Methods Inf Med 1983; 22(02): 93-101
DOI: 10.1055/s-0038-1635425
Original Artical
Schattauer GmbH

Comparison of Multivariate Discrimination Techniques for Clinical Data— Application to the Thyroid Functional State

Vergleich Multivariater Diskriminierungstechniken Für Klinische Daten — Anwendung Auf Den Funktionszustand Der Schilddrüsen
D. Coomans
1   (From the Farmaceutisch Instituut and Akademisch Ziekenhuis, Vrije Universiteit, Brussels, Belgium)
,
I. Broeckaert
1   (From the Farmaceutisch Instituut and Akademisch Ziekenhuis, Vrije Universiteit, Brussels, Belgium)
,
M. Jonckheer
1   (From the Farmaceutisch Instituut and Akademisch Ziekenhuis, Vrije Universiteit, Brussels, Belgium)
,
D. L. Massart
1   (From the Farmaceutisch Instituut and Akademisch Ziekenhuis, Vrije Universiteit, Brussels, Belgium)
› Institutsangaben
Weitere Informationen

Publikationsverlauf

Publikationsdatum:
20. Februar 2018 (online)

In this paper sixteen discrimination techniques are compared on the basis of a data base concerning the thyroid function. Five laboratory tests are available for 215 patients divided into three diagnostic classes, i. e. euthyroidism, hypothyroidism and hyperthyroidism. For all techniques correct classification rates were determined using the leave-one-out procedure. Moreover, for the probabilistic techniques, the quality of the obtained probabilities was evaluated. It has been shown that most of the techniques perform well. However, the probabilistic techniques are to be preferred.

In dieser Arbeit werden sechzehn Diskriminanzverfahren auf der Grundlage einer die Schilddrüsenfunktion betreffenden Datenbank miteinander verglichen. Zur Verfügung stehen fünf Laboratoriumstests für 215 Patienten, die in drei diagnostische Klassen (Euthyreoidismus, Hypothyreoidismus und Hyperthyreoidis-mus) aufgeteilt sind. Unter Benutzung des „leave-one-out“-Verfahrens wurden für alle Techniken richtige Klassifikationsraten bestimmt. Für die probabilistischen Techniken wurde darüber hinaus die Qualität der erhaltenen Wahrscheinlichkeiten bewertet. Es zeigte sich, daß die meisten Techniken gut funktionieren; jedoch sind die probabilistischen Verfahren vorzuziehen.

 
  • References

  • 1 Anderson T. W.. Classification by multivariate analysis. Psychometrika 1951; 16: 31-42.
  • 2 Brier G. W., Allen R. A.. Verification of Weather Forecasts. In Malone T. F.. (Edit.) Compendium of Meteorology, pp 841-848 Boston: Amer. Meteorol. Soc. 1951;
  • 3 Bryan J. G.. The generalized discriminant function: mathematical foundation and computational routine. Harvard Educ. Rev 1951; 21: 90-95.
  • 4 Chien Y. I., Fu K. S.. Selection and ordering of feature observations in pattern recognition system. Inform. Contr 1968; 12: 394-399.
  • 5 Coomans D., Broeckaert I., Jonckheer M., Blockx P., Massart D. L.. The application of linear discriminant analysis in the diagnosis of thyroid diseases. Anal. chim. Acta CTO 1978; 103: 409-415.
  • 6 Coomans D., Broeckaert I., Tassin A., Massart D. L.. Potential methods in pattern recognition, Part 1 : Classification aspects of the supervised method ALLOC. Anal. chim. Acta CTO 1981; 133: 215-224.
  • 7 Coomans D., Derde M. P., Broeckaert I., Massart D. L.. Potential methods in pattern recognition, Part 3: Feature selection with ALLOC. Anal. chim. Acta 1981; 133: 241-250.
  • 8 Coomans D., Broeckaert I., Massart D. L.. Potential methods in pattern recognition, Part 4: A combination of ALLOC and statistical linear discriminant analysis. Anal. chim. Acta 1981; 132: 69-74.
  • 9 Coomans D., Massart D. L.. Alternative k-nearest neighbour rules in supervised pattern recognition, Part 1 : k-nearest neighbour classification using alternative voting rules. Anal. chim. Acta 1982; 136: 15-25.
  • 10 Coomans D., Massart D. L.. Alternative k-nearest neighbour rules in supervised pattern recognition, Part 2: Probabilistic classification on the basis of the kNN method modified for direct density estimation. Anal. chim. Acta 1982; 138: 153-165.
  • 11 Coomans D., Massart D. L.. Alternative k-nearest neighbour rules in supervised pattern recognition, Part 3: Condensed nearest neighbour rules. Anal. chim. Acta 1982; 138: 167-176.
  • 12 Coomans D.. Pattern Recognition in Medical Diagnosis on the Basis of Clinical Laboratory Tests. Ph.D Thesis. Brussels: Free University of Brussels 1982
  • 13 Cover T. M., Hart P. E.. Nearest neighbour pattern classification. IEEE Trans. Inf. Theory IT- 1967; 13: 21-27.
  • 14 Croft D. J.. Is computerised diagnosis possible? Comp. biomed. Res 1972; 5: 351-367.
  • 15 Croft D. J., Machol R. E.. Mathematical methods in medical diagnosis. Ann. biomed. Engin 1974; 2: 69-89.
  • 16 Dixon W. J.. Biomedical Computer Programs. (BMD P7M) (Berkeley: Unversity of California Press 1981
  • 17 Fisher R. A.. The use of multiple measurements. Ann. Eugen. (London) 1936; 7: 179-188.
  • 18 Fix E., Hodges U. L.. Discriminatory analysis, non-parametric discrimination. United Air Force School of Avition Medicine, Report 1951 4. Contract AF 41-(128) 31
  • 19 Galen R. S., Gambino S. R.. Beyond Normality. New York: J. Wiley 1975
  • 20 Geisser S.. Posterior odds for multivariate normal classification. J. roy. statist. Soc. Ser. B 1964; 26: 69-76.
  • 21 Gilbert E. S.. On discrimination using qualitative variables. J. Amer. Statist. Ass 1968; 63: 1399-1412.
  • 22 Gilbert E. S.. The effect of unequal variance-covariance matrices on Fisher’s linear discrimination function. Biometrics 1969; 25: 505-516.
  • 23 Habbema J. D. F., Hermans J.. Selection of variables in discriminant analysis by F-statistic and error rate. Technomet-rics 1977; 19: 487-499.
  • 24 Harper A. M., Duewer D. L., Kowalski B. R., Fasching J. L.. ARTHUR and Experimental Data Analysis: the Heuristic Use of a Polyalgorithm. In Kowalski B. R.. (Edit.) Chemometrics, Theory and Application, pp 14-52 ACS Symposium Series No. 52. Washington D. C.: American Chemical Society 1977
  • 25 Healy M. J. R.. Descriptive uses of discriminant functions in mathematics and computer science in biology and medicine. London: Medical Research Council. Her Majesty’s Stationary Office 1965
  • 26 Hermans J., Habbema J. D. F.. Comparison of five methods to estimate posterior probabilities. EDV Med. Biol 1975; 6: 14-19.
  • 27 Hermans J., Habbema J. D. F.. The ALLOC package for multigroup discriminant analysis programs based on direct density estimation. COMPSTAT 1976, Proceedings in Computational Statistics Wien: Physica Verlag 1976
  • 28 Hermans J., Habbema J. D. F.. Manual of the ALLOC Discriminant Analysis Program. (Leiden: Department of Medical Statistics, University of Leiden 1976
  • 29 Hilden J., Habbema J. D. F., Bjerregaard B.. The measurement of performance in probabilistic diagnosis. II Trustworthiness of the exact values of the diagnostic probabilities. Meth. Inform. Med 1978; 17: 227-237.
  • 30 Hilden J., Habbema J. D. F., Bjerregaard B.. The measurement of performance in probabilistic diagnosis. III Methods based on continuous functions of the diagnostic probabilities. Meth. Inform. Med 1978; 17: 238-246.
  • 31 Hoel P. G., Peterson R. P.. A solution to the problem of optimum classification. Ann. Math. Stat 1949; 20: 433-338.
  • 32 Lachenbruch P. A., Mickey M. R.. Estimation of error rates in discriminant analysis. Technometrics 1968; 10: 1-11.
  • 33 Lachenbruch P. A.. Some Results on the Multiple Group Discriminant Problem. In T. Cacoullos (Edit.): Discriminant Analysis and Applications, pp 193-211 New York: Academic Press 1973;
  • 34 Loftsgaarden D. O., Quesenberry C. P.. A nonparamet-ric estimate of a multivariate density function. Ann. Math. Statist 1965; 36: 1049-1151.
  • 35 Marks S., Dunn O. J.. Discriminant functions when covariance matrices are unequal. J. Amer. Statist. Ass 1974; 69: 555-559.
  • 36 Massart D. L., Kaufman L.. Operations research in analytical chemistry. Anal. Chem 1975; 47: 1244A-1253A.
  • 37 Massart D. L., Kaufman L., Coomans D.. An operational research model for pattern recognition. Anal. chim. Acta 1980; 122: 347-354.
  • 38 Meisel W. S.. Computer-oriented Approaches to Pattern Recognition. London: Academic Press 1972
  • 39 Moore D. M.. Evaluation of five discrimination procedures for binary variables. J. Amer, statist. Ass 1973; 68: 399-404.
  • 40 Nakache J. P.. Multidimensional Data Analysis in Medical Decision. In de Dombal F. T., Grémy F.. (Eds) Decision Making and Medical Care, pp 113-136 Amsterdam: North-Holland Publ. Co. 1976;
  • 41 Nie N. H., Hull C. H., Jenkins J. G., Steinbrenner K., Bent D.. Statistical Package for the Social Sciences (SPSS). New York: Mc Graw-Hill 1975
  • 42 Nilsson N. J.. Learning Machines. New York: Mc Graw-Hill 1965
  • 43 Nordyke R. A., Kulikowski C. A., Kulikowski C. W.. A comparison of methods for the automated diagnosis of thyroid dysfunction. Comp. biomed. Res 1971; 4: 374-389.
  • 44 Patrick E. A.. Decision Analysis in Medicine: Methods and Applications. Boca-Raton: CRC Press 1979
  • 45 Rao C. R.. A statistical criterion to determine the group to which an individual belongs. Nature (London) 1947; 160: 835 ff.
  • 46 Rao C. R.. The utilization of multiple measurements in problems of biological classification. J. roy. Statist. Soc. Ser. B 1948; 10: 159-172.
  • 47 Rao C. R.. A general theory of discrimination when the information about alternative population distribution is based on samples. Ann. Math. Stat 1954; 25: 651-670.
  • 48 Rioux P., Nakache J. P.. Discriminant analysis: methods and program. Comp. Prog. Biomed 1979; 10: 43-47.
  • 49 Sadegh-Zadeh K.. Bayesian diagnostics: a bibliography. Part 1. Metamedicine 1980; 1: 107-119.
  • 50 Schmitz P. I. M., Habbema J. D. F., Hermans J., Kasan-moentalib E., Raatgever J. W.. Comparison of Six Discriminant Analysis Methods for Mixtures of Continuous and Discrete Variables. Technical Report. (Rotterdam: Institute of Biostatistics, Erasmus University 1982
  • 51 Smith C. A. B.. Some examples of discrimination. Ann. Eugen. (London) 1947; 13: 272-284.
  • 52 Victor N.. Non-parametric Allocation Rules. In de Dombal F. T., Grémy F.. (Eds) Decision Making and Medical Care, pp 515-527 Amsterdam: North-Holland Publ. Co. 1976
  • 53 Wahl P. W., Kronmal R. A.. Discriminant functions when covariances are unequal and sample sizes are moderate. Biometrics 1977; 33: 479-484.
  • 54 Wald A.. On a statistical problem arising in the classification of an individual into one of two groups. Ann. Math. Stat 1944; 15: 145-162.
  • 55 Watanabe S.. Karhunen-Loève Expansion and Factor Analysis—Theoretical Remarks and Application. Prague: Proc. 4th Conf. Information Theory 1965
  • 56 Welch B. L.. Note on discriminant functions. Biometrika 1939; 31: 218-220.