SFA vs. DEA for Measuring Healthcare Efficiency: A Systematic Review


  • George Katharakis Mathematician, MSc, Ph.D, National and Kapodistrian University, Athens, Greece
  • Maria Katharaki Operational Researcher, MSc, Ph.D, Visiting Lecturer, National and Kapodistrian University, Athens, Greece
  • Theofanis Katostaras Associate Professor, Laboratory of Clinical Epidemiology, Faculty of Nursing, University of Athens, Greece




Efficiency, Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), healthcare, systematic review


Frontier techniques have been used to measure healthcare provider efficiency in hundreds of published studies. Although these methods have the potential to be useful to decision makers, their utility is limited by both methodological questions concerning their application. The aim of this paper is to search articles applying combined data envelopment analysis (DEA) and stochastic frontier analysis (SFA) in order to facilitate a common understanding about the adequacy of these methods, defining any differences in healthcare efficiency estimation and the reasons that are behind this. A systematic review of 21 such studies published the last decade was conducted. Only studies written in English were considered. Results are summarized in a form of meta-analysis in order to synthesize results and draw out further implications. Overall, DEA and SFA were found to yield divergent efficiency estimates due to many factors such as statistical noise, how inputs and outputs were defined, as well as data availability. Researchers, besides the combination of models to measure efficiency, lately have introduced environmental variables in their analyses, aiming at better understanding the relationship of these factors to efficiency and thus achieving a better decision making process. In any case the analysis concludes that there is a need for careful attention by stakeholders since the nature of the data and its availability influence the measurement of efficiency and thus it is necessary to model the behavior which generates the data by choosing the appropriate mathematical form

Author Biography

Theofanis Katostaras, Associate Professor, Laboratory of Clinical Epidemiology, Faculty of Nursing, University of Athens, Greece

Laboratory of Clinical Epidemiology, Faculty of Nursing


IMF [International Monetary Fund]. Macro-Fiscal Implications of Healthcare Reform in Advanced and Emerging Economies 2010. DOI: https://doi.org/10.5089/9781498336420.007

Oliveira M, Maisonneuve C, Bjornerud S. Projecting OECD health and long term care expenditures: What are the main drivers? OECD Working Paper No. 477, Paris.

Cassel CK, Brennan TE. Managing medical resources: return to the commons? J Am Med Assoc 2007; 297(22): 2518-21. http://dx.doi.org/10.1001/jama.297.22.2518 DOI: https://doi.org/10.1001/jama.297.22.2518

Milstein A, Lee TH. Comparing physicians on efficiency. New Engl J Med 2007; 357(26): 2649-52. http://dx.doi.org/10.1056/NEJMp0706521

The Leapfrog Group and Bridges to Excellence. Measuring Provider Efficiency Version 1.0. January 5, 2009. Available at http://www.google.com/url? sa=t&source=web&ct=res&cd= 4&url=http%3A%2F%2Fbridgestoexcellence.org%2Documents%2FMeasuring_Provider_Efficiency_Version1_12-31-20041.pdf&ei=BGdi SduROZWksAOj0NyODQ&usg= AFQjCNHFoeZecG_99 bd3fmSFa EkBDAK K N A &sig2= UoU5OCgfaXePw2Yp8h5xeA

O'Kane M, Corrigan J, Foote SM, Tunis SR, Isham GJ, Nichols LM, et al. Crossroads in Quality. Health Affairs 2008; 27(3): 749-58. http://dx.doi.org/10.1377/hlthaff.27.3.749 DOI: https://doi.org/10.1377/hlthaff.27.3.749

Mortimer D. A Systematic Review of Direct DEA vs SFA/DFA Comparisons. Centre for Health and Evaluation, Australia, 2002, Working Paper 136.

Gong B, Sickles R. Finite sample evidence on the performance of stochastic frontiers and data envelopment analysis using panel data. J Economet 1992; 51: 259-84. http://dx.doi.org/10.1016/0304-4076(92)90038-S DOI: https://doi.org/10.1016/0304-4076(92)90038-S

Simar L, Wilson PW. Estimation and inference in two-stage, semi-parametric models of production processes. J Economet 2007; 136: 31-64. http://dx.doi.org/10.1016/j.jeconom.2005.07.009 DOI: https://doi.org/10.1016/j.jeconom.2005.07.009

Newhouse J. Frontier estimation: how useful a tool for health economics? J Health Econom 1994; 13: 317-22. http://dx.doi.org/10.1016/0167-6296(94)90030-2 DOI: https://doi.org/10.1016/0167-6296(94)90030-2

Coelli T, Rao D, O’Donnell C, Battese G. An introduction to efficiency and productivity analysis (2nd ed.). New York 2005; Springer.

Worthington A. Frontier Efficiency Measurement in Healthcare: A Review of Empirical Techniques and Selected Applications. Med Care Res Rev 2004; 61(2): 1-36. http://dx.doi.org/10.1177/1077558704263796 DOI: https://doi.org/10.1177/1077558704263796

Hollingsworth B. Efficiency and productivity change in the English National Health service: Can data envelopment analysis provide a robust and useful measure? J Health Serv Res Policy 2003; 8. DOI: https://doi.org/10.1258/135581903322403308

Hussey P, Vries H, Romley J, Wang M, Chen S, Shekelle P, McGlynn E. A Systematic Review of Health Care Efficiency Measures. Health Serv Res 2009; 44(3): 784-805. http://dx.doi.org/10.1111/j.1475-6773.2008.00942.x DOI: https://doi.org/10.1111/j.1475-6773.2008.00942.x

Giuffrida A, Gravelle H. Measuring performance in primary care: Econometric analysis and DEA. Appl Econom 2001; 33(2): 163-75. DOI: https://doi.org/10.1080/00036840122522

Jacobs R. Alternative methods to examine hospital efficiency: Data Envelopment Analysis and Stochastic Frontier Analysis. Health Care Management Sci 2001; 4: 103-15. http://dx.doi.org/10.1023/A:1011453526849 DOI: https://doi.org/10.1023/A:1011453526849

Chirikos TN, Sear AM. Measuring hospital efficiency: a comparison of two approaches. Health Serv Res 2000; 34(6): 1389-408.

Rosenman R, Li T. Cost Inefficiency in Washington Hospitals: A Stochastic Frontier Approach Using Panel Data. Health Care Management Sci 2001; 4: 73-81. http://dx.doi.org/10.1023/A:1011493209102 DOI: https://doi.org/10.1023/A:1011493209102

Bryce C, Engberg J, Wholey D. Comparing the Agreement among Alternative Models in Evaluating Hmo Efficiency. Health Serv J 2000; 35(2): 509-28.

Mortimer D. Methods for the Measurement of Hospital Efficiency: A Comparison of Frontier Estimation Techniques in a Sample of Victorian Public Hospitals. Department of Economics, Monash University: Unpublished Master of Economics (Honours) thesis, 2001.

Desaia A, Ratick S, Schinnar A. Data envelopment analysis with stochastic variations in data. Socio-Econom Plan Sci 2005; 39: 147-64. http://dx.doi.org/10.1016/j.seps.2004.01.005 DOI: https://doi.org/10.1016/j.seps.2004.01.005

Smith P, Street A. Measuring the efficiency of public services: the limits of analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society) 2005; 168(2): 401-17. http://dx.doi.org/10.1111/j.1467-985X.2005.00355.x DOI: https://doi.org/10.1111/j.1467-985X.2005.00355.x

Assaf A, Matawie K. Cost efficiency modelling in healthcare food service operations. Int J Hosp Managem 2008; 27(4): 604-13. http://dx.doi.org/10.1016/j.ijhm.2007.07.021 DOI: https://doi.org/10.1016/j.ijhm.2007.07.021

Lee R, Bott M, Gajewski B, Taunton R. Modelling Efficiency at the Process Level: An Examination of the Care Planning Process in Nursing Homes. Health Serv Res 2009; 44(1): 15-32. http://dx.doi.org/10.1111/j.1475-6773.2008.00895.x DOI: https://doi.org/10.1111/j.1475-6773.2008.00895.x

Kontodimopoulos N, Papathanasiou N, Flokou A, Tountas Y, Niakas D. The Impact of Non-Discretionary Factors on DEA and SFA Technical Efficiency Differences. J Med Syst 2010; 35(5): 981-89. http://dx.doi.org/10.1007/s10916-010-9521-0 DOI: https://doi.org/10.1007/s10916-010-9521-0

Martin S, Smith P. A comparison of English primary care trusts. Preliminary statistical analysis. The Health Foundation Inspiring Improvement 2010.

Veen S. Comparative Efficiency Analysis from the Perspective of the Dutch Health Care Insurer. Determining the Usefulness of Efficiency Measures for Contracting Primary Care Organizations. Health Economics at the Erasmus University Rotterdam (Master Thesis), 2012.

Nedelea C, Fannin J. Efficiency Analysis of Rural Hospitals: Parametric and Semi-parametric Approaches. No 119725, Annual Meeting, Birmingham, Alabama from Southern Agricultural Economics Association 2012.

Hollingsworth B. The measurement of efficiency and productivity of health care delivery. Health Econom 2008; 17(10): 1107-28. http://dx.doi.org/10.1002/hec.1391 DOI: https://doi.org/10.1002/hec.1391

Jacobs R, Smith PC, Street A. Measuring Efficiency in Health Care: Analytic Techniques and Health Policy, Cambridge, Cambridge University Press 2006. http://dx.doi.org/10.1017/CBO9780511617492 DOI: https://doi.org/10.1017/CBO9780511617492

Alshare K, Whiteside MM. Stability analysis for DEA models: an empirical example. Acad Inform Manag Sci J 2005; 8(2): 1-16.

Ballestero E, Segura J. Objective measurement of efficiency: applying single price model to rank hospital activities. Comp Operat Res 2004; 31: 515-32. http://dx.doi.org/10.1016/S0305-0548(02)00231-9 DOI: https://doi.org/10.1016/S0305-0548(02)00231-9

Banker RD, Charnes A, Cooper WW. Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Manag Sci 1984; 30: 1078-92. http://dx.doi.org/10.1287/mnsc.30.9.1078 DOI: https://doi.org/10.1287/mnsc.30.9.1078

Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision-making units. Eur J Operat Res 1978; 2: 429-44. http://dx.doi.org/10.1016/0377-2217(78)90138-8 DOI: https://doi.org/10.1016/0377-2217(78)90138-8

Charnes A, Cooper WW. Preface to topics in Data Envelopment Analysis. Ann Operat Res 1985; 2: 59-94. http://dx.doi.org/10.1007/BF01874733 DOI: https://doi.org/10.1007/BF01874733

Coelli T, Prasada Rao DS, Battese GE. An introduction to efficiency and productivity analysis (Boston, Kluwer Academic). Communication from the Commission to the Council and to the European Parliament. (COM/2006/0481 final) Efficiency and equity in European education and training systems {SEC(2006) 1096}.

Cooper W, Seiford M, Zhu J. Handbook on Data Envelopment Analysis. Boston (Kluwer Academic Publisher) 2004. DOI: https://doi.org/10.1007/b105307

Ferrier D, Valdmanis V. Rural hospital performance and its correlates. J Product Anal 1996; 7: 63-80. http://dx.doi.org/10.1007/BF00158477 DOI: https://doi.org/10.1007/BF00158477

Fried O, Lovell A, Schmidt S, Yaisawarng S. Accounting for environmental effects and statistical noise in data envelopment analysis. J Product Anal 2002; 17(1-2): 157-74. http://dx.doi.org/10.1023/A:1013548723393 DOI: https://doi.org/10.1023/A:1013548723393

Giokas D. The use of goal programming, regression analysis and data envelopment analysis for estimating efficient marginal costs of hospital services. J Multi-Criteria Decision Anal 2003; 11 (4-5): 261-68. http://dx.doi.org/10.1002/mcda.330 DOI: https://doi.org/10.1002/mcda.330

Katharaki M. Approaching the management of hospital units with an operation research technique. The Case of thirty two Greek Obstetric and Gynaecology Public Units. Health Policy 2008; 85(1): 19-31. http://dx.doi.org/10.1016/j.healthpol.2007.06.001 DOI: https://doi.org/10.1016/j.healthpol.2007.06.001

Katharaki M. A Data Envelopment Analysis model for measuring the efficiency impact of telemedicine on Greek obstetric and gynaecology services: Effects on individual hospital unit management. J Inform Technol Healthcare 2006; 4(6): 373-83.

Linna M. Measuring hospital cost efficiency with panel data models. Health Econom 1998; 7: 415-27. http://dx.doi.org/10.1002/(SICI)1099-1050(199808)7:5<415::AID-HEC357>3.0.CO;2-9 DOI: https://doi.org/10.1002/(SICI)1099-1050(199808)7:5<415::AID-HEC357>3.0.CO;2-9

McKay L, Deily E, Dorner H. Ownership and changes in hospital inefficiency, 1986-1991. Inquiry 2003; 39: 388-99. http://dx.doi.org/10.5034/inquiryjrnl_39.4.388 DOI: https://doi.org/10.5034/inquiryjrnl_39.4.388

McNamara E. Welfare effects of rural hospital closures: a nested logit analysis of the demand for rural hospital services. Am J Agric Econom 1999; 81(3): 686-91. http://dx.doi.org/10.2307/1244035 DOI: https://doi.org/10.2307/1244035

Milstein A, Lee TH. Comparing physicians on efficiency. New Engl J Med 2007; 357(26): 2649-52. http://dx.doi.org/10.1056/NEJMp0706521 DOI: https://doi.org/10.1056/NEJMp0706521

Mutter L, Rosko D, Greene H, Wilson W. Translating frontiers into practice: taking the next steps toward improving hospital efficiency. Med Care Res Rev 2011; 68(1): 35-195. http://dx.doi.org/10.1177/1077558710384878 DOI: https://doi.org/10.1177/1077558710384878

Nayar P, Ozcan A. Data envelopment analysis comparison of hospital efficiency and quality. J Med Syst 2008; 32(3): 193-99. http://dx.doi.org/10.1007/s10916-007-9122-8 DOI: https://doi.org/10.1007/s10916-007-9122-8

OECD. The Evaluation of Scientific Research: Selected Experiences (Paris: OECD 1997).

OECD Education at a Glance. OECD Indicators 2005 (OECD Publishing).

Ondrich J, Ruggiero J. Efficiency measurement in the stochastic frontier model. Eur J Operat Res 2001; 129: 434-42. http://dx.doi.org/10.1016/S0377-2217(99)00429-4 DOI: https://doi.org/10.1016/S0377-2217(99)00429-4

Ozgen H, Ozcan A. Longitudinal analysis of efficiency in multiple output dialysis markets. Health Care Manag Sci 2004; 7: 253-61. http://dx.doi.org/10.1007/s10729-004-7534-2 DOI: https://doi.org/10.1007/s10729-004-7534-2

Rosko D. Cost efficiency of U.S. hospitals: a stochastic frontier approach. Health Econom 2001; 10: 539-51. http://dx.doi.org/10.1002/hec.607 DOI: https://doi.org/10.1002/hec.607

Rosko D, Mutter L. Inefficiency differences between Critical Access Hospitals and prospectively paid rural hospitals. J Health Politics Policy Law 2010; 35(1): 95-126. http://dx.doi.org/10.1215/03616878-2009-042 DOI: https://doi.org/10.1215/03616878-2009-042

Rosko D, Mutter L. What have we learned from the application of stochastic frontier analysis to U.S. hospitals? Med Care Res Rev 2011; 68(1): 75S-100S. http://dx.doi.org/10.1177/1077558710370686 DOI: https://doi.org/10.1177/1077558710370686

Rosko D, Proenca J. Impact of network and system use on hospital X-efficiency. Health Care Manag Rev 2005; 30: 69-79. http://dx.doi.org/10.1097/00004010-200501000-00010 DOI: https://doi.org/10.1097/00004010-200501000-00010

Schmidt P, Sickles C. Production frontiers and panel data. J Business Econom Stud 1984; 2: 299-26. DOI: https://doi.org/10.2307/1391278

Sexton T, Leiken M, Sleeper S. The impact of prospective reimbursement on nursing home efficiency. Med Care 1989; 27: 154-63. http://dx.doi.org/10.1097/00005650-198902000-00006 DOI: https://doi.org/10.1097/00005650-198902000-00006

Thanassoulis E. Introduction to the theory and application of data envelopment analysis. A foundation text with integrated software (USA: Kluwer Academic Publishers 2001). http://dx.doi.org/10.1007/978-1-4615-1407-7 DOI: https://doi.org/10.1007/978-1-4615-1407-7

Worthington A. An Empirical survey of frontier efficiency measurement techniques in education. Educ Econom 2001; 9(3): 245-68. http://dx.doi.org/10.1080/09645290110086126 DOI: https://doi.org/10.1080/09645290110086126




How to Cite

Katharakis, G., Katharaki, M., & Katostaras, T. (2013). SFA vs. DEA for Measuring Healthcare Efficiency: A Systematic Review. International Journal of Statistics in Medical Research, 2(2), 152–166. https://doi.org/10.6000/1929-6029.2013.02.02.09



General Articles