Discriminant Analysis and its Applications in Epidemiology

This review article discusses current use of discriminant analysis in epidemiology. Contents include historical review, simple extensions and generalizations, examples, evaluation of rules, logistic discrimination, and robustness.

In diesem Übersichtsartikel wird die derzeitige Anwendung der Diskriminanzanalyse in der Epidemiologie erörtert. Der Artikel enthält eine historische Übersicht, einfache Erweiterungen und Verallgemeinerungen, Beispiele der Bewertung der Regeln der logistischen Diskriminierung und der Robustheit.

Key-Words:

Discriminant Analysis - Evaluation of Rides - Logistic Discrimination - Robustness

Schlüssel-Wörter:

Diskriminanzanalyse - Bewertung der Regeln - Logistische Diskriminierung - Robustheit

• References

• 1 Afifi A. A, Sacks S. T, Im V. Y, Weil M. H, Shubin H. Accumulative Prognostic Index for Patients with Barbiturate, Glutethimide and Meprobamate Intoxication. New Engl. J. Med 1971; 285: 1497-1502.
• 2 Ahmed S. W, Lachenbruch P. A. Discriminant Analysis when One or Both of the Initial Samples is Contaminated : Large Sample Results. EDV Med. Biol 1975; 6: 35-42.
• 3 Ahmed S. W, Lachenbruch P. A. Discriminant Analysis when Scale Contamination is Present in the Initial Sample. In Van Ryzin J. (Edit.): Classification and Clustering New York: Academic Press; 1977: 331-354.
• 4 Andrews D. F, Bickel P. J, Hampel F. R, Huber P. J, Rogers W. H, Tukey J. W. Robust Estimates of Location. Survey and Advances. Princeton: Princeton University Press; 1972
• 5 Bishop Y, Fienberg S, Holland P. Discrete Multivariate Analysis. Cambridge: MIT Press; 1975
• 6 Broffitt B, Clarke W. R, Lachenbruch P. A. Measurement Errors — A Location Contamination Problem in Discriminant Analysis. (Submitted to Communications in Statistics).
• 7 Carpenter R. G, Gardner R. G, Gardner A, Mcweenz P. M, Emery J. L. Multistage Scoring System for Identifying Infants at Risk of Unexpected Death. Arch. Dis. Childh 1977; 52: 606-612.
• 8 Clarke W. R, Lachenbruch P. A, Broffitt B. How Non-normality Affects the Quadratic Discriminant Function. Commun. Statist. A 8 1979; 1285-1301.
• 9 Cornfield J. Joint Dependence of Risk of Coronary Heart Disease on Serum Cholesterol and Systolic Blood Pressure : A Discriminant Function Approach. Fed. Proc 1962; 21: 58-61.
• 10 Cox D. R. Some Procedures Associated with the Logistic Response Curve. In David F. N, Fix E. (Eds): Research Papers in Statistics New York: Wiley; 1966: 55-71.
• 11 Das Gupta S. Some Aspects of Discriminant Function Coefficients. Sankhya A 1963; 30: 387-406.
• 12 Day N. É, Kebeidge D. F. A General Maximum Likelihood Discriminant. Biometrics 1967; 23: 313-323.
• 13 Dixon W. J. BMDP Biomedical Computer Programs P-Series 1979. Berkeley: University of California Press; 1979
• 14 Fisher R. A. The Use of Multiple Measurement in Taxonomic Problems. Ann. Eugen. (Lond.) 1936; 7: 179-188.
• 15 Gilbert E. S. On Discrimination Using Qualitative Variables. J. Amer. statist. Ass 1968; 63: 1399-1312.
• 16 Gilbert E. S. The Effect of Unequal Variance-Covariance Matrices on Fisher’s Linear Discriminant Function. Biometrics 1969; 25: 505-516.
• 17 Goldstein M, Dillon W. Discrete Discriminant Analysis. New York: Wiley; 1978
• 18 Halperin M, Blackwelder W. C, Verter J. I. Estimation of the Multivariate Logistic Risk Function : A Comparison of the Discriminant and Maximum Likelihood Approaches. J. chron. Dis 1971; 24: 125-188.
• 19 Hills M. Allocation Rules and their Error Rates. J. roy. statist. Soc. B 1966; 28: 1-20.
• 20 Lachenbruch P. A. Discriminant Analysis when the Initial Samples are Misclassified. Technometrics 1966; 8: 657-662.
• 21 Lachenbruch P. A. An Almost Unbiased Method of Obtaining Confidence Intervals for the Probability of Miselassifica-tion in Discriminant Analysis. Biometrics 1967; 23: 632-645.
• 22 Lachenbruch P. A. On Expected Probabilities of Mis-classification in Discriminant Analysis, Necessary Sample Size, and a Relation with the Multiple Correlation Coefficient. Biometrics 1968; 24: 823-834.
• 23 Lachenbruch P. A. Discriminant Analysis when the Initial Samples are Misclassified II : Non-random Misclassification Models. Technometrics 1974; 16: 419-424.
• 24 Lachenbruch P. A. Discriminant Analysis. New York: Hafner Press; 1975
• 25 Lachenbruch P. A. Note on Initial Misclassification Effects on the Quadratic Discriminant Function. Technometrics 1979; 21: 129-132.
• 26 Lachenbruch P. A, Kisker C. T, Stein M. N, Henriksen R. A. Statistical Approaches to Hemophilia A Carrier Detection. Proceedings of the Thirteenth Annual Hawaii International Conference on Systems Science. 1980
• 27 Lachenbruch P. A, Mickey M. R. Estimation of Error Rates in Discriminant Analysis. Technometrics 1968; 10: 1-11.
• 28 Lachenbruch P. A, Sneeringer C, Revo L. T. Robustness of the Linear and Quadratic Discriminant Function to Certain Types of Non-normality. Commun. Statist 1973; 1: 39-57.
• 29 Linhart H. Techniques for Discriminant Analysis with Discrete Variables. Metrika 1959; 2: 138-149.
• 30 Marks S, Dunn O. J. Discriminant Functions when Co-variance Matrices are Unequal. J. Amer, statist. Ass 1974; 69: 555-559.
• 31 Moore D. H. Evaluation of Five Discrimination Procedures for Binary Variables. J. Amer, statist. Ass 1973; 68: 399-404.
• 32 Revo L. T. On Classifying with Certain Types of Ordered Qualitative Variates : An Evaluation of Several Procedures. N. C. Inst. Statist. Mimeo Ser 1970: 708.
• 33 Toussaint G. T. Bibliographe on Estimation of Misclassification. IEEE Trans. Inform. Theor IT 1974; 20: 472-479.
• 34 Wahl P. W, Kronmal R. A. Discriminant Functions when Covariances are Unequal and Sample Sizes are Moderate. Biometries 1977; 33: 479-484.
• 35 Walker S. B, Duncan D. B. Estimation, of the Probability of an Event as a Function of Several Independent Variables. Biometrika 1967; 54: 167-179.
• 36 Welch B. L. Kote on Discriminant Functions. Biometrika 1939; 31: 218-220.