Some Problems Arising in the Statistical Treatment of Diagnosis

R. Zentgraf; N. Victor

doi:10.1055/s-0038-1636609

Methods of Information in Medicine, Table of Contents

Methods Inf Med 1978; 17(01): 10-15
DOI: 10.1055/s-0038-1636609

ALLOCATION RULES

Schattauer GmbH

Some Problems Arising in the Statistical Treatment of Diagnosis

EINIGE PROBLEME DER STATISTISCHEN BEHANDLUNG DER DIAGNOSE

R. Zentgraf

¹(From the German Cancer Research Center, Institute of Documentation, Information and Statistics, Heidelberg, and the Department of Biomathematics, Justus-Liebig-University, Giessen)

,

N. Victor

¹(From the German Cancer Research Center, Institute of Documentation, Information and Statistics, Heidelberg, and the Department of Biomathematics, Justus-Liebig-University, Giessen)

› Author Affiliations

Abstract

For the most frequently used model of a one-step diagnostic process, where a patient can be allocated to exactly one disease, a mathematical formulation is presented. Possible criticism of the model is discussed. Statistical problems arising from the determination of the allocation rules are outlined with special emphasis on plug-in-rules. Finally, mention is made of some problems occurring in the practical application of diagnostic algorithms.

Für das am häufigsten benutzte Modell eines einstufigen Diagnostikprozesses, bei dem ein Patient genau einer Krankheit zugeordnet werden kann, wird eine mathematische Formulierung angegeben. Möglichkeiten der Kritik an diesem Modell werden diskutiert. Statistische Probleme, die bei der Bestimmung der Zuteilungsregeln entstehen können, werden behandelt, wobei besonders Plug-in-rules Berücksichtigung finden. Weiter werden einige Probleme angesprochen, die beim praktischen Einsatz von Diagnose-Algorithmen auftreten.

Key-Words

Diagnostic Algorithms - Plug-in-rules - Allocation Rules

Schlüssel-Wörter

algorithmische Diagnostik - Plug-in-rules - Zuordnungsregeln

Full Text

References

References
1 Aitchison J, Aitken C. G. G. Multivariate Binary Discrimination by the Kernel Method. Biometrika 63 1976; 413-420.
2 Aitchison J, Begg C. B. Statistical Diagnosis when Basic Cases are not Classified with Certainty. Biometrika 63 1976; 1-12.
3 Aitchison J, Habbema J. D. F, Kay J. W. A Critical Comparison of Two Methods of Statistical Discrimination. Appl. Statist 26 1977; 15-25.
4 Aitchison J, Kay J. W. Principles, Practice and Performance in Decision Making in Clinical Medicine. In White D. J, Bowen K. C. (Eds): Proceedings of the 1973 NATO Conference on the Role and Effectiveness of Theories of Decision in Practice. London: Hodder and Stoughton; 1975
5 Bjerregaard B, Brynitz S, Holst-Christensen J, Kalaja E, Lund-Kristensen J, Hilden J, Dombal de F. T, Horrocks J. C. Computer-aided Diagnosis of the Acute Abdomen: A System from Leeds Used on Copenhagen Patients. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 165-171 Amsterdam: North-Holland Publ. Co; 1976
6 Čencov N. N. Evaluation of an Unknown Distribution Density from Observations. Soviet. Math 03 1962; 1559-1562.
7 Chan L. S, Dunn O. J. The Treatment of Missing Values in Discriminant Analysis — I. The Sampling Experiment. J. Amer. Statist. Ass 67 1972; 473-477.
8 Chan L. S, Dunn O. J. A Note on the Asymptotic Aspect of the Treatment of Missing Values in Discriminant Analysis. J. Amer. Statist. Ass 347 1974; 672-673.
9 Christl H. L. Time Dependence and Bayesian Approach. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. 467-476 North-Holland Publishing Company; 1976
10 Cornfield D. J. Discriminant Functions. Rev. Int. Statist 35 1967; 142-153.
11 Fix E, Hodges Jr. J. L. Discriminatory Analysis; Nonparametric Discrimination: Consistency Properties. USAF School of Aviation Med. Project No. 21.49-004, Rep. No. 4, Randolph AFB; 1951
12 Geisser S. Posterior Odds for Multivariate Normal Classifications. J. roy. statist. Soc. B 26 1964; 69-76.
13 Ginsberg A. S. The Diagnostic Process Viewed as a Decision Problem. In Jaccjuez J. A. (Ed.): Computer Diagnosis and Diagnostic Methods. 203-240 Springfield, Ill: C. C. Thomas; 1972
14 Glick N. Sample Based Classification Procedures Derived from Density Estimators. J. Amer. Statist. Ass 67 1972; 116-122.
15 Habbema J. D. F. Models for Diagnosis and Detection of Combinations of Diseases. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 399-410 Amsterdam: North-Holland Publ. Co; 1976
16 Habbema J. D. F, Hermans J, van den Broek K. A Stepwise Discriminant Analysis Program using Density Estimation. In Bruckmann G, Ferschl F, Schmetterer L. (Eds): COMPSTAT 1974, Proceedings in Computational Statistics. 101-110 Wien: Physica Verlag; 1974
17 Hermans J, Habbema J. D. F. Comparison of Five Methods to Estimate Posterior Probabilities. EDV Med. Biol 06 1975; 14-19.
18 Horrocks J. C. A Computer-aided Diagnostic System Using a Small Desk-top Computer-calculator. Meth. Inform. Med 13 1974; 83-88.
19 James W, Stein C. Estimation with Quadratic Loss. In Neyman J. (Ed.): Proc. Fourth Berkeley Symp. Math. Statist. Prob. Vol. 1, Berkeley and Los Angeles: nUniv. of Calif. Press; 1962
20 Jacquez J. A, Norusis M. J. The Importance of Symptom Non-independence in Diagnosis. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 379-390 Amsterdam: North-Holland Publ. Co; 1976
21 Lachenbrttch P. A. Estimation of Error Rates in Discriminant Analysis. Ph. D. Thesis (unpublished), University of California; Los Angeles: 1965
22 Lachenbruch P. A. Discriminant Analysis when the Initial Samples are Misclassified. Technometrics 08 1966; 657-662.
23 Lachenbruch P. A. Discriminant Analysis when the Initial Samples are Misclassified II: Non-random Misclassification Models. Technometrics 16 1974; 419-424.
24 Lange H-J. Decision-making by Doctors and Aided by Computers. In. Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 11-20 Amsterdam: North-Holland Publ. Co; 1976
25 Lindley D. V. Costs and Utilities. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 101-112 Amsterdam: NorthHolland Publ. Co; 1976
26 Loftsgaarden D. O, Quesenberry C. P. A Nonparametric Estimate of a Multivariate Density Function. Ann. Math. Statist 36 1965; 1049-1051.
27 McLachlan G. J. Asymptotic Results for Discriminant Analysis when the Initial Samples are Misclassified. Technometrics 14 1972; 415-422.
28 McLachlan G. J. A Criterion for Selecting Variables for the Linear Discriminant Function. Biometrics 32 1976; 529-534.
29 Moran M. A. The Effects of Selecting Variables for Use in the Linear Discriminant. EDV Med. Biol 06 1975; 24-30.
30 Parzen E. On Estimation of a Probability Density Function and Mode. Ann. Math. Statist 33 1962; 1065-1076.
31 Rao B. L. S. P. Estimation of a Unimodel Density. Sankhya (A) 31 1969; 26-36.
32 Révèsz P. On Empirical Density Function. Period. Math. Hung 02 1972; 85-110.
33 Rosenblatt M. Remarks on some Nonparametric Estimates of a Density Function. Ann. Math. Statist 27 1956; 832-835.
34 Tallis G. M. Some Extensions of Discriminant Function Analysis. Metrika 15 1970; 86-91.
35 Tautu P, Wagner G. Medical Diagnosis Process: Routes of Mathematical Investigations. Meth. Inform. Med 17 1978; 1-10.
36 Titterington D. M. Updating a Diagnostic System Using Unconfirmed Cases. J. roy. statist. Soc. C 25 1976; 238-247.
37 Titterington D. M. Analysis of Incomplete Multivariate Binary Data by the Kernel Method. Biometrika 64 1977; 355-360.
38 Toussaint G. R. Bibliography on Estimation of Misclassification. IEEE Transactions Information Theory 20 1974; 472-479.
39 Toussaint G. T, Sharpe P. M. An Efficient Method for Estimating the Probability of Misclassification Applied to a Problem in Medical Diagnosis. Comput. Biol. Med 04 1975; 269-278.
40 Victor N. Non-parametric Allocation Rules. In Dombal de F. T, Grémy F. (Eds): Decision Making and Medical Care. Can Information Science Help?. 515-529 Amsterdam: North-Holland Publ. Co; 1976
41 Victor N. Probleme der Auswahl geeigneter Zuordnungsregeln bei unvollständiger Information, insbesondere für kategoriale Daten. Biometrics 32 1976; 571-585.
42 Wardle A, Wardle L. Computer Aided Diagnosis in Medicine: A Review of the Research. Meth. Inform. Med 17 1978; 15-28.
43 Wegman E. J. Norip arame trie Probability Density Estimation: I. A Summary of Available Methods. Technometrics 14 1972; 533-546.
44 Zentgraf R. A Note on Lancaster’s Definition of Higher Order Interactions. Biometrika 62 1975; 375-378.