Download PDF
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)
› Author Affiliations
Further Information

Publication History

Publication Date:
20 February 2018 (online)

    Permissions and Reprints

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.

Key-Words

Discriminant Analysis - Pattern Recognition - Thyroid Function - Performance Criteria - Bayes-ian Classification

Schlüssel-Wörter

Diskriminanzanalyse - Mustererkennung - Schilddrüsenfunktion - Leistungskriterien - Bayes’sche Klassifikation
 

  • References

  • 1 Anderson T. W.. Classification by multivariate analysis. Psychometrika 1951; 16: 31-42.
    CrossrefPubMedGoogle Scholar
  • 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;
    PubMedGoogle Scholar
  • 3 Bryan J. G.. The generalized discriminant function: mathematical foundation and computational routine. Harvard Educ. Rev 1951; 21: 90-95.
    PubMedGoogle Scholar
  • 4 Chien Y. I., Fu K. S.. Selection and ordering of feature observations in pattern recognition system. Inform. Contr 1968; 12: 394-399.
    CrossrefPubMedGoogle Scholar
  • 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.
    PubMedGoogle Scholar
  • 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.
    PubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 12 Coomans D.. Pattern Recognition in Medical Diagnosis on the Basis of Clinical Laboratory Tests. Ph.D Thesis. Brussels: Free University of Brussels 1982
    PubMedGoogle Scholar
  • 13 Cover T. M., Hart P. E.. Nearest neighbour pattern classification. IEEE Trans. Inf. Theory IT- 1967; 13: 21-27.
    CrossrefPubMedGoogle Scholar
  • 14 Croft D. J.. Is computerised diagnosis possible? Comp. biomed. Res 1972; 5: 351-367.
    PubMedGoogle Scholar
  • 15 Croft D. J., Machol R. E.. Mathematical methods in medical diagnosis. Ann. biomed. Engin 1974; 2: 69-89.
    CrossrefPubMedGoogle Scholar
  • 16 Dixon W. J.. Biomedical Computer Programs. (BMD P7M) (Berkeley: Unversity of California Press 1981
    PubMedGoogle Scholar
  • 17 Fisher R. A.. The use of multiple measurements. Ann. Eugen. (London) 1936; 7: 179-188.
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 19 Galen R. S., Gambino S. R.. Beyond Normality. New York: J. Wiley 1975
    PubMedGoogle Scholar
  • 20 Geisser S.. Posterior odds for multivariate normal classification. J. roy. statist. Soc. Ser. B 1964; 26: 69-76.
    PubMedGoogle Scholar
  • 21 Gilbert E. S.. On discrimination using qualitative variables. J. Amer. Statist. Ass 1968; 63: 1399-1412.
    CrossrefPubMedGoogle Scholar
  • 22 Gilbert E. S.. The effect of unequal variance-covariance matrices on Fisher’s linear discrimination function. Biometrics 1969; 25: 505-516.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 26 Hermans J., Habbema J. D. F.. Comparison of five methods to estimate posterior probabilities. EDV Med. Biol 1975; 6: 14-19.
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 28 Hermans J., Habbema J. D. F.. Manual of the ALLOC Discriminant Analysis Program. (Leiden: Department of Medical Statistics, University of Leiden 1976
    PubMedGoogle Scholar
  • 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.
    PubMedGoogle Scholar
  • 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.
    PubMedGoogle Scholar
  • 31 Hoel P. G., Peterson R. P.. A solution to the problem of optimum classification. Ann. Math. Stat 1949; 20: 433-338.
    CrossrefPubMedGoogle Scholar
  • 32 Lachenbruch P. A., Mickey M. R.. Estimation of error rates in discriminant analysis. Technometrics 1968; 10: 1-11.
    CrossrefPubMedGoogle Scholar
  • 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;
    PubMedGoogle Scholar
  • 34 Loftsgaarden D. O., Quesenberry C. P.. A nonparamet-ric estimate of a multivariate density function. Ann. Math. Statist 1965; 36: 1049-1151.
    CrossrefPubMedGoogle Scholar
  • 35 Marks S., Dunn O. J.. Discriminant functions when covariance matrices are unequal. J. Amer. Statist. Ass 1974; 69: 555-559.
    CrossrefPubMedGoogle Scholar
  • 36 Massart D. L., Kaufman L.. Operations research in analytical chemistry. Anal. Chem 1975; 47: 1244A-1253A.
    CrossrefPubMedGoogle Scholar
  • 37 Massart D. L., Kaufman L., Coomans D.. An operational research model for pattern recognition. Anal. chim. Acta 1980; 122: 347-354.
    PubMedGoogle Scholar
  • 38 Meisel W. S.. Computer-oriented Approaches to Pattern Recognition. London: Academic Press 1972
    PubMedGoogle Scholar
  • 39 Moore D. M.. Evaluation of five discrimination procedures for binary variables. J. Amer, statist. Ass 1973; 68: 399-404.
    PubMedGoogle Scholar
  • 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;
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 42 Nilsson N. J.. Learning Machines. New York: Mc Graw-Hill 1965
    PubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 44 Patrick E. A.. Decision Analysis in Medicine: Methods and Applications. Boca-Raton: CRC Press 1979
    PubMedGoogle Scholar
  • 45 Rao C. R.. A statistical criterion to determine the group to which an individual belongs. Nature (London) 1947; 160: 835 ff.
    CrossrefPubMedGoogle Scholar
  • 46 Rao C. R.. The utilization of multiple measurements in problems of biological classification. J. roy. Statist. Soc. Ser. B 1948; 10: 159-172.
    PubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 48 Rioux P., Nakache J. P.. Discriminant analysis: methods and program. Comp. Prog. Biomed 1979; 10: 43-47.
    CrossrefPubMedGoogle Scholar
  • 49 Sadegh-Zadeh K.. Bayesian diagnostics: a bibliography. Part 1. Metamedicine 1980; 1: 107-119.
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 51 Smith C. A. B.. Some examples of discrimination. Ann. Eugen. (London) 1947; 13: 272-284.
    PubMedGoogle Scholar
  • 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
    PubMedGoogle Scholar
  • 53 Wahl P. W., Kronmal R. A.. Discriminant functions when covariances are unequal and sample sizes are moderate. Biometrics 1977; 33: 479-484.
    CrossrefPubMedGoogle Scholar
  • 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.
    CrossrefPubMedGoogle Scholar
  • 55 Watanabe S.. Karhunen-Loève Expansion and Factor Analysis—Theoretical Remarks and Application. Prague: Proc. 4th Conf. Information Theory 1965
    PubMedGoogle Scholar
  • 56 Welch B. L.. Note on discriminant functions. Biometrika 1939; 31: 218-220.
    PubMedGoogle Scholar