Download PDF
Methods Inf Med 1988; 27(02): 73-83
DOI: 10.1055/s-0038-1635519
Original Article
Schattauer GmbH

Bayes Theorem and Conditional Dependence of Symptoms: Different Models Applied to Data of Upper Gastrointestinal Bleeding

Bayes-Theorem und konditionale Abhängigkeit der Symptome: Anwendung verschiedener Modelle auf Daten des oberen Gastrointestinaltraktes
C. Ohmann
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
,
Qin Yang
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
,
M. Künneke
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
,
H. Stöltzing
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
,
K. Thon
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
,
W. Lorenz
1   (From the Theoretical Surgery Unit and the Department of General and Traumatic Surgery, Center of Operative Medicine I, University of Düsseldorf and the Institute of Theoretical Surgery, Center of Operative Medicine I, University of Marburg, FRG)
› Author Affiliations
Further Information

Publication History

Publication Date:
17 February 2018 (online)

  PDF Download  Permissions and Reprints

Summary:

In computer-aided prognosis theoretical arguments in favour of a sophisticated model often do not result in a markedly better performance. In this study, straightforward extensions of the simple and comprehensive independent Bayes model, taking interactions between variables into consideration, are investigated, using a clinical data set of upper gastrointestinal bleeding, four sets of variables and different measures of performance (discriminatory ability, sharpness, reliability). For all criteria of performance, the differences between the models were small in the sets with few variables. In the sets with many variables there were marked differences between the models; however, no model was superior in all aspects of performance. Incorporation of interactions in models based upon Bayes’ theorem are worthwhile if many variables are used and the discriminatory ability is considered.

Bei der computerunterstützten Prognose führen theoretische Argumente für ein anspruchsvolles Modell nicht unbedingt zu besseren Ergebnissen. In dieser Studie wurden naheliegende Erweiterungen des einfachen und leicht verständlichen Unabhängigkeits-Bayes-Modells unter Berücksichtigung von Interaktionen zwischen Variablen mit Hilfe eines klinischen Datensatzes zur oberen Gastrointestinalblutung, vier Variablensätzen und verschiedenen Erfolgskriterien (Diskriminierungsfähigkeit, Schärfe, Zuverlässigkeit) untersucht. Die Unterschiede zwischen den Modellen waren gering bei den Datensätzen mit wenigen Variablen und allen Erfolgskriterien. Größere Unterschiede wurden bei den Datensätzen mit vielen Variablen beobachtet. Jedoch zeigte sich kein Modell hinsichtlich aller Kriterien überlegen. Die Berücksichtigung von Interaktionen im Bayes-Modell erscheint sinnvoll bei Datensätzen mit vielen Variablen und bei Betrachtung der Diskriminierungsfähigkeit.

Key-Words:

Computer-aided Prognosis - Independent Bayes Model - Conditional Dependence - Linear Logistic Regression - Performance Criteria - Upper Gastrointestinal Bleeding

Schlüssel-Wörter:

Computerunterstützte Prognose - Unabhängigkeits-Bayes-Modell - bedingte Abhängigkeit - lineare logistische Regression - Leistungskriterien - obere Gastrointestinalblutung
 

  • REFERENCES

  • 1 Anderson J. A. Separate sample logistic discrimination. Biometrika 1972; 59: 19-36.
    CrossrefPubMedGoogle Scholar
  • 2 Bishop Y. M. M, Fienberg S. E, Holland P. W. Discrete Multivariate Analy sis. Cambridge: MIT; 1978
    Google Scholar
  • 3 Chow C. K, Liu C. N. Approximating discrete probability distributions with dependence trees. IEEE Trans. Inform. Theor 1968; 14: 462-467.
    CrossrefPubMedGoogle Scholar
  • 4 Coomans D, Broeckaert I, Jonckheer M, Massart D. L. Comparison of multivariate discrimination techniques for clinical data application to the thyroid functional state. Meth. Inform. Med 1983; 22: 93-101.
    PubMedGoogle Scholar
  • 5 Copas J. B. Regression, prediction and shrinkage (with discussion). J. roy. Statist. Soc B 1983; 45: 311-354.
    PubMedGoogle Scholar
  • 6 Croft D. J, Machol R. E. Mathematical models in medical diagnosis. Ann. biomed. Engin 1974; 2: 69-89.
    CrossrefPubMedGoogle Scholar
  • 7 Dawid A. P. Properties of diagnostic data distributions. Biometrics 1976; 32: 647-658.
    CrossrefPubMedGoogle Scholar
  • 8 Engelman L. Stepwise logistic regression. In Dixon W. J. (Edit.) BMDP Statistical Software. Berkeley: University of California; 1983
    Google Scholar
  • 9 Fryback D. G. Bayes’ theorem and conditional nonindependence of data in medical diagnosis. Comp. biomed. Res 1978; 11: 423-434.
    CrossrefPubMedGoogle Scholar
  • 10 Habbema J. D. F, Hilden J, Bjerregaard B. The measurement of performance in probabilistic diagnosis: I. The problem, descriptive tools, and measures based on classification matrices. Meth. Inform. Med 1978; 17: 217-226.
    PubMedGoogle Scholar
  • 11 Habbema J. D. F, Gelpke G. F. A computer program for selection of variables in diagnostic and prognostic problems. Comp. Prog. Biomed 1981; 13: 251-270.
    CrossrefPubMedGoogle Scholar
  • 12 Hall G. H. The clinical application of Bayes’s theorem. Lancet 1967; II: 555-557.
    PubMedGoogle Scholar
  • 13 Hartigan J. Cluster analysis of variables. In Dixon W. J. (Edit.) BMDP Statistical Software. Berkeley: University of California; 1983
    Google Scholar
  • 14 Hilden J, Habbema J. D. F, Bjerregaard B. The measurement of performance in probabilistic diagnosis. II: Trust-worthiness of the exact values of the diagnostic probabilities. Meth. Inform. Med 1978; 17: 227-237.
    PubMedGoogle Scholar
  • 15 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
  • 16 Lincoln T. L, Parker R. D. Medical diagnosis using Bayes theorem. Health Serv. Res 1967; 2: 34-45.
    PubMedGoogle Scholar
  • 17 Morgan A. G, Clamp S. E. O.M.G.E. International upper gastrointestinal bleeding survey 1978–1982 Scand. J. Gastroenterol 1984; 19 Suppl (Suppl. 95) 41-58.
    PubMedGoogle Scholar
  • 18 Norusis M. J, Jacquez J. A. Diagnosis. I. Symptom nonindependence in mathematical models for diagnosis. Cornput. Biomed. Res 1975; 8: 156-172.
    PubMedGoogle Scholar
  • 19 Norusis M. J, Jacquez J. A. Diagnosis. II. Diagnostic models based on attribute clusters: a proposal and comparisons. Comput. Biomed. Res 1975; 8: 173-188.
    CrossrefPubMedGoogle Scholar
  • 20 Ohmann C, Künneke M, Zaczyk R, Thon K, Lorenz W. Selection of variables using “independence Bayes” in computeraided diagnosis of upper gastrointestinal bleeding. Stat. Med 1986; 5: 503-515.
    CrossrefPubMedGoogle Scholar
  • 21 Ohmann C, Thon K, Stöltzing H, List E, Zaczyk R, Ennis M, Lorenz W, Röher H. D. The personal computer as an aid to documentation of upper gastrointestinal endoscopy. Theor. Surg 1986; 1: 69-83.
    PubMedGoogle Scholar
  • 22 Ohmann C, Thon K, Stöltzing H Qin Yang, Lorenz W. Upper gastrointestinal tract bleeding: assessing the diagnostic contributions of the history and clinical findings. Med. Dec. Mak 1986; 6: 208-215.
    CrossrefPubMedGoogle Scholar
  • 23 Press S. J, Wilson S. Choosing between logistic regression and discriminant analysis. J. Amer. Stat. Ass 1978; 73: 699-705.
    CrossrefPubMedGoogle Scholar
  • 24 Roy S. N, Mitra S. K. An introduction to some non-parametric generalizations of analysis of variance and multivariate analysis. Biometrika 1956; 43: 361-376.
    CrossrefPubMedGoogle Scholar
  • 25 Russek E, Kronmal R. A, Fisher L. D. The effect of assuming independence in applying Bayes theorem to risk estimation and classification in diagnosis. Comput. biomed. Res 1983; 16: 537-552.
    CrossrefPubMedGoogle Scholar
  • 26 Thon K, Ohmann C, Stöltzing H, Lorenz W. Medical decision making in upper gastrointestinal bleeding: the impact of clinical criteria for the diagnosis of recurrent hemorrhage. Theor. Surg 1986; 1: 32-39.
    PubMedGoogle Scholar
  • 27 Titterington D. M, Murray G. D, Murray L. S, Spiegelhalter D. J, Skene A. M, Habbema J. D. F, Gelpke G. J. Comparison of discrimination techniques applied to a complex data set of head injured patients. J. roy. Statist. Soc. A 1981; 144: 145-175.
    CrossrefPubMedGoogle Scholar
  • 28 Toussaint G. T, Sharpe P. M. An efficient method for estimating the probability of misclassification applied to a problem in medical diagnosis. Comp. Biol. Med 1975; 4: 269-278.
    CrossrefPubMedGoogle Scholar
  • 29 Trampisch H. I. Zuordnungsprobleme in der Medizin: Anwendung des Lokations-modells. In Überla K, Reichertz P. L, Victor N. (Eds) Medizinische Informatik und Statistik, Vol. 63. Berlin: Springer; 1986
    Google Scholar