resource generation from (ii) service delivery in order to bridge this gap. This structure aligns with the health system performance framework proposed by Papanicolas et al. (2022) [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] and allows for a stage-specific efficiency assessment.\u003c/p\u003e \u003cp\u003ePrevious cross-country efficiency studies have often incorporated contextual variables directly into second-stage regressions (e.g. [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]). However, structural and socioeconomic characteristics such as income distribution, demographic composition, or institutional system type do not constitute healthcare production inputs in a strict sense. Including them directly in the DEA model would risk conflating production technology with environmental conditions.\u003c/p\u003e \u003cp\u003eBy contrast, cluster analysis allows grouping countries according to shared structural constellations (e.g. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]) without altering the underlying efficiency frontier. In this study, clustering therefore serves as a contextualisation strategy rather than as a component of the efficiency measurement itself.\u003c/p\u003e "},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003cp\u003eThe study comprises three analytical steps. First, the technical efficiency of national healthcare systems is assessed using a two-stage NDEA. Second, countries are clustered to identify structural similarities in socioeconomic and healthcare system characteristics. Finally, the relationship between structural characteristics and efficiency scores is examined using fractional regression models.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTwo-stage NDEA\u003c/h3\u003e\n\u003cp\u003eDEA is a widely used non-parametric method for cross-country efficiency analysis, derived from production theory and initially introduced by Charnes et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. As a non-parametric, linear programming technique, DEA evaluates the relative efficiency of decision-making units (DMUs) by comparing their ability to convert inputs (e.g., health expenditure, digital infrastructure) into outputs or outcomes. In this study, \u0026ldquo;outputs\u0026rdquo; refer to the immediate results of healthcare services, whereas \u0026ldquo;outcomes\u0026rdquo; capture their effects on patients\u0026rsquo; and populations\u0026rsquo; health status [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAn empirical production frontier is defined by the most efficient country or countries within the sample. Countries located on the efficiency frontier receive an efficiency score of one, while countries below the frontier receive efficiency scores between zero and one [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDEA is well suited for analysing the efficiency of healthcare systems, as it does not require any prior assumptions about the functional form or parameterisation. Standard DEA models yield a single efficiency score for the healthcare system as a whole. In contrast, a two-stage NDEA model allows the estimation of both overall efficiency and stage-specific efficiencies, where outputs from one stage serve as inputs to subsequent stages.\u003c/p\u003e \u003cp\u003eThe NDEA is based on F\u0026auml;re and Grosskopf [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. We opted for an input-oriented DEA model assuming constant returns to scale (CRS), treating scale as part of the production technology rather than as a factor to be controlled for [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. The orientation is appropriate because healthcare systems typically have limited control over outputs and outcomes, whereas inputs can, at least potentially, be influenced by policy decisions.\u003c/p\u003e \u003cp\u003eSeveral robustness checks were conducted, including alternative scale assumptions (CRS vs. VRS), alternative model orientation (input vs. output), and bootstrapped DEA models with 2,000 replications. Rank correlation tests were used to assess the stability of efficiency rankings. All DEA and NDEA analyses were conducted using \u0026ldquo;R\u0026rdquo; software (version 4.4.1).\u003c/p\u003e \u003cp\u003eThe number of variables included in the model was deliberately limited to maintain sufficient discriminatory power relative to the number of DMUs and to avoid the curse of dimensionality in DEA. Variable selection was guided by the literature on economic efficiency measurement in healthcare. In particular, we draw on the systematic reviews by Varabyova and M\u0026uuml;ller [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] and Mbau et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] \u0026ndash; updated by Dlouh\u0026yacute; and Havl\u0026iacute;k [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u0026ndash; for the selection of input and output/outcome variables. The selection of variables was undertaken in accordance with the conceptual framework developed by Papanicolas [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eGuided by the health system performance framework and data availability, the overall concept of the two-stage NDEA model is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The framework distinguishes three core system functions, financing, resource generation, and service delivery, that ultimately shape the efficiency of service delivery in healthcare system performance [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. These functions are encompassed by the \u0026lsquo;governance\u0026rsquo; function, which in turn is broken down to four sub-functions: policy and vision, stakeholder voice, information and intelligence, legislation and regulation [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Governance is not explicitly included in the model for two reasons. First, no suitable cross-country indicator is available that captures governance or its sub-functions in a comparable way. Second, governance can be interpreted less as an input and more as a contextual determinant of system performance.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the two-stage design disentangles the efficiency of \u0026lsquo;resource generation\u0026rsquo; in the first stage from the efficiency of \u0026ldquo;service delivery\u0026rdquo; in the second stage.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSource: own depiction\u003c/p\u003e \u003cp\u003eIn order to align our two-stage model with the three core functions of the framework, financing, resource generation, and service delivery, we combine the function of financing (healthcare expenditures) with the inputs of \u0026ldquo;resource generation\u0026rdquo;, i.e. the access to digital health infrastructure and the density of GPs and hospital beds per 1,000 population. This is justified insofar as all resource generation must be financed by healthcare expenditures, and conversely, all financial healthcare resources ultimately flow into resource generation and are used for the purchase of goods and services [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates this graphically by depicting \u0026lsquo;healthcare expenditures\u0026rsquo; somewhat apart from the other elements. The intermediate output at the first stage is the avoidable hospitalisation rate due to diabetes. Such admissions are largely avoidable and therefore commonly used as a marker of quality and access to primary care [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Lower avoidable hospitalisation rates are expected were digital health infrastructure and appropriate supply of primary care resources support effective disease management, while excessive hospital capacity may increase the risk of avoidable admissions [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. As avoidable hospitalisations represent an undesirable output, the indicator was transformed accordingly so that lower rates indicate better performance. Comparable measures for other conditions were not consistently available across countries.\u003c/p\u003e \u003cp\u003eAt the second stage of our model, we used doctor visits and bed-days as inputs for \u0026ldquo;service delivery\u0026rdquo;. In addition, avoidable hospitalisation due to diabetes, the intermediate output at the first stage was also used as an input in the second stage. Thus, the first stage captures the efficiency of the resources generation in producing quality healthcare, whereas the second stage reflects patients\u0026rsquo; use of, and thus access to, medical care, even if it cannot be ascertained whether use is always medically justified or not.\u003c/p\u003e \u003cp\u003eThe outcomes at the second stage were measured by two factors: treatable mortality and self-assessed health status (SAH). Treatable (or amenable) mortality is a well-established indicator of healthcare system performance, also reflecting the effectiveness of service delivery, while SAH is widely used as a patient-reported outcome measure [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\n\u003ch3\u003eCluster Analysis\u003c/h3\u003e\n\u003cp\u003eCluster analysis (CA) is a statistical technique used to group objects or cases into clusters based on their similarity, allowing for the identification of patterns or structures within complex datasets. A cluster can be defined as a group where the characteristics within the group are as similar as possible, while being as distinct as possible from other groups [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Given the combination of continuous and categorical variables and the unknown number of clusters, a hierarchical agglomerative clustering approach using Complete Linkage method and Gower\u0026rsquo;s dissimilarity measure was applied. In Complete Linkage, the distance between two clusters is defined as the largest distance between any pair of observations belonging to the two clusters, and clusters are merged stepwise such that this maximum inter-cluster distance is minimised at each step [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Agglomerative methods proceed step by step, with each unit initially representing a single cluster, and end with all objects being grouped together in one large cluster. The optimal number of clusters was determined using the Calinski\u0026ndash;Harabasz criterion, the Duda\u0026ndash;Hart stopping rule, and visual inspection of the dendrogram. Cluster robustness was assessed by varying country inclusion and applying alternative clustering methods.\u003c/p\u003e \u003cp\u003eThe countries were grouped based on six variables. In contrast to previous studies, which employed a range of indicators, including characteristics of the healthcare system and preventive measures [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], we used: (1) GDP per capita, (2) Gini coefficient, (3) percentage of the population aged 65 and older, (4) share of population living in rural areas, (5) a composite index of preventive health policies (alcohol, smoking, obesity), and (6) a typology of healthcare system models according to B\u0026ouml;hm et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] and [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. These variables capture core socioeconomic and system-level factors.\u003c/p\u003e \u003cp\u003eThe resulting clusters provide a structural context for interpreting efficiency differences across countries and allow efficiency scores to be compared among systems with broadly similar socioeconomic and institutional characteristics. CA was conducted with STATA Version BE 19.\u003c/p\u003e\n\u003ch3\u003eFractional Regression Analysis\u003c/h3\u003e\n\u003cp\u003eTo examine whether institutional and socioeconomic characteristics are associated with efficiency differences, fractional regression models were estimated [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. As DEA efficiency scores are bounded between zero and one, conventional linear regression models are inappropriate due to potential heteroskedasticity and the possibility of predicted values outside the admissible range. We therefore apply a fractional logit model with a logit link function, originally proposed by Papke and Wooldridge [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], which is specifically designed for proportion-type dependent variables constrained to the unit interval [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSeparate models were estimated for overall efficiency as well as stage-1 and stage-2 efficiency scores. Robust standard errors were used to account for potential heteroskedasticity. Given the relatively small sample size and the cross-sectional design, the regression analysis is exploratory and aims to identify associations rather than causal relationships. Cluster analysis and health system typology capture partially overlapping but conceptually distinct structural dimensions.\u003c/p\u003e\n\u003ch3\u003eData source\u003c/h3\u003e\n\u003cp\u003eOur analysis primarily relies on data from OECD Health Statistics (2025) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Missing values were complemented using data from Eurostat (2025) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], and one key variable was obtained from the European Commission (2023) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. A detailed overview of variables, data sources, and availability is provided in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe final sample comprises 30 countries, predominantly located in Europe, with two additional cases from outside the region. Most countries are OECD members.\u003c/p\u003e \u003cp\u003eCountry inclusion was driven by the availability of complete and harmonised data for all DEA variables in 2022. Restricting the sample to countries with comparable data ensures internal consistency of the efficiency frontier and avoids distortions due to missing information. A detailed overview of the variables used in the DEA and their values for each country, including the respective data sources, is provided in the additional file 1. As two countries (Turkey and Israel) were identified as outliers in the CA, fractional regressions are based on 28 countries.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVariables and Data Sources for the 2-stage NDEA\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eStage\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eVariable Name\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eRole\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eDescription\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eUnit\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eSource\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHealthcare Expenditures\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePublic and mandatory health expenditure per capita, PPP adjusted and expressed in constant prices\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUSD PPP per capita\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDigital Health Infrastructure Index\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eComposite eHealth score capturing national digital health capacity across thematic layers (e.g., electronic records, interoperability, e-prescriptions, data exchange)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eIndex score (0\u0026ndash;100)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGP Density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003enumber of general practitioners per 1,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePer 1,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHospital Bed Density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNumber of hospital beds per 1,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePer 1,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAvoidable Hospital Admissions\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIntermediate output/ Input stage 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003enumber of avoidable hospital admissions related to diabetes per 100,000 population (undesirable output; transformed for DEA)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePer 100,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBed-Days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003etotal number of inpatient hospital days per person in the population per year\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDays per population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDoc Consultations\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eaverage number of physician consultations per capita per year\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eVisits per capita\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTreatable Mortality\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOutcome\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMortality from causes amenable to timely and effective healthcare\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePer 100,000 population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1, 3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSelf-Assessed Health Status (SAH)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOutcome\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShare of individuals in the lowest income quintile reporting \u0026ldquo;very good\u0026rdquo; or \u0026ldquo;excellent\u0026rdquo; health\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e% of respondents\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1, 3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eLegend\u003c/h2\u003e \u003cp\u003e1 OECD \u003cem\u003eHealth Statistics\u003c/em\u003e (2025) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e2 European Commission (2023) (Digital Health Infrastructure Index, composite score) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e3 Eurostat Database (2025) [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/p\u003e \u003cp\u003e4 Values inverted for analysis\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarises descriptive statistics for the input, intermediate output, and outcome variables included in the two-stage NDEA model across the 30 countries. Considerable variation is observed across all variables, indicating substantial cross-country differences in resource endowment, service delivery patterns, and health outcomes. In terms of resource generation inputs, per capita health expenditure and hospital bed density display particularly wide dispersion. Germany records the highest values for both indicators within the sample. The intermediate output \u0026ldquo;avoidable hospitalisations\u0026rdquo; and service delivery indicators (bed-days and consultations) exhibit substantial heterogeneity. Germany again ranks among the countries with the highest bed-day intensity. In terms of final health outcomes, Germany performs below the sample mean for both outcome indicators.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive Statistics of DEA Variables\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMin\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMax\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGermany\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHealthcare Expenditures\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2347.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1013.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e724.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4347.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4347.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDigital Health\u003c/p\u003e \u003cp\u003eInfrastructure Index\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e16.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e100.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e87.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGP Density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHospital Bed Density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAvoidable Hospital\u003c/p\u003e \u003cp\u003eAdmissions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e108.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e236.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e179.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBed-Days\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDoc Consultation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e9.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTreatable Mortality\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e80.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e40.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e179.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e66.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelf-Assessed\u003c/p\u003e \u003cp\u003eHealth Status (SAH)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e58.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e98.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e51.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003eStage-specific efficiency\u003c/h3\u003e\n\u003cp\u003eStage-specific efficiencies reveal notable differences between resource generation (stage 1) and service delivery (stage 2), as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The mean efficiency score for the first stage is 0.85, exceeding the mean efficiency at the second stage (0.65) and the overall efficiency score, suggesting greater performance losses in the transformation of services into health outcomes. For 20 of the 30 countries, stage-1 efficiency exceeds stage-2 efficiency, suggesting that efficiency losses predominantly occur in the second stage of the production process. Germany follows this general pattern. Its overall efficiency score lies below the sample mean and ranks 29th out of 30 countries. The efficiency gap is particularly pronounced in stage 2 (efficiency value 0.29), where Germany performs substantially weaker relative to most other countries under consideration. While the first stage has an average efficiency of 0.85, this drops to just 0.65 in the second stage. This illustrates how much more difficult it is to achieve an efficient outcome transformation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eCaption: The figure plots stage-1 (resource generation) against stage-2 (service delivery) efficiency scores for all countries. The dashed 45-degree line indicates equal efficiency across stages. Most countries lie below the line, indicating lower efficiency in service delivery than in resource generation.\u003c/em\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eOverall efficiency\u003c/h2\u003e \u003cp\u003eAs illustrated in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, overall efficiency scores derived from the two-stage NDEA model range from 0.46 to 1, with a sample mean of 0.75. Iceland, Israel, and Sweden are located on the efficiency frontier and thus represent the most efficient systems within the sample. Fifteen countries exhibit overall efficiency scores above the sample mean. Germany\u0026rsquo;s overall efficiency score is 0.51, placing it among the lowest-performing systems.\u003c/p\u003e \u003cp\u003eRobustness checks based on alternative network DEA specifications (CRS vs. VRS; input vs. output orientation; bootstrapped DEA models with 2,000 replications) broadly confirm the main pattern of higher stage-1 than stage-2 efficiency and the comparatively low relative position of Germany (see additional file 3). In addition, bootstrap inference for the overall DEA model with 2,000 replications shows that the relative position of Germany is robust to sampling variation. Spearman rank correlations across network DEA specifications are uniformly positive, ranging from 0.43 to 0.91 (median ρ\u0026thinsp;=\u0026thinsp;0.78), indicating a broadly stable ordering of DMUs across alternative model assumptions (see additional file 4). The highest agreement is observed between input- and output-oriented specifications under CRS, suggesting that the choice of orientation has only a limited effect on the ranking. Correlations involving VRS specifications are more moderate, indicating that the rankings are somewhat sensitive to assumptions regarding returns to scale and suggesting that scale effects contribute to cross-country differences in efficiency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eOverall and Stage-Specific Efficiency Scores\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCountry\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1. Stage Efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2. Stage Efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOverall Efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRank overall\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIceland\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIsrael\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSweden\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNetherlands\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItaly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNorway\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTurkey\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePortugal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUnited Kingdom\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDenmark\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMalta\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlovenia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBelgium\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFinland\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRomania\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEstonia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHungary\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIreland\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSwitzerland\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoland\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLithuania\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLatvia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCroatia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLuxembourg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCzechia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlovakia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGermany\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.72\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.29\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.51\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e29\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAustria\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003emean\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.85\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.65\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.75\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003emin\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.51\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.24\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e0.46\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003emax\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e1.00\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.00\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1.00\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eCluster Analysis\u003c/h2\u003e \u003cp\u003eWhile the NDEA results reveal cross-country differences in efficiency, they do not account for structural similarities between health systems. To provide contextual orientation, a hierarchical cluster analysis based on socioeconomic and institutional characteristics was conducted.\u003c/p\u003e \u003cp\u003eThe analysis identifies five distinct clusters comprising four to eight countries each, as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Two countries (Turkey and Israel) were found as outliers. Alternative cluster solutions (k\u0026thinsp;=\u0026thinsp;4 and k\u0026thinsp;=\u0026thinsp;6) yielded less interpretable group structures and lower cluster validity indices (refer to additional file 5a, 5b and 5c). The clusters differ primarily with respect to healthcare system type, economic development, demographic structure, rural population share, and the prevention index. Cluster A predominantly consist of social health insurance systems; Cluster B is mainly composed of state-organised healthcare systems with comparatively low rural population shares; Cluster C combines high prevention index values with etatist social health insurance systems; Cluster D is characterised by lower economic resources and the highest mean share of rural population; Cluster E includes countries with the highest level of economic development and the smallest proportion of elderly individuals in comparison with the other clusters.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCluster Characteristics (mean values)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCluster\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGDP per Capita\u003c/p\u003e \u003cp\u003e(USD)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGini\u003c/p\u003e \u003cp\u003eCoeff.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRural Population\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eElderly Population\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePrevention\u003c/p\u003e \u003cp\u003eIndex\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003ePre-dominant Health\u003c/p\u003e \u003cp\u003eSystem\u003c/p\u003e \u003cp\u003eTypes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eStage 1 Efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eStage 2 Efficiency\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eOverall Efficiency\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e21.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e47.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSocietal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e68.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eState\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59452\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e18.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e73.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eEtatist\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45263\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e47.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e61.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eEtatist\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e120954\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e30.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e15.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e68.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMixed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eLegend: Cluster means for socioeconomic indicators and efficiency scores from the two-stage NDEA model are presented. Stage 1 captures resource generation efficiency; Stage 2 captures service delivery efficiency. Efficiency scores are bounded between 0 and 1.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eHealth System Types are classified according to B\u0026ouml;hm et al (2013), distinguishing systems by financing, provision, and regulation. \u0026ldquo;State\u0026rdquo; systems are tax-funded with public provision; \u0026ldquo;Societal\u0026rdquo; systems rely on social health insurance; \u0026ldquo;Etatist\u0026rdquo; systems combine social insurance with strong state control. Cluster E combines the types: \u0026ldquo;State\u0026rdquo;, \u0026ldquo;Societal\u0026rdquo; and \u0026ldquo;Etatist\u0026rdquo;.\u003c/em\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eCountry-level data are provided in the Appendix.\u003c/em\u003e \u003c/p\u003e \u003cp\u003eTo contextualise potential production differences, cluster-specific means of DEA input and outcome variables were compared (see additional file 6 \u003cem\u003efor details including tests of differences\u003c/em\u003e). Cluster A shows significantly higher bed density consultation frequency (p\u0026thinsp;\u0026lt;\u0026thinsp;0,05) in comparison to Cluster B, whereas latter combines comparatively higher GP density and digital maturity. The mean values for health care expenditures, hospital beds, and consultations in Cluster C are comparatively higher than those in Cluster B, although the outcome measures lag behind those of Cluster B. Cluster D exhibits lowest average expenditure levels and highest treatable mortality in comparison to the other Clusters. Conversely, Cluster E exhibits the highest mean healthcare expenditures and the lowest treatable mortality rate, while concurrently demonstrating the highest rate of self-assessed health status.\u003c/p\u003e \u003cp\u003eDespite observable mean differences, Kruskal\u0026ndash;Wallis tests do not indicate statistically significant differences in overall efficiency across clusters (p\u0026thinsp;=\u0026thinsp;0.17). However, fractional logit models suggest weak evidence of cluster differences for overall efficiency (Wald χ\u0026sup2; = 8.46, p\u0026thinsp;=\u0026thinsp;0.076) and stage-2 efficiency (Wald χ\u0026sup2; = 9.26, p\u0026thinsp;=\u0026thinsp;0.055), whereas no differences are observed for stage-1 efficiency (p\u0026thinsp;=\u0026thinsp;0.63). Taken together, the results indicate that cluster membership is not robustly associated with stage-1 efficiency and only weakly associated with overall and stage-2 efficiency. Small cluster sizes likely contribute to limited statistical power.\u003c/p\u003e \u003cp\u003eAcross Clusters A to D, stage-1 efficiency exceeds stage-2 efficiency, whereas Cluster E exhibits a more balanced stage-specific pattern. Germany is assigned to Cluster A and mirrors the general pattern of comparatively lower second-stage efficiency within this group. However, its efficiency score ranks among the lowest within the cluster, indicating that structural similarity alone does not account for its comparatively weak performance.\u003c/p\u003e \u003cp\u003eIn contrast to the cluster results, health system type is significantly associated with efficiency levels. Fractional logit models indicate statistically significant differences across system types for stage-1 efficiency (Wald χ\u0026sup2; = 15.59, p\u0026thinsp;=\u0026thinsp;0.0036), stage-2 efficiency (Wald χ\u0026sup2; = 16.10, p\u0026thinsp;=\u0026thinsp;0.0029), and overall efficiency (Wald χ\u0026sup2; = 30.71, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Marginal effects indicate that system types 3 (social health insurance systems) and 4 (etatist social health insurance systems) are associated with markedly lower expected stage-2 efficiency compared to type 1 (Δ = -0.39 and \u0026minus;\u0026thinsp;0.31, respectively). Non-parametric Kruskal\u0026ndash;Wallis tests confirm significant differences for stage-2 efficiency (p\u0026thinsp;=\u0026thinsp;0.034) and overall efficiency (p\u0026thinsp;=\u0026thinsp;0.005).\u003c/p\u003e \u003cp\u003eExploratory fractional logit models examining individual structural indicators show limited and partly inconsistent associations. GDP per capita is negatively associated with stage-1 efficiency (p\u0026thinsp;=\u0026thinsp;0.012), while rural population share displays a marginal negative association with stage-2 efficiency (p\u0026thinsp;=\u0026thinsp;0.065). The prevention index is weakly positively related to overall efficiency (p\u0026thinsp;=\u0026thinsp;0.089). No statistically significant associations are observed for income inequality or elderly population share.\u003c/p\u003e \u003cp\u003eGiven the small sample size and multiple exploratory tests, regression results are interpreted as exploratory and were not adjusted for multiple comparisons. Results should be interpreted with caution.\u003c/p\u003e \u003cp\u003eOverall, structural clusters do not robustly explain systematic efficiency, although weak evidence suggests that some disparities may be related to cluster affiliation. In contrast, institutional system type appears more closely related to both overall and stage-specific efficiency. Associations with individual socioeconomic indicators remain weak and statistically fragile. Germany belongs to health system type 3 (social health insurance systems), which exhibits comparatively lower stage-2 efficiency. This aligns with Germany\u0026rsquo;s below-average second-stage efficiency observed in the NDEA results.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eSeveral frontier countries combine comparatively favourable health outcomes with less resource intensity than higher-spending systems. This suggests that countries with abundant resources do not necessarily have an efficiency advantage. Against this backdrop, the cluster analysis suggests that structural similarity alone does not robustly explain these efficiency differences. However, in all clusters except Cluster E, mean stage-1 efficiency exceeds stage-2 efficiency. This pattern suggests that performance losses predominantly occur in the transformation of healthcare services into health outcomes rather than in resource generation. Importantly, DEA measures relative technical efficiency conditional on observed inputs and outcomes and therefore does not imply that countries with lower efficiency scores are under-resourced. While care coordination and institutional design may play a role, the present analysis does not allow causal inferences regarding underlying mechanisms.\u003c/p\u003e \u003cp\u003eDescriptively, Cluster B exhibits comparatively high overall and stage-specific efficiency score. Many systems in this cluster combine structural features typical of predominantly state-organised systems, including strong primary care orientation, gatekeeping arrangements, and comparatively advanced digital infrastructure. However, these observations should be interpreted cautiously given the absence of statistically significant cluster-level differences. Previous studies suggest that gatekeeping may reduce specialist utilisation and contribute to cost control (e.g., [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]). However, the present study does not directly test these mechanisms, and any interpretation linking institutional coordination structures to efficiency outcomes therefore remains tentative.\u003c/p\u003e \u003cp\u003eCluster E, which comprises countries with high GDP levels and relatively younger populations, demonstrates a comparatively balanced stage-efficiency pattern. While these countries may benefit from favourable socioeconomic conditions, the regression analysis does not provide robust evidence that GDP systematically improves efficiency advantages. Unobserved contextual factors may nevertheless contribute to this pattern.\u003c/p\u003e \u003cp\u003eWithin Cluster A, several structurally similar countries achieve higher stage-2 efficiency levels, suggesting that Germany\u0026rsquo;s comparatively weak performance cannot be attributed solely to shared institutional characteristics. Importantly, DEA measures relative technical efficiency conditional on observed inputs and outcomes and therefore does not imply that Germany is under-resourced. Germany\u0026rsquo;s comparatively weak outcome transformation may be related to service delivery patterns, including high hospital bed density, high inpatient utilisation, and comparatively high rates of avoidable hospitalisations in international comparison [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Prior research has also identified ambulatory care-sensitive conditions as an area of potential efficiency gains in Germany (e.g. [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]).\u003c/p\u003e \u003cp\u003eBecause digital maturity enters the first stage of the DEA model as a proxy for structural capacity, its relevance for efficiency depends not only on availability but also on whether it is effectively integrated into care coordination and service delivery. While some digitally advanced countries exhibit favourable efficiency levels, the overall pattern does not reveal a systematic or statistically robust association between digital capacity and efficiency outcomes. In Germany, recent investments in digital infrastructure do not appear to coincide with stronger stage-2 efficiency in the present cross-sectional comparison, suggesting that resource expansion alone is insufficient to improve outcome performance. To further examine whether structural characteristics are systematically associated with efficiency differences, fractional regression models were estimated. These models complement the descriptive cluster analysis by assessing whether the observed patterns are also reflected in multivariable associations. In contrast to the cluster results, health system type is significantly associated with both overall and stage-specific efficiency. Specifically, social health insurance systems (type 3) and etatist social health insurance systems (type 4) exhibited lower efficiency levels compared to national health service systems (type 1), particularly in stage 2. This pattern is consistent with the broader finding that institutional arrangements appear to matter more for outcome transformation than for resource generation.\u003c/p\u003e \u003cp\u003eAssociations with individual socioeconomic indicators were weaker and less consistent. GDP per capita showed a weak negative association with stage-1 efficiency, while rural population share showed a marginal negative relationship with stage-2 efficiency. No robust associations were observed for income inequality or elderly population share. Given the limited sample size, these regression findings should be interpreted as exploratory rather than confirmatory.\u003c/p\u003e \u003cp\u003eSeveral limitations should be considered. First, both data availability and methodological constraints affect the analysis. International data sets such as OECD Health Statistics offer substantial advantages for cross-country comparisons but may lack harmonised information for very recent developments, such as digitalisation. Second, DEA requires careful variable selection and is sensitive to the sample size, variable specification, and modelling choices. Given the relatively small sample size, the statistical significance of the results is limited. Although the sample covers a wide range of countries with comparable data availability, the results should therefore be interpreted as indicative patterns rather than precise parameter estimates. Third, the analysis is based on a cross-sectional design and therefore captures efficiency patterns at a single point in time. Temporal dynamics in health system performance or potential lagged effects between resource investments and health outcomes cannot be assessed within this framework. Longitudinal analyses could provide additional insights into how efficiency evolves over time.\u003c/p\u003e \u003cp\u003eFourth, the specification of the NDEA model relies on a single intermediate indicator\u0026mdash;avoidable hospital admissions related to diabetes\u0026mdash;as a proxy for primary care effectiveness. Although this measure is widely used as an indicator of ambulatory care performance, it captures only one dimension of the care process but represents a widely used proxy for primary care effectiveness in international comparisons [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Data limitations prevented the inclusion of comparable indicators for other conditions.\u003c/p\u003e \u003cp\u003eFinally, one of the outcome indicators, self-assessed health status (SAH), refers specifically to individuals in the lowest income quintile. While this choice allows consideration of population groups potentially most affected by health system performance, it may also reflect broader socioeconomic conditions beyond healthcare delivery alone.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study assessed the relative efficiency of 30 healthcare systems using a two-stage NDEA framework that distinguishes resource generation from service delivery. The results reveal substantial cross-country variation, with an average overall efficiency level of 0.75 and pronounced efficiency losses in the second stage of the production process. Germany ranks among the lowest-performing systems, primarily due to comparatively weak efficiency in transforming healthcare services into health outcomes.\u003c/p\u003e \u003cp\u003eWhile socioeconomic clusters do not explain systematic efficiency differences, institutional system type appears more closely associated with variation in efficiency, particularly in stage 2. The two-stage network approach allows inefficiencies in resource generation to be distinguished from those in service delivery, thereby providing more policy-relevant insights than traditional one-stage DEA models.\u003c/p\u003e \u003cp\u003eThese findings suggest that enhancing coordination mechanisms, such as gatekeeping and primary care integration, could yield efficiency gains in outcome transformation, especially in hospital-centric systems like Germany, where high inpatient utilisation persists despite structural expansions [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Similarly, digital maturity requires effective integration into care processes to improve outcomes beyond mere availability.\u003c/p\u003e \u003cp\u003eGiven the cross-sectional design and limited sample size, results should be interpreted cautiously. Efficiency scores reflect relative performance within the sample and remain sensitive to modelling assumptions and variable selection. Future research could extend these findings using longitudinal data or quasi-experimental approaches to examine temporal dynamics and causal mechanisms underlying stage-specific inefficiencies.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eDEA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eData Envelopment Analysis\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eNDEA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eNetwork Data Envelopment Analysis\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eDMU\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eDecision Making Unit\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eOECD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eOrganisation for Economic Co-operation and Development\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSHARE\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eThe Survey of Health, Ageing and Retirement in Europe\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCA\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eCluster Analysis\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eWHO\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eWorld Health Organisation\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eVRS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eVariable returns to scale\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eCRS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eConstant returns to scale\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSAH\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSelf-Assessed Health\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eGP\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eGeneral practitioner\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eDoc (consultations)\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eDoctor consultations\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSD\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eStandard deviation\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eGDP\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eGross Domestic Product\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data used in this study are derived from publicly available sources, including databases from the OECD (OECD Health Statistics) and the European Commission (Eurostat). The compiled dataset used in this study is provided as additional file 1 and additional file 2.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis article is part of the first author\u0026apos;s doctorate in the doctoral college \u003cem\u003eHealth Services Research: Health Equity\u003c/em\u003e. This is supported by the federal state of Baden-W\u0026uuml;rttemberg, Germany, through state graduate funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIF conceived the study, drafted the manuscript, performed the data analysis, and serves as the corresponding author. MC contributed to the conceptual development of the study, critically revised the manuscript, and reviewed the data analysis. EB contributed to the conceptual development and reviewed the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eOECD. Rethinking Health System Performance Assessment: A Renewed Framework. 1st ed. Paris: Organization for Economic Cooperation \u0026amp; Development; 2024.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHollingworth B. The measurement of efficiency and productivity of health care delivery. 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Stuttgart: Schattauer GmbH Verlag f\u0026uuml;r Medizin und Naturwissenschaften; 2016. pp. 149\u0026ndash;60.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-health-services-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bhsr","sideBox":"Learn more about [BMC Health Services Research](http://bmchealthservres.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/BHSR/default.aspx","title":"BMC Health Services Research","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Health system efficiency, Two-stage Network DEA, Cross-country comparison, Structural clustering, Efficiency determinants, Germany’s health care efficiency","lastPublishedDoi":"10.21203/rs.3.rs-9246265/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9246265/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e\u003cbr\u003e\nIn the context of demographic ageing, rising healthcare expenditure, and persistent health outcome differences, improving the efficiency of healthcare systems has become a key policy priority across many high-income countries. While previous cross-country studies often assess overall system efficiency, they provide limited insight into where inefficiencies arise within the healthcare production process. This study therefore examines healthcare system efficiency across two functional stages - resource generation and service delivery - and investigates whether structural country characteristics are associated with efficiency patterns.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e\u003cbr\u003e\nA two-stage Network Data Envelopment Analysis (NDEA) was applied to assess the efficiency of 30 national healthcare systems using cross-sectional data for 2022. Stage 1 represents resource generation and includes healthcare expenditure, hospital beds, general practitioner density, and digital health infrastructure. The intermediate output, avoidable hospitalisations, enters Stage 2 (service delivery), which additionally incorporates bed-days and doctor consultations. System outcomes are captured by treatable mortality and self-assessed health status\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCountries were subsequently grouped according to contextual similarity using hierarchical clustering. Exploratory associations between efficiency scores and structural factors were examined using fractional logit regression models and non-parametric tests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e\u003cbr\u003e\nAverage overall efficiency across countries was 0.75, with mean stage-1 efficiency (0.85) exceeding stage-2 efficiency (0.65), indicating that efficiency losses predominantly occur in the transformation of healthcare services into health outcomes. Considerable cross-country variation was observed. Germany ranks among the lowest-performing systems within the sample, primarily due to comparatively weak second-stage efficiency. Cluster analysis revealed structural differences between country groups; however, efficiency differences across clusters were not statistically robust. In contrast, healthcare system type showed significant associations with efficiency, with social health insurance systems displaying lower stage-2 efficiency compared to national health service systems.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions\u003c/strong\u003e\u003cbr\u003e\nThe findings suggest that inefficiencies in healthcare systems primarily arise in service delivery rather than in resource generation. Institutional system characteristics appear more closely related to efficiency variation than socioeconomic context. Differences in care coordination may be associated with variation in the translation of healthcare services into health outcomes. The two-stage NDEA approach helps identify where efficiency losses occur and provides a more detailed understanding of how resources are translated into health outcomes.\u003c/p\u003e","manuscriptTitle":"Decomposing Health System Inefficiency: A Cross-National Two-Stage Network Analysis of 30 Nations and the German Case","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-22 05:46:22","doi":"10.21203/rs.3.rs-9246265/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"282305027028141775817453635124139937101","date":"2026-05-13T21:23:08+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T16:48:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"336534184803275830953926945159689388499","date":"2026-04-14T16:23:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"332453046119341015456706143914297644975","date":"2026-04-14T13:19:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-14T09:45:18+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-04-01T18:20:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-01T02:52:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-01T02:51:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Health Services Research","date":"2026-03-27T14:58:53+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-health-services-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bhsr","sideBox":"Learn more about [BMC Health Services Research](http://bmchealthservres.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/BHSR/default.aspx","title":"BMC Health Services Research","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"619d25ba-9a78-4bbc-af83-d103b68b75d8","owner":[],"postedDate":"April 22nd, 2026","published":true,"recentEditorialEvents":[{"type":"reviewerAgreed","content":"282305027028141775817453635124139937101","date":"2026-05-13T21:23:08+00:00","index":77,"fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-05-11T16:48:40+00:00","index":72,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-22T05:46:22+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-22 05:46:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9246265","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9246265","identity":"rs-9246265","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}