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Measuring the Performance Efficiency of Hospitals: PCA – DEA Combined Model Approach

Affiliations

  • Department of Statistics, S.D.N.B. Vaishnav College for Women, Chromepet, Chennai - 600044, Tamil Nadu, India
  • Department of Statistics, Presidency College, Kamarajar Salai, Chennai - 600005, Tamil Nadu, India

Abstract


Objectives: The Government provides primary health care services to the poor and needy people through District Hospitals. Primary care is an ongoing care being focused on person over time that fulfils the health related requirements of people. This necessitates studying the efficient functioning of public hospitals. So the author concentrated and considered to analyse the performance of District Hospitals in the state of Tamil Nadu. Methods/Statistical Analysis: To attain the above objective one of the nonparametric methods namely Data Envelopment Analysis (DEA) has applied. It is a mathematical technique based on linear programming problem and it measures the relative efficiency of similar type of organizations termed as Decision Making Units (DMUs). In this study each DMU refers to the District Hospital in the state of Tamil Nadu. In DEA, normally there exists a significant correlation between the inputs and outputs. Inclusion of more number of inputs and /or outputs in DEA results in getting a more number of efficient units. Therefore, select the appropriate inputs and outputs based on the experts’ advice who know their characteristics very well. A clear understanding of the characteristics of input/output variables will nullify the above deficiency and will really results with exact number of efficient units. An attempt is made to rectify the deficiency in introducing the technique viz., Principal Component Analysis. Principal Component Analysis helps the decision maker to reduce the data structure into certain principal components which are essential for identifying efficient DMUs. It is important to note that we have used the basic BCC model for the entire analysis. Findings: The author has considered 31 DMUs for the study using BCC model. The data results with 13 DMUs out of 31 DMUs as efficient. Subsequently with the same original data 3 PCs on input and output explains 98 percent of the total variance and this has resulted with only 3 DMUs as efficient. Then we have considered 2PCs on input and output. This has resulted with 90.31 percent variance in the case of input and 95.78 percent variance in the case of output. Normally in Principal Component analysis, if the variance lies between 80 percent to-90 percent it is judged as a meaningful one. The above computations result with 2 DMUs efficient. Finally, we have attempted to identify the efficient units with the above expected variance interval 80 percent to 90 percent. This has resulted with 90 percent variance explained with 2 input variable and one output variable with 89 percent explained variance. This also resulted with only 2 efficient DMUs. It is concluded that Principal Component Analysis plays an important role in the reduction of input output variables and helps in identifying the efficient DMUs and improves the discriminating power of DEA. Application/Improvements: Introduction of PCA with DEA is definitely is an improvement which helps the decision maker to apply in wider sense and to take proper managerial decision.

Keywords

Data Envelopment Analysis, Decision Making Unit, Principal Component Analysis, Principal Components.

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References


  • Farrell MJ. The measurement of productive efficiency. Journal of the Royal Statistical Society Series A. 1957; 120(3):253–90. doi:10.2307/2343100.
  • Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operation Research. 1978; 2(6):429–44. doi:10.1016/03772217(78)90138-8.
  • Banker RD, Charnes A, Cooper WW. Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science. 1984; 30(9):1078–92. doi:10.1287/mnsc.30.9.1078.
  • Jacobs R. Alternative methods to examine hospital efficiency: Data envelopment analysis and stochastic frontier analysis. Health Care Management Science. 2001; 4:103–11. doi:10.1023/A:1011453526849.
  • Hollingsworth B, Dawson PJ, Maniadakis N. Efficiency measurement of health care: A review of non-parametric methods and applications. Health Care Management Sciences. 2008; 2(3):161–72. doi:10.1023/A:1019087828488.
  • Valdmanis VG, Rosko MD, Mutter RL. Hospital quality, efficiency, and in slack differentials. Health Services Research. 2008; 43(5 Pt 2):1830–48. doi:10.1111/j.14756773.2008.00893.x.
  • Prakash V, Annapoorni D. Performance evaluation of Public Hospitals in Tamil Nadu – DEA approach.
  • Journal of Health Management. 2015; 17:417–24.
  • doi:10.1177/0972063415606267.
  • Wan Mohd Aminuddin W, Ismail W, Harunarashid H. Estimating emergency department maximum capacity using simulation and data envelopment analysis. Indian Journal of Science and Technology. 2016 Jul; 9(28). doi:10.17485/ ijst/2016/v9i28/97352.
  • Buyukkayikci H, Sahin I. The comparative analysis of patient’s costs with reimbursement in surgical services in Turkish. hacettepe Saglik Idaresi Dergisi. 2000; 5(3):119– 38.
  • Worthington A. Frontier efficiency measurement in health care: A review of empirical techniques and selected applications. Medical Care Research and Review. 2004; 61(2):135– 70. doi:10.1177/1077558704263796.
  • Ersoy K, Kavuncubasi S, Ozcan Y, Harris J. Technical efficiencies of Turkish hospitals: DEA approach. Journal of Medical System. 1997; 21(2):67–74. doi:10.1023/A:1022801222540.
  • Jacobs R, Smith PC, Street A. Measuring efficiency in health care. Cambridge University Press, New York; 2006. doi:10.1017/CBO9780511617492.
  • Ozcan Y. Health care benchmarking and performance evaluation: An assessment using data envelopment analysis. Springer Publishing, New York; 2008. doi:10.1007/978-0387-75448-2.
  • Sahin I, Ozcan Y. Public sector hospital efficiency for provincial markets in Turkey. Journal of Medical System. 2000; 24(6):307–20. doi:10.1023/A:1005576009257.
  • Ueda T, Hoshiai Y. Application of principal component analysis for parsimonious summarization of DEA inputs and/or outputs. Journal of Operational Research Society Japan. 1997; 40:446–78.
  • Adler N, Golany B. Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe. European Journal of Operational Research. 2001; 132:260–73. doi:10.1016/S0377-2217(00)00150-8.
  • Adler N, Golany B. Including principal component weights to improve discrimination in data envelopment analysis. Journal of Operational Research Society. 2002; 53:985–91. doi:10.1057/palgrave.jors.2601400.
  • Adler N, Golany B. Data reduction through principal component analysis (DEA-PCA). In: Cook W, Zhu J, editors. Modeling data irregularities and structural complexities in data envelopment analysis, Springer: New York; 2007. p. 139–53. doi:10.1007/978-0-387-71607-7_8.
  • Adler N, Yazhemsky E. Improving discrimination in data envelopment analysis: PCA-DEA or variable reduction. European Journal of Operational Research. 2010; 202(1):273– 84. doi:10.1016/j.ejor.2009.03.050.
  • Johnson RA, Wichern DW. Applied multivariate analysis, Prentice-Hall Inc.: New Jersey; 1982.
  • Charnes A, Cooper WW, Golany B, Seiford L, Stutz J. Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production function. Journal of Econometric. 1985; 30:91–107. doi:10.1016/0304-4076(85)901332.
  • Emrouznejad A, Anouze AL, Thanassoulis E. A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. European Journal of Operational Research. 2010a; 200:297–304. doi:10.1016/j.ejor.2009.01.001.
  • Kordrostami S, Noveiri MJS. Evaluating the efficiency of decision making units in the presence of flexible and negative data. Indian Journal of Science and Technology. 2012 Dec; 5(12). doi:10.17485/ijst/2012/v5i12/30612.
  • Ali AI, Seiford LM. Translation invariance in data envelopment analysis. Operations Research Letters. 1990; 9:403–5. doi:10.1016/0167-6377(90)90061-9.
  • Pastor J. Translation invariance in data envelopment analysis: A generalization. Annals of Operations Research. 1996; 66:93–102. doi:10.1007/BF02187295.
  • Allen R, Athanassopoulos A, Dyson RG, Thanassoulis E. Weight’s restrictions and value judgments in Data Envelopment Analysis: Evolution, development and future directions. Annals of Operations Research. 1997; 73, pp.13-34. doi:10.1023/A:1018968909638.
  • Dyson R, Allen R, Camanho AS, Podinovski VV, Sarrico CS, Shale EA. Pitfalls and protocols in DEA. European Journal of Operational Research. 2001; 132:245–59. doi:10.1016/ S0377-2217(00)00149-1.
  • Andersen P, Petersen NC. A procedure for ranking efficient units in data envelopment analysis. Management Science. 1993; 39(10):1261–94. doi:10.1287/mnsc.39.10.1261.
  • Reshadi M, Noroozi E. Ranking method based on cross-efficiency and aggregate units in data envelopment analysis. Indian Journal of Science and Technology. 2015 Jul; 8(13). doi:10.17485/ijst/2015/v8i13/54113.

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