Abstract
The purpose of this paper is to study the effect of the socio-economic status of patients on the efficiency of orthopedic wards in acute hospitals in Israel (20 hospitals), from the viewpoint of the regulator—Israel Ministry of Health. At the first stage, data envelopment analysis is used with two inputs, and three outputs, where one output is undesirable—“number of deaths”—which also reflects the quality of the health services. At the second stage, various nonparametric tests are utilized to test the relationship between the socio-economic status of patients and the efficiency. As by-product DEA provides benchmark analysis, which indicates the peers of each inefficient ward, and the I/O improvements are needed for achieving efficiency. Two versions of DEA were used: the output oriented version (variable returns to scale), and the non-oriented version (Additive). Further analysis provides comparison of the results with other simple efficiency measures. We also compare between the efficiency from the regulator viewpoint and the hospitals’ viewpoint.
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References
Adler N, Sinuany-Stern Z, Friedman L (2002) Review of ranking methods in the data envelopment analysis context. Eur J Oper Res 140:249–265
Ali AI, Seiford LM (1990) Translation invariance in data envelopment analysis. Oper Res Lett 9:403–405
Aringhieri R (2009) Composing medical crews with equity and efficiency. Cent Eur J Oper Res 17:343–357
Averbuch E, Avni S (2013) Coping with health inequalities. Management, strategic and Economic Planning Division. Israel Ministry of Health (in Hebrew)
Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci 30:1078–1092
Barmeli-Greenberg S, Medina-Hartum T (2013) When an Israeli meets the health system, is it important where he lives? In: Averbuch E, Avni S (eds) Coping with health inequalities. Management, Strategic and Economic Planning Division, Israel Ministry of Health
Ben-David D (2011) Report on the country state: society, economics and policy. Taub Research Center of Social policy in Israel. www.taubcenter.org.il (in Hebrew)
Bilsel M, Davutyan N (2014) Hospital efficiency with risk adjusted mortality as undesirable output: the Turkish case. Ann Oper Res 221:73–83
Burk L et al (2013) Characterizing geographical units and their clustering according to the socio-economic level of their population in 2008. Central Bureau of Statistics of Israel publication no. 1530. www.cbs.gov.il (in Hebrew)
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Chernichovsky D, Friedman L, Sinuany-Stern Z, Hadad Y (2009) Hospitals efficiency in Israel via data envelopment analysis. Econ Q 56(2):119–142 (in Hebrew)
Chernichovsky D, Regev E (2013) Trends in Israel’s health care system policy. Paper no. 2013.14. In: Ben-David D (ed) Report on the country state: society, economics and policy. Taub Research Center of Social policy in Israel. www.taubcenter.org.il
Chilingerian JA, Sherman HD (2011) Health-care applications: from hospitals to physicians, from productive efficiency to quality frontiers. In: Cooper WW, Seiford LM, Zhu J (eds) Handbook on data envelopment analysis. Springer, New York, pp 445–493
DeTombe D (2015) Handling societal complexity: a study of the theory and the methodology of societal complexity and the COMPRAM methodology. Springer, Heidelberg
Du J, Wang J, Chen Y, Chou S-Y, Zhu J (2014) Incorporating health outcomes in Pennsylvania hospital efficiency: an additive supper-efficiency DEA approach. Ann Oper Res 221:161–172
Hollingsworth B (2008) The measurement of efficiency and productivity of health care delivery. Wiley, New-York
Levary RR, Cesse I (2009) Determining the relative efficiency of gynecological departments Using DEA. Appl Manag Sci 13:261–273
Levi S (2011) Health services in the North district. Report submitted to the Parliament Committee of Labor, Welfare, and Health. www.knesset.gov.il/mmm (in Hebrew)
Liu JS, Lu LYY, Lu WM, Lin BJY (2013) A survey of DEA applications. Omega 41:893–902
Lovell CAK, Pastor JT (1995) Units invariant and translation invariant DEA models. Oper Res Lett 18:147–151
Ministry of Health Israel (2014) Bed acceptancy in Hospitals by Department. http://www.health.gov.il/UnitsOffice/HR/ITandINFO/info/Pages/hospital_Beds.aspx
OECD (2013) Health at a glance 2013: OECD indicators. OECD Publishing. doi:10.1787/health_glance-2013-en
O’Neill L, Rauner M, Heidenbergerb K, Kraus K (2008) A cross-national comparison and taxonomy of DEA-based hospital efficiency. Socio Econ Plan Sci 42(3):158–189
Ozcan YA (2014) Health care benchmarking and performance evaluation: an assessment using data envelopment analysis (DEA), 2nd edn. Springer, Newton, MA
Pastor T (1996) Translation invariance in DEA: a generalization. Ann Oper Res 66:93–102
Rauner MS, Behrens DA, Wild C (2005) Preface: quantitative decision support for health services. CEJOR 13(4):319–323
Sahin I, Ozcan Y, Ozgen H (2011) Assessment of hospital efficiency under health transformation program in Turkey. CEJOR 9(1):19–37
Seiford LM, Zhu J (2002) Modeling undesirable factors in efficiency evaluation. Eur J Oper Res 142:16–20
Siegel S (1956) Nonparametric statistics for the Behavioral Sciences. McGraw-Hill Series in Psychology
Simões P, Marques R (2011) Performance and congestion analysis of the Portuguese hospital services. Cent Eur J Oper Res 19:39–63
Sinuany-Stern Z, Sherman HD (2014) Operations research in the public sector and nonprofit organizations. Ann Oper Res 221(1):1–8
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Appendices
Appendix 1: The socio-economic index
The SEI includes 16 variables which compose SEI for each census tract:
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1.
The median age
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2.
Dependency ratio—the ratio between young (0–19) plus old (65+) populations and the working age population (20–64).
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3.
Average number of persons per household
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4.
Average years of schooling of aged 25–54
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5.
Percent of academic degree of age group 25–54
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6.
Percent of workers in academic or managerial occupations
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7.
Percent of wage and income earners of ages 15 and over
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8.
Percent of women aged 25–54 not in civilian labor force
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9.
Percent of wage and income earners above twice the average wage
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10.
Percent of sub-minimum wage earners
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11.
Percent of recipients of income support and income supplement to old-age pension
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12.
Monthly income per standard person
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13.
Average number of vehicles at household disposal per aged 18 and over
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14.
Average number of rooms per person in households
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15.
Average number of bathrooms per person in household
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16.
Percent of households with PC and internet access
SEI is composed of 16 variables, which are grouped into 4 main components:
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a.
Demography—items 1–3
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b.
Education—items 4–6
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c.
Employment and pensions—items 7–11
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d.
Standard of living—items 12–16
For more details see Burk et al. (2013).
Appendix 2: Health care data in Israel by district
Appendix 3: Data envelopment analysis (DEA)
The basic DEA model was developed by Charnes, Cooper and Rhodes (CCR - 1978); it assumes Constant Returns to Scale (CRS). CRS version of DEA measures the total efficiency of n Decision Making Units (DMUs), where each has s outputs, sharing m inputs. Given, \(\hbox {x}_{\mathrm{ij}}\), the past value of input i, of DMU j (for all i \(=\) 1, ..., m and j \(=\) 1, ..., n), and, \(\hbox {y}_{\mathrm{rj}}\), the past value of output r of DMU j (for all r \(=\) 1, ..., s), we solve n problems, one for each DMU. The problem of DMU k finds, \(\hbox {v}_{\mathrm{ik}}\), the optimal weight of input i, and \(\hbox {u}_{\mathrm{rk}}\), the optimal weight of output r of DMU k, which maximize its relative efficiency measure, \(\hbox {h}_{\mathrm{kk}}\). The basic ratio used here is: \(h_{kj} =\sum \nolimits _{r=1}^s {u_{rk}} y_{rj} /\sum \nolimits _{i=1}^m {v_{ik}} x_{ij}\)
The problem of DMU k is: \(\max h_{kk} \), subject to: \(h_{kj} \le 1, j=1, \ldots , n, u_{rk} ,v_{ik} \ge 0,i=1, \ldots , m,r=, \ldots , s\)
If with its ideal weights DMU k does not receive the maximal efficiency score 1 (100 %), then DMU k is not efficient (i.e., other DMUs or a combination of DMUs received the maximal score 1 in the ideal weights of DMU k). However, if DMU k receives the maximal efficiency rate 1 then, unit k is relatively efficient. This maximization problem is called: the output oriented version. The input oriented version minimizes the reciprocal of the above objective function.DEA provides the efficient frontier. Obviously, the input and output weights vary greatly from one DMU to another.
Variable Return to Scale version
Banker, Charnes and Cooper (BCC -1984) introduced the Variable Returns to Scale (VRS) version of DEA by adding a constant variable, \(-\omega _k\), to the numerator of \(h_{kj}\) in the above problem k. BCC provides technical efficiency (see Banker et al. 1984). The ratio between CCR and BCC efficiency, provides the Scale Efficiency, which is always less than or equal to 1.
The Linear Programming (LP) formulation of BCC
This is the output oriented version. In the input oriented version, the denominator of the original ratio is minimized subject to the numerator equal to 1.
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Sinuany-Stern, Z., Cohen-Kadosh, S. & Friedman, L. The relationship between the efficiency of orthopedic wards and the socio-economic status of their patients. Cent Eur J Oper Res 24, 853–876 (2016). https://doi.org/10.1007/s10100-015-0420-9
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DOI: https://doi.org/10.1007/s10100-015-0420-9