Methods Inf Med 1978; 17(01): 1-10
DOI: 10.1055/s-0038-1636611
CLINICAL DECISION-MAKING
Schattauer GmbH

The Process of Medical Diagnosis: Routes of Mathematical Investigations

MATHEMATISCHE ASPEKTE DER MEDIZINISCHEN DIAGNOSESTELLUNG
P. Tautu
1   From the German Cancer Research Center, Heidelberg, Institute of Documentation, Information and Statistics Director: Prof. Dr. med. G. Wagner
,
G. Wagner
1   From the German Cancer Research Center, Heidelberg, Institute of Documentation, Information and Statistics Director: Prof. Dr. med. G. Wagner
› Author Affiliations
Further Information

Publication History

Publication Date:
15 February 2018 (online)

This paper is an analysis of the most important mathematical aspects of medical diagnosis: logical probability, rationality and decision theory, gambling models, pattern analysis, hazy and fuzzy subsets theory and, finally, the stochastic inquiry process.

Diese Arbeit stellt eine Analyse der wichtigsten mathematischen Aspekte der medizinischen Diagnose dar: logische Wahrscheinlichkeiten, Entscheidungstheorie, spieltheoretische Modelle, Theorie der »hazy« und »fuzzy« Teilmengen, Musteranalyse sowie stochastische Untersuchungsprozesse.

 
  • References

  • 1 Ackoff R. L, Emery F. E. On Purposeful Systems. Tavistock; London: 1972
  • 2 Adams E. W. Prior Probabilities and Counterfactual Conditionals. In Harper W. L, Hooker C. A. (Eds): Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Vol. 1, 1-21 Reidel; Dordrecht: 1976
  • 3 Albin M. Fuzzy Sets and their Application to Medical Diagnosis and Pattern Recognition. Ph. D. Thesis, Univ. of California; Berkeley: 1975
  • 4 Alperovitch A, Lelloucjh J. Methods of Aiding Medical Decisions: Application to Diagnosis of Round Intra-thoracic X-Rays Picture. Comp. Biomed. Res 07 1974; 127-141.
  • 5 Amlador E. Health and Normality. J. Amer. Med. Ass 232 1975; 953-955.
  • 6 Aström K. J. Optimal Control of Markov Processes with Incomplete State Information. J. Math. Anal. Appl 10 1965; 174-205.
  • 7 Bahtholomay A. F. Some Mathematical Aspects of the Medical Diagnostic Process. I. A General Mathematical Model. Bull. Math. Biophys 33 1971; 413-424.
  • 8 Bartholomay A. F. Some Mathematical Aspects of the Medical Diagnosis. II. A Mathematical Model of Electrocardiographic Diagnosis. Bull. Math. Biophys 35 1973; 535-547.
  • 9 Belis M, Guiasu S. A Quantitative-qualitative Measure of Information in Cybernetic Systems. IEEE Trans. Inform. Theory 14 1968; 593-594.
  • 10 Betaqtje N. E, Gorry A. Automating Judgmental Decisionmaking for a Serious Medical Problem. Management Sci 17 1971; B421-434.
  • 11 Blackwell D. The Stochastic Processes of Borel Gambling and Dynamic Programming. Ann. Statist 04 1976; 370-374.
  • 12 Bouchon B. Useful Information and Questionnaires. Information and Control 32 1976; 368-378.
  • 13 Bremerman H. Pattern Recognition by Deformable Prototypes. Lecture Notes Mathematics No. 525. 15-57 Springer; Berlin-Heidelberg-New York: 1976
  • 14 Britton K. E, Quinn V, Brown B. L, Ekins R. P. A Strategy for Thyroid Function Tests. Brit. med. J 1975; 03: 350-352.
  • 15 Buchanan B. G, Sutherland G. L, Feigenbaum E. A. Rediscovering Some Problems of Artificial Intelligence in the Context of Organic Chemistry. Machine Intelligence. Vol. 5, 253-280 Edinburgh University Press; Edinburgh: 1970
  • 16 Carnap R. Inductive Logic and Rational Decisions. In Carnap R, Jeffrey R. C. (Eds): Studies in Inductive Logic and Probability. 5-31 Univ. California Press; Berkeley: 1971
  • 17 Carnap R. A Basic System of Inductive Logic. Part I. In Carnap R, Jeffrey R. C. (Eds): Studies in Inductive Logic and Probability. 33-165 Univ. California Press; Berkeley: 1971
  • 18 Christl H. L. Die Anwendung der dynamischen Programmierung bei sequentiellen Diagnoseverfahren. In Lange H. J, Wagner G. (Hrsg.): Computerunterstützte ärztliche Diagnostik, S. 209-214 Schattauer; Stuttgart: 1973
  • 19 Christl H. L. Zum Problem der Bestimmung optimaler Diagnosestrategien. EDV in Medizin und Biologie 06 1975; 44-49.
  • 20 Copeland D. Concepts of disease and diagnosis. Perspect. Biol. Med 20 1977; 528-538.
  • 21 Croft D. J, Machol R. E. Mathematical Methods in Medical Diagnosis. Ann. Biomed. Eng 02 1974; 69-89.
  • 22 De Groot M. H, Feder P. I, Goel P. K. Matchmaking. Ann. Math. Statist 42 1971; 578-593.
  • 23 De Leve G, Federgruen A, Tijms H. C. A General Markov Decision Method. I. Model and Techniques. Advances Appl. Probability 09 1977; 296-315.
  • 24 Dudley H. A. F. Pay-off, Heuristics, and Pattern Recognition in the Diagnostic Process. Lancet 1968; 02: 723-726.
  • 25 Duncan G. T. Optimal Diagnostic Questionnaires. Operations Res 23 1975; 22-32.
  • 26 Duncker K. On Problemsolving. Psychol. Monogr. 58. 1945 No. 270..
  • 27 Dybkaee R, Gräsbeck R. Theory of Reference Values. Scand. J. Clin. Lab. Invest 32 1973; 1-7.
  • 28 Figueras J. The Restriction Set Approach to Stochastic Decision Systems. Ph. D. Thesis, Univ. Michigan; Ann Arbor: 1972
  • 29 Forst B. E. Decision Analysis and Medical Malpractice. Operations Res 22 1974; 1-12.
  • 30 Garey M. R. Optimal Binary Decision Trees for Diagnostic Identification Problems. Ph. D. Thesis; Univ. Wisconsin: 1970
  • 31 Gentilhomme Y. Les ensembles flous en linguistique. Cahiers linguist, théor. appl 05 1968; 47-57.
  • 32 Gill A, Gottlieb D. The Identification of a Set by Successive Intersections. Information and Control 24 1974; 20-35.
  • 33 Ginsberg A. S. The Diagnostic Process Viewed as a Decision Problem. In Jacquez J. A. (Edit.): Computer Diagnosis and Diagnostic Methods. 203-240 Thomas; Springfield: 1972
  • 34 Ginsberg A. S, Offensend F. L. An Application of Decision Theory to a Medical Diagnosis-Treatment Problem. IEEE Trans. Syst. Sci. Cybern., SSC-âf 1968; 355-362.
  • 35 Goguen J. A. The Logic of Inexact Concepts. Synthèse 19 (1968–1969) 325-373.
  • 36 Good I. J. How Rational Should a Manager Be?. Management Sci 08 1962; 383-393.
  • 37 Good I. J. Some Statistical Methods in Machine Intelligence Research. Math. Biosci 06 1970; 185-208.
  • 38 Good I. J. The Bayesian Influence, or How to Sweep Subjectivism under the Carpet. In Harper W. L, Hooker C. A. (Eds): Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Vol. 2, 125-174 Reidel; Doidrecht: 1976
  • 39 Good I. J. Dynamic Probability, Computer Chess, and the Measurement of Knowledge. Machine Intelligence. Vol. 8, 139-150 Horwood; Chichester: 1977
  • 40 Good I. J, Card W. I. The Diagnostic Process with Special Reference to Errors. Meth. Inform. Med 10 1971; 176-188.
  • 41 Grenander U. A Unified Approach to Pattern Analysis. Advances in Computers 10 1970; 175-216.
  • 42 Grenander U. Pattern Synthesis. Springer; Berlin-Heidelberg-New York: 1976
  • 43 Guiasu S. On an Algorithm for Recognition. In Hodson F. R, Kendall D. G, Tautu P. (Eds): Mathematics in the Archaeological and Historical Sciences. 96-102 Edinburgh Univ. Press; Edinburgh: 1971
  • 44 Guiasu S. Weighted Entropy. Rep. Math. Phys 02 1971; 165-179.
  • 45 Hockstra D. J. Partially Observable Markov Decision Processes with Applications. Techn. Rep. No. 156, Dept. Operations Res., Stanford Univ; Stanford: 1973
  • 46 Hockstra D. J, Miller S. D. Sequential Games and Medical Diagnosis. Comp. Biomed. Res 09 1976; 205-215.
  • 47 Hogarth R. B. Cognitive Processes and the Assessment of Subjective Probability Distributions. J. Amer. Statist. Ass 70 1975; 271-294.
  • 48 Iosifescu M, Tautu P. Bayesian Inference in an Archaeological Problem. In Hodson F. R, Kendall D. G, Tautu P. (Eds): Mathematics in the Archaeological and Historical Sciences. 82-84 Edinburgh Univ. Press; Edinburgh: 1971
  • 49 Kahneman D, Tversky A. Subjective Probability: A Judgment of Representativeness. Cognitive Psychology 3 1972; 430-454.
  • 50 Kochen M, Galanter E. H. The Acquisition and Utilization of Information in Problem Solving and Thinking. Information and Control 01 1958; 267-288.
  • 51 Kowalski R. Search Strategies for Theorem-proving. Machine Intelligence. Vol. 5, 181-201 Edinburgh Univ. Press; Edinburgh: 1969
  • 52 Krischer J. P. Diagnostic Nets. Bio-Med. Comp 02 1971; 27-38.
  • 53 Kulikowski C. A. Pattern Recognition Approach to Medical Diagnosis. IEEE Trans. Syst. Sci. Cybern SSC-6 1970; 173-178
  • 54 Kuznetzov P. I, Pchelintzev L. A. The Application of Some Mathematical Methods in Medical Diagnostics. Math. Biosci 05 1969; 365-377.
  • 55 Lasker G. E. Application of Sequential Pattern-recognition Technique to Medical Diagnosis. Bio-Med. Comp 01 1970; 173-186.
  • 56 Ledley R. S, Lusted L. B. Medical Diagnosis and Modern Decision Making. Proc. Synip. Appl. Math 14 1962; 117-158.
  • 57 Lee R. C. T, Chang C. L. Some Properties of Fuzzy Logic. Information and Control 19 1971; 417-431.
  • 58 Lindley D. V. Costs and utilities. In de Dombal F. T, Grémy F. (Eds): Decision Making and Medical Care: Can Information Science Help ?. 101-110 North-Holland; Amsterdam: 1976
  • 59 Luce R. D, Raiffa H. Games and Decisions. Wiley; New York: 1957
  • 60 Michie D. A Theory of Advice. Machine Intelligence. Vol. 8, 151-168 Horwood; Chichester: 1977
  • 61 Mosteller F, Wallace D. L. Inference in an Authorship Problem. J. Amer. Statist. Ass 5S 1963; 275-309.
  • 62 Neisser U. The Multiplicity of Thought. Brit. J. Psychol 54 1963; 1-14.
  • 63 Nemhauser G. L. A Generalized Permanent Label Setting Algorithm for the Shortest Path between Specified Nodes. J. Math. Anal. Appl 3S 1972; 328-334.
  • 64 Newell A, Shaw J. C, Simon H. A. Report on a General Problem-solving Program. Information Processing. 256-264 UNESCO-Oldenbourg-Butterworth, Paris-Müinchen-London: 1960
  • 65 Patrick A. E, Stelmack F. P, Shen L. Y. L. Review of Pattern Recognition in Medical Diagnosis and Review of Consulting Relative to a New System Model. IEEE Trans. Syst. Man, Cybern. SMC-df 1974; 1-16.
  • 66 Pauker S. G, Gorry G. A, Kassirer J. P, Schwartz W. B. Towards the Simulation of Clinical Cognition. Taking a Present Illness by Computer. Amer. J. Med 60 1976; 981-996.
  • 67 Pavel M. Pattern Recognition Categories. Pattern Recognition 08 1976; 115-118.
  • 68 Peterson C. R, Beach L. R. Man as Intuitive Statistician. Psychol. Bull 6S 1967; 29-46.
  • 69 Plotkin G. D. A Further Note on Inductive Generalization. Machine Intelligence. Vol. 6, 101-124 Edinburgh Univ. Preps; Edinburgh: 1971
  • 70 Polya G. Heuristic Reasoning and the Theory of Probability. Amer. Math. Monthly 4S 1941; 450-465.
  • 71 Polya G. How to Solve It. Princeton Univ. Press; Princeton: 1945
  • 72 Popper K. R. The Logic of Scientific Discovery. Hutchinson; London 1959; 8th Impression: 1975
  • 73 Popper K. R. Objective KnowledgeAn Evolutionary Approach. Clarendon Press; Oxford: 1972
  • 74 Renyi A. On a New Axiomatic Theory of Piobability. Acta Math. Acad. Sci. Hung 06 1955; 285-335.
  • 75 Renyi A. Foundations of Probability. Holden-Day; San Francisco: 1970
  • 76 Rhenius D. Incomplete Information in Markovian Decision Models. Ann. Statist 02 1974; 1327-1334.
  • 77 Rudemo M. State Estimation for Partially Observed Markov Chains. J. Math. Anal. Appl 44 1973; 581-611.
  • 78 Sadegh-Zadeh K. Subjektive Wahrscheinlichkeit und Diagnose. Meth. Inform. Med 13 1974; 97-102.
  • 79 Sadegh-Zadeh K. Grundlagenprobleme einer Theorie der klinischen Praxis. Metamed 01 1977; 76-102.
  • 80 Scadding J. G. Meaning of Diagnostic Terms in Bronchopulmonary Disease. Brit. med. J 1963; 02: 1425-1430.
  • 81 Scheff T. J. Decision Rules, Types of Errors, and their Consequences in Medical Diagnosis. Behavioral Sci S 1963; 97-107.
  • 82 Schmidt S. A. Measuring Uncertainty: An Elementary Introduction to Bayesian Statistics. Addison-Wesley; Reading: 1968
  • 83 Shiryaev A. N. On Optimum Methods in Quickest Detection Problem. Theor. Probability Appl 08 1963; 22-46.
  • 84 Slagle J. R, Lee R. C. T. Application of Game Tree Searching Techniques to Sequential Pattern Recognition. Comm. ACM 14 1971; 103-110.
  • 85 Smallwood R. D, Sondik E. J. The Optimal Control of Partially Observable Markov Processes Over a Finite Horizon. Operations Res 21 1973; 1071-1088.
  • 86 Smets P, Vadstsel H, Bernard R, Kornreich F. Bayesian Probability of Fuzzy Diagnosis. MEDINFO 77. 121-122 IFIP; North-Holland, Amsterdam: 1977
  • 87 Sttndeeman F. W. Current Concepts of »Normal Values«, »Reference Values«, and »Discrimination Values« in Clinical Chemistry. Clin. Chem 21 1975; 1873-1877.
  • 88 Tatjtu P. Simulating Chronic Diseases. Screening and Therapy Problems. In press 1978
  • 89 Taylor T. R, Aitchison J, McGirr E. M. Doctors as Decision Makers: A Computer Assisted Study of Diagnosis as a Cognitive Skill. Brit. med. J 1971; 03: 35-40.
  • 90 Teller P. Conditionalization, Observation, and Change of Preference. In Harper W. L, Hooker C. A. (Eds): Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Vol. 1, 205-259 Reidel; Dordrecht: 1976
  • 91 Terrenoire M, Tounissottx D. Pseudo questionnaires and information. In de Dombai F. T, Grémy F. (Eds): Decision Making and Medical Care: Can Information Science Help ?. 413-420 North-Holland; Amsterdam: 1976
  • 92 Ttjkey J. W. Conclusions vs. Decisions. Technometrics 02 1960; 423-433.
  • 93 Tversky A, Kahneman D. Judgment under Uncertainty: Heuristics and Biases. Science 185 1974; 1124-1131.
  • 94 White C. C. Optimal Diagnostic Questionnaires which Allow Less than Truthful Responses. Information and Control 32 1976; 61-74.
  • 95 Wortman P. M. Representation and Strategy in Diagnostic Problem Solving. Human Factors 08 1966; 48-53.
  • 96 Zadeh L. A. Fuzzy Sets. Information and Control S 1965; 338-353.
  • 97 Zadeh L. A. Toward a Theory of Approximate Reasoning. Proc. Conf. Computer Graphics, Pattern Recognition & Data Structure. 214 Inst. IEEE; 1975