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Journal of Medical Systems

, Volume 26, Issue 5, pp 427–438 | Cite as

An Application of Linear Programming Discriminant Analysis to Classifying and Predicting the Symptomatic Status of HIV/AIDS Patients

  • N. K. Kwak
  • Seong Ho Kim
  • Chang W. Lee
  • Tae Sung Choi
Article

Abstract

This study presents an application of linear programming discriminant analysis (LPDA) to classify and to predict the symptomatic status of HIV/AIDS patients. We applied LPDA as well as several traditional discriminant analysis methods to the AIDS Cost and Services Utilization Survey data set in order to demonstrate the use of LPDA to classify the symptomatic status of HIV/AIDS patients. The potential benefit of LPDA in terms of the classification accuracy was also analyzed.

linear programming discriminant analysis health-care application 

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REFERENCES

  1. 1.
    Fisher, R. A., The use of multiple measurements in taxonomy problems. Ann. Eugen. 7:179-188, 1936.Google Scholar
  2. 2.
    Smith, C. A. B., Some examples of discrimination. Ann. Eugen. 13:272-282, 1947.Google Scholar
  3. 3.
    Hand, D. J., Discrimination and Classification, Wiley, New York, 1981.Google Scholar
  4. 4.
    Hand, D. J., Kernel Discriminant Analysis, Research Studies Press, Chichester, NY, 1982.Google Scholar
  5. 5.
    Kwak, N. K., and Lee, C. W., A neural network application to classification of health status of HIV/AIDS patients. J. Med. Syst. 21(2):87-97, 1997.Google Scholar
  6. 6.
    Patuwo, E., Hu, M. Y., and Hung, M. S., Two-group classification using neural networks. Decis. Sci. 24(4):825-845, 1993.Google Scholar
  7. 7.
    Erenguc, S. S., and Koehler, G. J., Survey of mathematical programming models and experimental results for linear discriminant analysis. Manager. Decis. Econ. 11:215-225, 1990.Google Scholar
  8. 8.
    Joachimsthaler, E. A., and Stam, A., Mathematical programming approaches for the classification problem in two-group discriminant analysis. Multivar. Behav. Res. 25(4):427-454, 1990.Google Scholar
  9. 9.
    Stam, A., Nontraditional approaches to statistical classification: Some perspectives on LP-norm methods. Ann. Oper. Res. 74:1-36, 1997.Google Scholar
  10. 10.
    Freed, N., and Glover, F., Simple but powerful goal programming models for discriminant problems. Eur. J. Oper. Res. 7(1):44-60, 1981.Google Scholar
  11. 11.
    Freed, N., and Glover, F., Applications and implementation: A linear programming approach to the discriminant problem. Decis. Sci. 12(1):68-72, 1981.Google Scholar
  12. 12.
    Bajgier, S. M., and Hill, A. V., An experimental comparison of statistical and linear programming approaches to the discriminant problem. Decis. Sci. 13(4):604-618, 1982.Google Scholar
  13. 13.
    Freed, N., and Glover, F., Resolving certain difficulties and improving the classification power of the LP discriminant analysis procedure. Decis. Sci. 17(3):589-595, 1986.Google Scholar
  14. 14.
    Glover, F., Improved linear programming models for discriminant analysis. Decis. Sci. 21(4):771-785, 1990.Google Scholar
  15. 15.
    Glover, F., Improved linear and integer programming models for discriminant analysis. In Ijiri, Y. (ed.), Creative and Innovative Approaches to the Science of Management, Quorum Books, Westport, CT, pp. 365-395, 1993.Google Scholar
  16. 16.
    Glover, F., Keene, S., and Duea, B., A new class of models for the discriminant problem. Decis. Sci. 19(2):269-280, 1988.Google Scholar
  17. 17.
    Lam, K. F., Choo, E. U., and Moy, J. W., Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem. Eur. J. Oper. Res. 88(2):358-367, 1996.Google Scholar
  18. 18.
    Retzlaff-Roberts, D. L., A ratio model for discriminant analysis using linear programming. Eur. J. Oper. Res. 94(1):112-121, 1996.Google Scholar
  19. 19.
    Robin, P. A., Evaluating the maximize minimum distance formulation of the linear discriminant problem. Eur. J. Oper. Res. 41(2):240-248, 1989.Google Scholar
  20. 20.
    Silva, P. D., and Stam, A., Second order mathematical programming formulations for discriminant analysis. Eur. J. Oper. Res. 72(1):4-22, 1994.Google Scholar
  21. 21.
    Stam, A., and Ragsdale, C. T., On the classification gap in mathematical-programming-based approaches to the discriminant problem. Naval Res. Logist. 39(4):545-559, 1992.Google Scholar
  22. 22.
    Sueyoshi, T., DEA-discriminant analysis in the view of goal programming, Eur. J. Oper. Res. 115:564-582, 1999.Google Scholar
  23. 23.
    Freed, N., and Glover, F., Evaluating alternative linear programming models to solve the two-group discriminant problem. Decis. Sci. 17(2):151-162, 1986.Google Scholar
  24. 24.
    Joachimsthaler, E. A., and Stam, A., Four approaches to the classification problem in discriminant analysis: An experimental study. Decis. Sci. 19(2):322-333, 1988.Google Scholar
  25. 25.
    Lam, K. F., and Moy, J.W., An experimental comparison of some recently developed linear programming approaches to the discriminant problem. Comput. Oper. Res. 24(7):593-599, 1997.Google Scholar
  26. 26.
    Markowski, C. A., and Markowski, E. P., An experimental comparison of several approaches to the discriminant problem with both qualitative and quantitative variables. Eur. J. Oper. Res. 28(1):74-78, 1987.Google Scholar
  27. 27.
    Rubin, P. A., A comparison of linear programming and parametric approaches to the two-group discriminant problem. Decis. Sci. 21(2):373-386, 1990.Google Scholar
  28. 28.
    Retzlaff-Roberts, D., and Puelz, R., Classification in automobile insurance using a DEA and discriminant analysis hybrid. J. Prod. Anal. 7(4):417-427, 1996.Google Scholar
  29. 29.
    Gordon, K. R., Palmer, M., and Glover, F., Modeling international loan portfolios through linear programming discriminant analysis. J. Pol. Modeling 15(3):297-312, 1993.Google Scholar
  30. 30.
    Koehler, G. J., Characterization of unacceptable solutions in LP discriminant analysis. Decis. Sci. 20(2):239-257, 1989.Google Scholar
  31. 31.
    Koehler, G. J., Unacceptable solutions and the hybrid discriminant model. Decis. Sci. 20(4):844-848, 1989.Google Scholar
  32. 32.
    Koehler, G. J., Improper linear discriminant classifiers. Eur. J. Oper. Res. 50(2):188-198, 1991.Google Scholar
  33. 33.
    Silva, P. D., and Stam, A., Nonparametric two-group classification: Concepts and a SAS-based software package. Am. Statist. 52(2):185-197, 1998.Google Scholar
  34. 34.
    Berk, M. L., Maffeo, C., and Schur, C. L., Research design and analysis objectives. AIDS Cost and Services Utilization Survey (ACSUS) Reports No. 1; AHCPR Pub. No. 93-0019, Agency for Health Care Policy and Research, Rockville, MD, (http://www.ahcpr.gov/data/acsus1.htm), 1993.Google Scholar
  35. 35.
    SAS Institute Inc. SAS/STAT User's Guide, Version 6, 4th edn., Vol. 1, SAS Institute Inc, Cary, NC, 1989.Google Scholar
  36. 36.
    SAS Institute Inc. SAS/IML Software: Usage and Reference, Version 6, 1st edn., SAS Institute Inc, Cary, NC, 1989.Google Scholar
  37. 37.
    SAS Institute Inc. SAS/OR User's Guide, Version 6, 1st edn., SAS Institute Inc, Cary, NC, 1989.Google Scholar
  38. 38.
    Fisher, R. A., The precision of discriminant functions. Ann. Eugen. 10:422-429, 1940.Google Scholar
  39. 39.
    Lancaster, H. O., Some properties of the bivariate normal distribution considered in the form of a contingency table. Biometrika 44:289-292, 1957.Google Scholar
  40. 40.
    Overall, J., and Woodward, J. A., Discriminant analysis with categorical data. Appl. Psychol. Meas. 1:371-384, 1977.Google Scholar
  41. 41.
    Huberty, C. J., Applied Discriminant Analysis, Wiley, New York, 1994.Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • N. K. Kwak
    • 1
  • Seong Ho Kim
    • 1
  • Chang W. Lee
    • 2
  • Tae Sung Choi
    • 3
  1. 1.Department of Decision Sciences and MISSt. Louis UniversitySt. Louis
  2. 2.Department of Business AdministrationChinju National UniversityChinjuSouth Korea
  3. 3.School of Business and EconomicsInha UniversityInchonSouth Korea

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