A New Procedure for Analysis of Medical Classification

A number of classification techniques have been applied to the analysis of medical diagnostic systems and decision making. Commonly used approaches such as cluster analysis, linear discriminant analysis and Bayesian classification are subject to logical and statistical limitations. In this paper we present a methodology, called »grade of membership« analysis, which resolves many of those limitations. This methodology deals simultaneously with the dual problems of case clustering and estimation of discriminant coefficients. The methodology also permits the assessment of the reliability of externally defined medical diagnoses, multiple diagnoses for individuals, disease progression and severity, and permits the representation of patient heterogeneity within diagnostic category. Maximum likelihood principles are invoked both to obtain parameter estimates and as a basis for likelihood ratio testing of complex hypotheses about the model structure. The model is illustrated by an analysis of data on abdominal symptoms and disease.

Verff. haben eine Anzahl von Klassifikationstechniken auf die Analyse medizinisch-diagnostischer Systeme und die Entscheidungsfindung angewandt. Allgemein benutzte Methoden wie Cluster-Analyse, lineare Diskriminanzanalyse, Bayes’ Klassifikation unterliegen logischen und statistischen Einschränkungen. In dieser Arbeit wird eine Methodik vorgestellt, die »grade of membership«-Analyse genannt wird und die viele dieser Einschränkungen aufhebt. Die Methodik behandelt gleichzeitig die zweifachen Probleme des Fall-Clustering und der Abschätzung der Diskriminanzkoeffizienten. Die Methodik gestattet auch die Einschätzung der Zuverlässigkeit andernorts definierter medizinischer Diagnosen, Mehrfachdiagnosen für Einzelfälle, Progressionsgrad und Schwere der Krankheit und ermöglicht die Darstellung der Heterogenität des Patientengutes innerhalb einer diagnostischen Kategorie. Prinzipien der Maximum Likelihood werden zur Parameterschätzung und als Grundlage der Maximum-Likelihood-Quotienten-Testung komplexer Hypothesen über die Modellstrukturierung herangezogen. Das Modell wird anhand einer Analyse von Daten über Abdominalsymptome und -krankheiten beleuchtet.

Key-Words

Cluster Analysis - Discriminant Function - Medical Diagnosis - Maximum Likelihood - Heterogeneity

Schlüssel-Wörter

Cluster-Analyse - Diskriminanzfunktion - medizinische Diagnose - Maximum Likelihood - Heterogenität

• References

• 1 Bartko J. Clustering: Some Problems, Strategies, and Techniques. Chapter 6 in National Institute of Mental Health, Series GN, No. 1. Multivariate Statistical Methodologies Used in the International Pilot Study of Schizophrenia DHHS Pub. No. (ADM) 80-630 Washington, D.C.: Sup. Public Documents, U.S. Government Printing Office; 1980: 68-76.
• 2 Dempster A. P. Elements of Continuous Multivariate Analysis. Reading, Massachusetts: Addison—Wesley; 1969
• 3 Galbinat W, Hirshfeld R. M, Jablensky A, Sar-torius N, Shapiro R. Bayes’ Theorem and Methods of Classification in Psychiatry. Chapter 5 in National Institute of Mental Health Series GN, No. 1 Multivariate Statistical Methodologies Used in the International Pilot Study of Schizophrenia Washington, D.C.: Sup. Public Documents, U.S. Government Printing Office; 1980. DHHS Pub. No. (ADM) 80-630 54-67.
• 4 Gardner M.J, Barker J. P. A Case Study in Techniques of Allocation. Biometrics 1975; 31: 931-942.
• 5 Gorry G. A, Barnett G. O. Experience with a Model of Sequential Diagnosis. Comput. biomed. Res 1968; 1: 490-507.
• 6 Jablensky A. Symptoms, Patterns of Course and Predictors of Outcome in the Functional Psychoses: Some Nosological Implications. In Lader M, Tognoni G, Bellantuono C. (Eds): Epidemiology Impact of Psychotropic Drugs Amsterdam: Elsevier/North Holland Biomedical Press; 1981: 71-97.
• 7 Norusis M. J, Jacquez J. A. Diagnosis : I. Symptom Non-Independence in Mathematical Models for Diagnosis. Comput. biomed. Res 1975; 8: 156-172.
• 8 Norusis M.J, Jaquez J. A. Diagnosis: II. Diagnostic Models Based on Attribute Clusters: A Proposal and Comparisons. Comput. Biomed. Res 1975; 8: 173-188.
• 9 Scheinok P. Symptom Diagnosis: Bayes Theorem and Bahadur’s Distribution. Comput. biomed. Res 1972; 3: 17-28.
• 10 Scheinok P.A, Rinaldo J. A. Symptom Diagnosis: Optimal Subsets for Upper Abdominal Pain. Comput. biomed. Res 1967; 1: 211-236.
• 11 Scott A. J, Symons M.J. Clustering Methods Based on Likelihood Ratio Criteria. Biometrics 1971; 27: 387-397.
• 12 Wardle A, Wardle L. Computer-Aided Diagnosis: A Review of Research. Meth. Inform. Med 1978; 17: 15-28.
• 13 World Health Organization: Schizophrenia: An International Follow-up Study New York: Wiley; 1979