A mathematical approach to medical decisions: application of Bayes' rule to a mixture of continuous and discrete clinical variables.

Abstract Conditional probability formulations have frequently been used to form decision models relating disease probabilities to a set of descriptors or symptoms. The formulations have usually assumed the symptoms to be either all discrete-valued or all continuously valued. A mixed-data model (for both continuously valued and discrete valued symptoms) is presented and shown to represent a general class of models of which non-mixed-data models are special cases. By testing independence of symptoms prior to developing the decision model, one can take advantage of a potential reduction in the number of parameters that must be estimated.

[1]  H R Warner,et al.  A mathematical approach to medical diagnosis: application of polycythemic states utilizing clinical findings with values continuously distributed. , 1969, Computers and biomedical research, an international journal.

[2]  J A Rinaldo,et al.  Symptom diagnosis: optimal subsets for upper abdominal pain. , 1967, Computers and biomedical research, an international journal.

[3]  J. Cornfield.  Joint dependence of risk of coronary heart disease on serum cholesterol and systolic blood pressure: a discriminant function analysis. , 1962, Federation proceedings.

[4]  H. Warner,et al.  EXPERIENCE WITH BAYE'S THEOREM FOR COMPUTER DIAGNOSIS OF CONGENITAL HEART DISEASE * , 1964, Annals of the New York Academy of Sciences.

[5]  F. H. Tyler,et al.  PROBABILITY THEORY IN THE DIAGNOSIS OF CUSHING'S SYNDROME. , 1964, The Journal of clinical endocrinology and metabolism.

[6]  G. Gorry,et al.  Experience with a model of sequential diagnosis. , 2011, Computers and biomedical research, an international journal.

[7]  H. Warner,et al.  A mathematical approach to medical diagnosis. Application to congenital heart disease. , 1961, JAMA.

[8]  James E. Grizzle,et al.  Log Linear Models and Tests of Independence for Contingency Tables , 1972 .

[9]  J M Vanderplas,et al.  A method for determining probabilities for correct use of Bayes's theorem in medical diagnosis. , 1967, Computers and biomedical research, an international journal.

[10]  C F Starmer,et al.  A comparison of frequency distributions for use in a model for selecting treatment in coronary artery disease. , 1974, Computers and biomedical research, an international journal.

[11]  Wojtek J. Krzanowski,et al.  Discrimination and Classification Using Both Binary and Continuous Variables , 1975 .

[12]  Abdelmonem A. Afifi,et al.  Classification Based on Dichotomous and Continuous Variables , 1974 .

[13]  H. Linhart.  Techniques for discriminant analysis with discrete variables , 1959 .

[14]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.