Recent evidence on the Spanish National Health System (SNHS) reveals a considerable margin for hospital efficiency and quality improvement. However, those studies do not consider both dimensions together. This study aims at jointly studying both technical efficiency (TE) and quality, classifying the public SNHS hospitals according to their joint performance.
Stochastic frontier analysis is used to estimate TE and multilevel logistic regressions to build a low-quality composite measure (LQ), which considers in-hospital mortality and safety events. All hospitalizations discharged in Spain in 2003 and 2013, in 179 acute-care general hospitals, were studied. Four scenarios of resulting performance were built setting yearly medians as thresholds for the overall sample, and according to hospital-complexity strata.
Overall, since 2003, median TE improved and LQ reduced -from TE2003:0.89 to TE2013:0.93 and, from LQ2003:42.6 to LQ2013:27.7 per 1,000 treated patients. The time estimated coefficient showed technical progress over the period. TE across hospitals showed scarce variability (CV2003:0.08 vs. CV2013:0.07), not so the rates of LQ (CV2003:0.64 vs. CV2013:0.76). No correlation was found between TE values and LQ rates. When jointly considering technical efficiency and quality, hospitals dealing with the highest clinical complexity showed the highest chance to be placed in optimal scenarios, also showing lesser variability between hospitals.
Citation: Gorgemans S, Comendeiro-Maaløe M, Ridao-López M, Bernal-Delgado E (2018) Quality and technical efficiency do not evolve hand in hand in Spanish hospitals: Observational study with administrative data. PLoS ONE 13(8): e0201466. https://doi.org/10.1371/journal.pone.0201466
Editor: Sandra C. Buttigieg, University of Malta Faculty of Health Sciences, MALTA
Received: January 8, 2018; Accepted: July 15, 2018; Published: August 2, 2018
Copyright: © 2018 Gorgemans et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The access to data supporting the manuscript findings is restricted in accordance with the System Level Security Policy of the Unit for Health Services and Policy Research (ARiHSP) at the Institute for Health Sciences in Aragon (IACS) (www.atlasvpm.org/grupo-coordinador/ARiHSPinformationsecuritypolicy) within the framework of the Spanish legal system, in particular, the Law 37/2007 on the Public Sector Information Reuse, the Law 14/2007 on Biomedical Research and the Law 15/1999 on Personal Data Protection. As a consequence, truncated aggregated data may be accessed upon request throughout ARiHSP data sharing agreement, contacting the senior author of the manuscript Enrique Bernal-Delgado (firstname.lastname@example.org) and/or the legal officer Ramón Launa-Garcés (email@example.com).
Funding: This manuscript is part of the works developed in the national grant ECO2017-83771-C3-2-R aimed at Research, Development and Innovation oriented to the challenges of society. Manuel Ridao-López is partially funded by Institute for Health Carlos III through a public competitive grant (RD16/0001/0007) as part of the network for Health Services Research on Chronic Patients (REDISSEC). The funders, both public nation-wide funding bodies, had no role in the study design, data collection and analyses, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Health systems performance assessment (HSPA) has become a major priority in Europe as a way to strengthen health systems effectiveness . In Spain, HSPA is getting momentum as a reaction to the deep financial crisis endured by the Spanish National Health System (SNHS) since 2010 . In the context of the statutory SNHS where public hospital activity is purchased according to quasi-retrospective global bundled payments with no particular incentives for value improvement, and where the transfer of risks is not present (penalties for bad performance or bonuses for good performance are negligible), competition throughout HSPA benchmarking may serve as an alternative.
The most prevalent HSPA conceptual framework  suggests monitoring a set of dimensions such as equity in access, sufficiency in terms of financial endowment and quality as central focus, considering this last one as a nested matrix of the sub-dimensions patient-centred care, efficiency and patient safety. (See here for a graphical representation of the mentioned HSPA framework http://www.oecd.org/els/health-systems/health-care-quality-indicators.htm). Usually, HSPA dimensions are measured as if they were independent phenomena when, on the contrary, multiple trade-offs are possible; for example, quality and efficiency are usually reported separately when both, are closely related when aiming the maximization of healthcare value (i.e., increasing efficiency while improving quality) . Actually, one of the major concerns when measuring and reporting technical efficiency (TE) lays on the frequent coexistence of hospitals equally efficient although exhibiting differences in quality [5–7]. More specifically, the direction of the association between quality of care and technical efficiency has shown mixed evidence. Some authors found that lower TE was associated with poorer quality outcomes  while others found that technically efficient hospitals were performing well with regard to quality , remaining unclear whether hospitals that successfully improve quality necessarily sacrifice production efficiency [10–11].
Recent evidence on the SNHS public hospitals reveals a considerable margin for hospital efficiency and quality improvement [12–13]. However, these studies do not consider both dimensions together. This study aims at jointly studying both TE and quality, and classifying public SNHS hospitals according to their joint performance.
Methods and design
Design and population
Observational cross-sectional study on virtually all hospital admissions discharged in two years, 2003 and 2013, in 179 acute-care public hospitals of the SNHS. The sample accounted for the 64% of the SNHS general hospitals and 83.3% of the overall admissions. Those non-existing hospitals in 2003 and hospitals with less than 30 episodes a year for those clinical conditions and procedures composing the measure of quality were excluded to avoid statistical noise.
Main endpoints: Technical efficiency and quality
TE, measured as the distance from each observed hospital to a theoretical optimum, was estimated through Stochastic Frontier Analysis (SFA) using 3 inputs, 2 outputs and 2 contextual variables. Because of the funding, purchasing and reimbursement features of the strongly regulated SNHS , where prices are not playing the same role as in market-oriented health systems, our approach builds on physical measures (i.e., inputs). Input variables regarded i) functioning beds as proxy to physical capital and, ii) full-time equivalent physicians and iii) full-time equivalent nursing staff’ as human capital. In turn, two output variables were included: i) discharges weighted by Diagnosis-Related Group as a measure of risk-adjusted inpatient activity, and ii) outpatient activity (the sum of outpatient visits and emergency contacts). Time (year of observation) meant to capture the hospitals’ technological development (i.e., any eventual frontier displacement), and the teaching status of the hospital, meant to seize any eventual effect of academic environments, were included in the model as contextual factors.
Low-Quality (LQ) was defined as a weighted composite of events including: a) in-hospital mortality during the episode of admission of a cardiovascular event (Acute Myocardial Infarction, Angina or Cardiac insufficiency) or a scheduled intervention like Percutaneous Coronary Intervention or elective Coronary Artery Bypass Grafting; and, b) the presence of a safety event along the episode of admission, specifically, the presence of post-surgery pulmonary thromboembolism or a deep venous thrombosis (PTE), c) post-operative sepsis (POS), or d) the presence of bacteraemia associated to catheter (CRI). The composite aimed at seizing the overall hospital quality as included medical, surgical and nursing care. The indicators composing the LQ measure had been previously validated and reported [15–17].
TE was estimated through SFA a parametric method based on a panel regression model where the residuals are expected to represent stochastic noise and inefficiency. For that purpose an input orientation approach was used when estimating the Cobb-Douglas (CB) function of production. As compared to other functions, CB better controls multicollinearity, is easily transferrable to a linear regression model, and allows straightforward interpretation of the estimated parameters without major algebraic transformations [18–20]. Goodness of fit of CB was estimated using a Log-likelihood test . Inefficiency would then result from the below distance of each observed hospital to the theoretical optimum estimate. In order to assess the evolution of TE (i.e., technical progress), the rate of progress was calculated by multiplying the model’s time coefficient by the elasticity of scale.
In-hospital risk-adjusted mortality and incidence of adverse events were calculated as the ratio of the observed to the expected cases, multiplied by the crude rate. The expected cases for each quality indicator were assessed by specifying multilevel logistic regressions, allowing for a general hospital cluster effect . The estimation model included as covariates age, sex and the presence (or not) of the Elixhauser comorbidity conditions to reduce confounding phenomena across hospitals [22–23]. A single composite measure was finally obtained by weighting each quality indicator according to its death toll–indicator’s fatality rate to the overall death rate. TE and LQ, and their variation across hospitals (as coefficient of variation) were estimated for the overall sample of 179 hospitals.
Although the analyses used contextual variables and risk adjustment measures to reduce bias, subgroup analyses were additionally carried out to address the eventual effect on estimates of unobserved (latent) or not considered (e.g., not available) variables. For that purpose, SNHS acute-care hospitals were stratified into quartiles according to their actual treated complexity, measured throughout the overall sum of APR-DRGs weights per hospital. So, hospitals in this sample were clustered into four groups, as follows: group 1, included those hospitals with overall APR-DRG weight less than 4,860.3 (11 hospitals); group 2 with hospitals whose overall weight ranged from 4,860.3 to 10,253.8 (43 hospitals); group 3 included hospitals with overall weight ranging from 10,253.9 to 21,553.5 (56 hospitals); and, group 4 included those hospitals with overall complexity weight above 21,553.5 (69 hospitals).
Finally, hospitals were assigned to four scenarios, based on the joint performance of technical efficiency and quality. Quadrants were built upon the median values of TE (x axis) and LQ (y axis) for both, 2003 and 2013 (Fig 1). TE outcomes closer to 1 would represent more efficiency, and lower in-hospital LQ rates would represent better quality.
All specified models were coded and assessed using Stata v.14 and Frontier 4.1. Mathematical specifications are included in S1 Methodological Appendix.
Sources of information
Three main data sources were used: 1) the Annual Hospital Survey (in Spanish, Estadística de Establecimientos Sanitarios en Régimen de Internado) from which inputs and outputs from the SFA were retrieved (https://www.msssi.gob.es/estadisticas/microdatos.do); 2) APR-DRGs weights using the APR-DRGs grouper licensed to the AtlasVPM group by 3M; and, 3) The AtlasVPM project data infrastructure, that contains administrative and clinical data from virtually all the hospitalizations produced in the SNHS since 2002. This data source was used in the extraction of quality indicators using the codes developed by the Atlas VPM project .
This study, observational in design, uses retrospective anonymized non-identifiable and non-traceable data, and was conducted in accordance with the amended Helsinki Declaration, the International Guidelines for Ethical Review of Epidemiological Studies, and Spanish laws on data protection and patients’ rights. The study implies the use of pseudonymised data, using double dissociation (i.e., in the original data source and once the data are stored in the database for analysis) and analyses and reporting are based on aggregated information, which impedes patients’ re-identification. The study was reviewed and approved by the Research Ethics Committee of Aragon (CEICA), who waived the need for written informed consent from the participants.
In 2013 (Table 1), the hospital activity (inpatient and outpatient care) accounted for 68 million episodes, a 17.7% more than in 2003. The increase was mainly due to outpatient contacts—18% (outpatient visits and emergencies) in contrast to the 9.9% increase of hospitalisations. In terms of inputs, overall, the amount of functioning beds decreased a 6.5% over the period, although more intensely in more complex hospitals (group 4), whose decrease reached a 9.1%. Fulltime physicians increased up to a 29.3% along the period, showing the highest increase (40.9%) in hospitals included in the third group (median to high complexity). Nursing staff increased overall, up to a 13.8%; by groups, in groups 2 and 3 nurses increased a 23%, while group 1 increased a 5%, and group 4 a 12%. Teaching status of hospitals did not vary along the period, with an 83.8% of teaching hospitals in both years. Descriptive figures for inputs and outputs showed low variability across hospitals within each group (Table 1).
In turn, quality figures also improved over the period of study; thus, for the in-hospital mortality due to cardiovascular events a 26.9 per thousand points reduction was observed between 2003 and 2013. By groups, lesser complex hospitals experienced the deepest decrease in mortality rate (77.9 per thousand points). Finally, for safety events, incidence remained almost the same for CRI, although slightly increased in the case of PTE (1.2 per thousand points) and POS (3 per thousand points), mainly in hospitals of median-higher complexity (group 3).
Looking separately at the performance dimensions (Table 2), from 2003 to 2013, the overall median TE improved, from 0.89 to 0.93 (frontier equals 1). Hospitals with middle to higher complexity (groups 2 to 4) improved their TE in four-hundredths, while hospitals in group 1, got closest to the optimum TE in 2013 (0.96). Very small variations in TE were observed, both across hospitals and over time, the lowest in group 1 (CV2003 0.03 vs. CV2013 0.04).
In general terms, LQ reduced along the period with a remarkable decrease of negative events from 42.6 to 27.7 per 1,000 treated patients (median value). Unlike TE, the variation in LQ across hospitals was remarkably high overall, mainly in hospitals with low or median-low complexity, and was observed to increase along the years—from CV2003 0.64 to CV2013 0.76 (Fig 2 shows the magnitude of variation across hospitals -turnip plots, overall and by hospitals complexity).
Violin graphs allow visualizing the distribution of quality (left) and efficiency (right) using a Kernel density function (the shape of the violin), and a boxplot representing the median value (hollow dots), the interquartile intervals (box) and percentiles 95th and 5th (the spikes).Group of hospitals 1: complexity case-mix out of APR-DRG less than 4,860.27 (11 hospitals). Group of hospitals 2: complexity case-mix out of APR-DRG from 4,860.27 to 10,253.82 (43 hospitals). Group of hospitals 3: complexity case-mix out of APR-DRG: from 10,253.82 to 21,553.54 (56 hospitals) and, group of hospitals 4: complexity case-mix out of APR-DRG above 21,553.54 (69 hospitals). Crude and Risk-adjusted Rates are per thousand patients at risk. CV: coefficient of variation.
Interestingly, the coefficient of the contextual variable of time showed technical progress over the period, so the rate of progress implied that an efficient hospital, with the same inputs, in 2013 would obtain 14.23% more outputs than in 2003.
No correlation was observed between TE and LQ, neither in 2003 nor in 2013, suggesting that not all hospitals experiencing improvements in efficiency equally improved their quality, nor vice versa. This finding was irrespective of the teaching status of the hospital.
According to the graphical joint analysis (Fig 3), 47 out the 179 hospitals in the sample remained (19 hospitals) or evolved (28 hospitals) to the optimal scenario (highly efficient and high-quality hospitals); out of those, the 80.9% were hospitals with mild-to-high or high complexity -14 and 24 hospitals, respectively. On the contrary, 46 out of the 179 hospitals remained (19 hospitals) or evolved (27 hospitals) to the worst scenario (highly inefficient and poor-quality hospitals). Out of those, a 43.5% were mild-to-low complexity hospitals, and 41.3% were mild-to-high complexity hospitals -20 and 19 hospitals, respectively.
Each bubble represents a hospital's outcome, blue bubbles account for 2003 figures and orange bubbles for 2013. Bubble size is related to the amount of functioning beds at each hospital. Lines placed at median values of TE and LQ delimits hospital's relative position. Low-quality (LQ) is measured in terms of per thousand patient at risk.
Acute hospitals in the SNHS experienced the improvement of both, efficiency and quality, between 2003 and 2013, although the overall improvement in quality was observed uneven across hospitals. Not all hospitals experiencing improvements in efficiency equally improved its quality, nor vice versa. Contradicting the commonplace that big hospitals are naturally inefficient, particularly if they are publicly tenured, and provide lower-quality, the more complex hospitals in our sample were placed at the optimal quality-efficiency trade-off scenario in 2013; nonetheless, lower-complexity hospitals showed to be more efficient (closer to the frontier) and experienced the deepest improvement in quality over the period.
In the Spanish context, where healthcare decision-making processes are decentralised to the Autonomous Communities, the heterogeneity of the accountability systems among the Regional Health Systems cause difficulties at creating a comprehensive strategy to assess efficiency across the SNHS . On the other hand, although insistently demanded, the inclusion of quality in the efficiency models is rarely found, partly due to the difficulty in the selection of an overarching hospital quality indicator, comparable across different type of hospitals. Therefore, the joint assessment of efficiency and quality has rarely been approached in Spain. Those few studies [26–29] focused on the assessment to a particular region, used alternatively Data Envelopment Analysis (DEA) and included a variety of quality indicators (e.g., nosocomial infection as a non-quality indicator, PSIs, Inpatient Quality Indicators (IQIs), readmissions or patient perceived quality), concluding, so does this paper, that better efficiency does not necessarily mean higher quality. Only one of the papers  estimated TE introducing composite measure of IQIs and PSIs establishing an overall increase of efficiency in Andalusian hospitals. Similar conclusion was obtained for hospitals dealing with moderate complexity .
Regarding international literature, only few studies using SFA examined the relationship between hospital efficiency and quality [31–33] and they also revealed no systematic association between TE and quality of care, nor impact on hospitals’ ranking.
To this respect, two elements should be discussed: on the one hand, on the use of SFA instead of DEA; and, on the other hand, on the use of a composite measure to seize overall hospitals quality.
When it comes to the utilisation of SFA vs. DEA, SFA may be more helpful to understand the future behaviour of the entire population of hospitals while DEA centered on individual behaviors , is being increasingly used in the analysis of efficiency and although it is still underused in the field of hospitals efficiency  and, finally, DEA health-care applications supposed a serious distortion because of the nature of the product in health care (neither homogeneous, nor unidimensional) . SFA is a parametric method based on the principle of econometrics and the theories of the micro-econometrics, which use panel data regression models to estimate a conventional Cobb-Douglas function of production. In contrast, DEA is a non-parametric deterministic method which estimates efficiency based on multiple productivities.
An important strength of SFA lies on its ability to diagnose latent heterogeneities among hospitals and, as TE in SFA is measured by using the residuals of the regression, which are supposed to be caused by stochastic noise and inefficiency [37–38], estimations are less sensible to error than DEAs, owning a greater discrimination capacity between those efficient and inefficient units, while allowing statistical testing of hypotheses concerning production structure and degree of inefficiency . However, SFA adds greater difficulty at modeling since its production frontier requires all outputs (or inputs) to be meaningfully aggregated into a single measure.
When it comes to seizing hospital quality, the use of composite measures is rather unusual, although individual measures only provide a partial picture of the overall quality of a hospital [40–45]. In this paper, providing an empirical weighting for those events composing ‘quality’ allows covering a broad range of quality elements concerning hospital activity (medical services, surgical services and nursing care), while allowing the identification of high-quality hospitals. Indeed, the discriminatory accuracy of the LQ measure (AUC and AUCw weighted) [21,46], reached figures above the 80%. Nevertheless, quality assessment methods and techniques using administrative data might endure well-known limitations, in particular, miss-classification biases that should be considered and controlled . In the particular case of the indicators used in this study, their previous validation for Spanish hospitals  as well as the stratification of hospitals in complexity subgroups fosters a safer use in the measure of LQ.
In the context of the SNHS, a system where public hospitals purchasing mechanisms lack of incentives to improve technical efficiency while increasing quality, monitoring the joint evolution of the technical efficiency and low-quality, providing hospital benchmarks, might foster performance improvement policies.
So, public purchasers, after monitoring hospital-providers evolution across TE vs. LQ trade-off scenarios, might compare the ‘distance’ between those hospitals and the benchmarks (those that remain in the optimal quadrant overtime) and nuance the ‘purchasing’ decisions accordingly.
Acute hospitals in the SNHS experienced an improvement in both, technical efficiency and quality, between 2003 and 2013. Not all hospitals experiencing improvements in efficiency equally improved their quality, nor vice versa. The joint analysis of both dimensions allowed identifying those optimal hospitals according to the optimal TE vs. LQ trade-off.
The authors would like to acknowledge the collaboration of the Atlas VPM research group (http://www.atlasvpm.org) and the data authorities who allowed us to access the data used in this study. This manuscript is part of the works developed in the national grant ECO2017-83771-C3-2-R aimed at Research, Development and Innovation oriented to the challenges of society. Manuel Ridao-López is partially funded by a public competitive grant (RD16/0001/0007) as part of the network for Health Services Research on Chronic Patients (REDISSEC). The funders, both public nation-wide funding bodies, had no role in the study design, data collection and analyses, decision to publish, or preparation of the manuscript.
- 1. European Commission. Communication on effective, accessible and resilient health systems. COM (2014) 215 final. Available at: https://ec.europa.eu/health//sites/health/files/systems_performance_assessment/docs/com2014_215_final_en.pdf [Accessed 2017, August 3rd].
- 2. Bandrés E, González R. La reducción del gasto sanitario en España durante la crisis. Cuadernos de Información Económica. 2015; 248.:37–48. Available at: https://www.funcas.es/Publicaciones/Detalle.aspx?IdArt=21986 [accessed March2017].
- 3. Arah OA, Westert GP, Hurst J, Klazinga NS. A conceptual framework for the OECD Health Care Quality Indicators Project. International Journal for Quality in Health Care 2006;18:5–13. pmid:16954510
- 4. Porter M. What is value in health care? N Engl J Med 2010, 363;26:2477–81. pmid:21142528
- 5. Nayar P, Ozcan Y, Yu F, Nguyen A.Benchmarking urban acute care hospitals: Efficiency and quality perspectives. Health Care Management Review 2013; 38:137–145. pmid:22469911
- 6. Jacobs R, Goddard M, Smith PC. How robust are hospital ranks based on composite performance measures? Medical Care, 2005, 43:1177–1184. pmid:16299428
- 7. Hussey PS, de Vries H, Romley J, Wang MC, Chen SS, Shekelle PG, et al. A Systematic Review of Health Care Efficiency Measures. Health Serv Res. 2009; 44(3):784–805. pmid:19187184
- 8. Clement J, Valdmanis V, Bazzoli G, Zhao M, Chukmaito A. Is more better? An analysis of hospital outcomes and efficiency with a DEA model of output congestion. Health Care Manage Sci. 2008; 11: 67–77.
- 9. Nayar P, Ozcan Y. Data Envelopment Analysis Comparison of Hospital Efficiency and Quality. J Med Syst. 2008; 32:193–199. pmid:18444355
- 10. Khushalani J, Ozcan Y. Are hospitals producing quality care efficiently? An analysis using Dynamic Network Data Envelopment Analysis (DEA). Socio-Economic Planning Sciences. 2017; 60:15–23.
- 11. Valdmanis V., Rosko M., Mutter R. Hospital Quality, Efficiency, and Input Slack Differentials. HSR: Health Services Research. 2008; 43(5). 1830–1845. pmid:18783457
- 12. Pérez-Romero C, Ortega-Díaz MI, Ocaña-Riola R, Martín-Martín JJ. Análisis de la eficiencia técnica en los hospitales del Sistema Nacional de Salud español. Gaceta Sanitaria. 2017;31:108–15 –Vol. 31, N 2. pmid:28043697
- 13. European Collaboration for Healthcare Optimization (ECHO) Project. www.echohealth.eu. Zaragoza (Spain): Instituto Aragonés de Ciencias de la Salud—Instituto Investigación Sanitaria Aragón; c2010. García-Armesto S, Comendeiro-Maaløe M, Martinez-Lizaga N, Angulo-Pueyo E, Bernal-Delgado E on behalf of the ECHO consortium. “ECHO Atlas on Coronary Revascularisation”; February 2014 [accessed:14/06/2017]; Available from: www.echo-health.eu/echo-atlas-reports. https://doi.org/10.1093/eurpub/cku219.
- 14. García-Armesto S, Abadía-Taira MB, Durán A, Hernández-Quevedo C, Bernal-Delgado E. Spain: Health system review. Health Systems in Transition, 2010, 12(4):1–295. pmid:21224176
- 15. Validation of Patient Safety Indicators (PSIs) for the Spanish National Health System. Summary 2008. Madrid: Ministerio de Sanidad y Consumo; 2008. [accessed: 2018-04-02]; Available at: http://www.msc.es/organizacion/sns/planCalidadSNS/docs/Summary_Validation_Patient_Safety_Indicators.pdf
- 16. Bernal-Delgado E, García-Armesto S, Martínez-Lizaga N, Abadía-Taira MB, Beltrán-Peribañez J, Peiró S. Should policy-makers and managers trust PSI? An empirical validation study of five patient safety indicators in a national health service. BMC Med Res Methodol. 2012; 27:12:19. pmid:22369291
- 17. European Collaboration for Healthcare Optimization (ECHO) Project. www.echo-health.eu. Zaragoza (Spain): Instituto Aragonés de Ciencias de la Salud—Instituto Investigación Sanitaria Aragón; c2010. García-Armesto S, Comendeiro-Maaloe M, Martinez-Lizaga N, Angulo-Pueyo E, Bernal-Delgado E on behalf of the ECHO consortium. ECHO Atlas on Coronary Revascularisation; February 2014 [accessed: 2018-04-02]; Available from: www.echo-health.eu/echo-atlas-reports.
- 18. Battese G,. Coelli T. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics. 1995; 20:325–332.
- 19. Bogetoft P, Otto L. Benchmarking with DEA, SFA and R. International Series in Operations Research and Management Science, vol. 157, Stanford University, USA; 2011. https://doi.org/10.1007/978-1-4419-7961-2_9
- 20. Greene WH. The Econometric Approach to Efficiency Analysis in Fried HO, Knox-Lovell CA and Schmidt SS. The Measurement of Productive Efficiency and Change. 2008. Oxford Scholarship Online. https://doi.org/10.1093/acprof:oso/9780195183528.003.0002
- 21. Ghith N, Wagner P, Frølich A, Merlo J. Short Term Survival after Admission for Heart Failure in Sweden: Applying Multilevel Analyses of Discriminatory Accuracy to Evaluate Institutional Performance. PLoS ONE 2016; 11(2): e0148187. pmid:26840122
- 22. Elixhauser A, Steiner C, Harris DR, Coffey RM. Comorbidity measures for use with administrative data. Med Care. 1998; 36(1):8–27. pmid:9431328
- 23. Iezzoni L. I. (Ed.). Risk adjustment for measuring health care outcomes (3rd ed.). Chicago: Health Administration Press; 2003.
- 24. Tebé C, Martinez N, Ibañez-Beroiz B, Ridao M, Librero-López J, Bernal-Delgado E. et al. Metodología del Atlas de Variaciones en la Práctica Médica. (actualización). Atlas de Variaciones en el manejo de la enfermedad cerebrovascular isquémica. Atlas Var Prac Med Sist Nac Salud 2013; 5(1): 418–24 Available at: http://atlasvpm.org/documents/10157/38164/NotasMetodologicas9.pdf [accessed: 1st March 2017].
- 25. Peiró S. “Algunas reflexiones sobre la organización de la información sanitaria en el Sistema Nacional de Salud”. Revista de Administración Sanitaria. 2006;4 (I): 81–94.
- 26. Prior D. Efficiency and total quality management in health care organizations: a dynamic frontier approach. Ann Oper Res. 2006;145:281–99.
- 27. Navarro-Espigares L, Hernández E. Efficiency and quality in health services: a crucial link. Service Industries Journal. 2011;31(3):385–403.
- 28. Gorgemans S. Production efficiency and functional dependence: Evidence in the Spanish health sector (in Spanish). PhD Dissertation; 2013. University of Zaragoza.
- 29. Herrero-Tabanera L. Efficiency Measurement of Andalusian hospitals in the Spanish Public Health System through border models (in Spanish). PhD Dissertation; 2015. University of Granada.
- 30. Martín JC, Ortega-Díaz MI. Rendimiento hospitalario y benchmarking. Revista de Economía Aplicada. 2016; 24(70): 27–51.
- 31. Laine J, Linna M, Häkkinen U, Noro A. Measuring the productive efficiency and clinical quality of institutional long-term care for the elderly. Health Econ. 2005;14(3):245–56. pmid:15386654
- 32. Mutter R, Rosko M, Wong H. Measuring Hospital Inefficiency: The Effects of Controlling for Quality and Patient Burden of Illness. Health Serv Res. 2008;43(6):1992–2013. pmid:18783458
- 33. Frogner B, Frech H, Parente S. Comparing efficiency of health systems across industrialized countries: a panel analysis. BMC Health Serv Res. 2015; 15(1): 415. pmid:26407626
- 34. Cooper WW,; Seiford LM, Zhu J. Handbook on Data Envelopment Analysis. 2nd edition. Springer, New York; 2011.
- 35. Hollingsworth B. The measurement of efficiency and productivity in Health Care delivery. JHE 2008; 17:1107–28. pmid:18702091
- 36. Newhouse JP. Frontier estimation: how useful a tool for health economics? J Health Econ. 1994;13:317–22. pmid:10138857
- 37. O’Donnell C, Nguyen K. An econometric approach to estimating support prices and measures of productivity change in public hospitals. J Prod Anal. 2013, 40: 323–335.
- 38. Jacobs R, Goddard M, Smith PC. How robust are hospital ranks based on composite performance measures? Medical Care. 2005; 43:1177–1184. pmid:16299428
- 39. Jacobs R. Alternative methods to examine hospital efficiency: data envelopment analysis and stochastic frontier analysis. Health Care Manag Sci. 2001; 4:103–115. pmid:11393739
- 40. O’Brien SM, Shahian DM, DeLong ER, Normand S, Edwards F, Ferraris V, et al. Quality measurement in adult cardiac surgery: part 2—statistical considerations in composite measure scoring and provider rating. Ann Thorac Surg. 2007; 83:S13–S26. pmid:17383406
- 41. Shwartz M, Restuccia J, Rosen AK. Composite Measures of Health Care Provider Performance: A Description of Approaches. The Milbank Quarterly. 2015; 93: 788–825. , pmid:26626986
- 42. Reeves D, Campbell S, Adams J, Shekelle P, Kontopantelis E, Roland M. Combining multiple indicators of clinical quality. An evaluation of different analytic approaches. Medical Care. 2007; 45:489–496. pmid:17515775
- 43. Shwartz M, Peköz EA, Christiansen CL, Burgess JF, Berlowitz D. Shrinkage estimators for a composite measure of quality conceptualized as a formative construct. Health Serv Res. 2013; 48:271–289. pmid:22716650
- 44. Werner RM, Bradlow ET. Relationship between Medicare’s hospital compare performance measures and mortality rates. JAMA. 2006; 296: 2694–2702. pmid:17164455
- 45. Zaslavsky AM, Shaul JA, Zaborski LB, Cioffi M; Cleary P. Combining health plan performance indicators into simpler composite measures. Health Care Financ Rev. 2002; 23:101–115. pmid:12500473
- 46. Merlo J, Wagner P, Ghith N, Leckie G. An original stepwise multilevel logistic regression analysis of discriminatory accuracy: the case of neighbourhoods and health. PLoS ONE. 2016; 11(4):e0153778. pmid:27120054
- 47. Jha AK, Li Z, Orav EJ, Epstein AM. Care in U.S. Hospitals–The Hospital Quality Alliance Program. New England Journal of Medicine. 2005;353:265–74. pmid:16034012