The Diagnostic Process with Special Reference to Errors

An analysis is made of the losses due to errors in the diagnostic process. The basic assumption is that the doctor should try to maximize expected utility, where the utility allows both for the health of the patient and for »costs« of various kinds. This assumption leads to the view that in general the doctor should make use of a diagnostic search tree. Owing to the difficulty of estimating utilities and of back-tracking in a large tree it is convenient for him to use substitutes for utility, called quasi-utilities, such as mean information transfer or expected weight of evidence. After listing a number of such quasi-utilities, the effect on their expectations due to error is considered. The losses can be larger than might have been supposed. Much of the analysis could also be applied to scientific problems other than to medical diagnosis.

Verfasser analysieren den Verlust infolge von Fehlern im diagnostischen Prozeß. Ihre grundsätzliche These ist, daß der Arzt versuchen sollte, den erwarteten Nutzen (»utility«) zu maximalisieren, wobei sich der Nutzen nicht nur auf die Gesundheit des Patienten, sondern auch auf »Kosten« aller Art erstrecken sollte. Diese Konzeption führt zu der Ansicht, daß der Arzt im allgemeinen diagnostische Verzweigungsprozesse benutzen sollte. Wegen der Schwierigkeit der Abschätzung des Nutzens und des Rückspulens in einem logischen Verzweigungsprozeß ist der Arzt geneigt, statt der echten Kriterien für den Nutzen Ersatzkriterien (sogenannte »Quasi-Utilities«) anzuwenden, wie etwa die mittlere Menge der übertragenen Information oder das erwartete Beweisgewicht. Nach Aufzählung einer Reihe von Quasi-Utilities wird der Effekt von Fehlern auf ihren Erwartungswert diskutiert. Diese Verluste können größer sein, als gemeinhin angenommen wird.

Ein Großteil der Analyse gilt nicht nur für die medizinische Diagnose, sondern läßt sich auch auf andere wissenschaftliche Probleme anwenden.

Key-Words:

Diagnostic Process - Role of Error - Statistical Analysis - Weight of Evidence.

Schlüsnel-Wörler:

Diagnostischer Prozeß - Fehlerforschung - Statistische Analyse - Beweisgewicht.

• References

• 1 Boyle J. A, Greig W. R, Franklin D. A, Harden R. McG, Buchanan W. W, McGihr E. M. Construction of a model for computer-assisted diagnosis: application to the problem of non-toxic goitre. Quart. J. Med 35 1966; 565-588.
• 2 Buck S. F, Wicken A. J. Models for use in estimating the risk of mortality from lung cancer and bronchitis. J. roy. statist. Soc. C 36 1967; 185-210.
• 3 Card W. I, Good I. J. The estimation of the implicit utilities of medical consultants. Math Biosci 6 1970; 45-54.
• 4 Cox D. R. The Analysis of Binary Data. London: Methuen; 1970
• 5 Cronbach L. J. A consideration of information theory and utility theory as tools for psychometric problems. Technical Report, College of Education, University of Illinois, Urbana; 1953
• 6 Good I. J. Probability and the Weighing of Evidence. London: Griffin; New York: Hafners; 1950
• 7 Good I. J. Contribution to discussion on »The statistical approach to the analysis of time-series«. Bartlett M. S.. Symposium on Information Theory, Ministry of Supply. 1950: 180 Reprinted in Trans. I.R.E., Professional Group on Information Theory; (1953)
• 8 Good I. J. On the population frequencies of species and the estimation of population parameters. Biometrika 40 1953; 237-264.
• 9 Good I. J. Mathematical Tools. In Carter C. F, Meredith G. P, Shackle G. L. S. (Eds.) Uncertainty and Business Decisions. Liverpool: University Press; 1954: 20-36.
• 10 Good I. J. Some terminology and notation in information theory. Proc. Inst. Electr. Engrs. C 103 1956; 200-204.
• 11 Good I. J. The surprise index for the multivariate normal distribution. Ann. math. Statist 27 1956; 1130-1135. erratum: 28 (1957) 1055
• 12 Good I. J. Contribution to the discussion of a paper by E. M. L. Beale »Confidence regions in non-linear estimation«. J. roy. statist. Soc. B 22 1960; 79-82.
• 13 Good I. J. Weight of evidence, corroboration, explanatory power, information and the utility of experiments. J. roy. statist. Soc. B 22 1960; 319-331. corrigenda, 30 (1968) 203
• 14 Good I. J. Weight of evidence, causality and false-alarm probabilities. In Cherry C. (Ed.) Information Theory. London: Butterworths; 1961: 125-136.
• 15 Good I. J. How rational should a manager be?. Management Sci. 8 1962; 383-393.
• 16 Good I. J. Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables. Ann. math. Statist. 34 1963; 911-934.
• 17 Good I. J. Measurements of decisions. In Cooper W. W, Leavitt H. J, Shelly M. W. (Eds.) New Perspectives in Organization Research. New York, London, Sydney: Wiley; 1964: 391-404.
• 18 Good I. J. The Estimation of Probabilities: An Essay on Modern Bayesian Methods. Cambridge/Mass: M.I.T. Press; 1965
• 19 Good I. J. Categorization of classification. Proc. of a Conference on Mathematics and Computer Science in Biology and Medicine at Balliol College, Oxford. London: HMSO; 1965: 115-128.
• 20 Good I. J. How to estimate probabilities. J. Inst. math. Applic. 2 1966; 364-383.
• 21 Good I. J. Contribution to the discussion of a paper by Buck and Wicken (see Ref. [2]). J. roy. statist. Soc. C 16 1967; 206-208.
• 22 Good I J. Some statistical methods in machine-intelligence research. Virginia J. Sci. 19 1968; 101-110.
• 23 Good I. J. Corroboration, explanation, evolving probability, simplicity, and a sharpened razor. Brit. J. philos. Sci. 19 1968; 123-143.
• 24 Good I. J. Utility of a distribution. Nature 219 1968; 1392
• 25 Good I. J. A five-year plan for automatic chess. In Dale E, Michie D. (Eds) Machine Intelligence, Vol 2. 89-118. Edinburgh: Oliver and Boyd; 1968
• 26 Good I. J. What is the use of a distribution?. In Krishnaiah P. R.. (Ed.) Multivariate Analysis, Vol. 2. New York: Academic Press; 1969: 183-203.
• 27 Good I. J. The probabilistic explication of information, evidence, surprise, causality, explanation, and utility. Int. Statist. Symposium, Waterloo, 1970. Toronto: Holt, Rein-hart and Winston; 1971
• 28 Good I. J. Information, rewards, and quasi-utilities. To appear in. J. J Leach. (Ed.) Science, Decision, and Value. Dordrecht: D. Reidel; 1971
• 29 Good I. J, Toulmin G. H. The number of new species, and the increase of population coverage, when a sample is increased. Biometrika 43 1956; 45-63.
• 30 Gohry G. A. A system for computer-aided diagnosis. Project MAC, Massachusetts Institute of Technology. Thesis. 1967
• 30a Grew N. Cosmología Sacra: or, a Discourse of the Universe, as it is the Creature and Kingdom of God. London: W. Rogers, S. Smith, and B. Walford; 1701: 66
• 31 Jaynes E. T. Information theory and statistical mechanics. Phys. Rev. 106 1957; 620-630.
• 32 Jeffreys H. Theory of Probability, 3. ed. Oxford: University Press; 1961
• 33 Jeffreys H. An invariant form fur the prior probability in estimation problems. Proc. roy. Soc. A 186 1946; 453-461.
• 34 Kerhidge D. F. Inaccuracy and inference. J. roy. statist. Soc. B 23 1961; 184-194.
• 35 Koopman B. O. Relaxed motion in irreversible molecular statistics. Advanc. Chem. Phys. 15 1969; 37-63.
• 36 Kullback S. Information Theory and Statistics. New York Wiley London: Chapman and Hall; 1959
• 37 Ledley R. S, Lusted L. B. Reasoning foundations of medical diagnosis. Science 130 1959; 9-21.
• 38 Lindley D. V. On the measure of the information provided by an experiment. Ann. math. Statist. 27 1956; 986-1005.
• 39 Luce R. D, Raiffa H. Gaines and Decisions. New York: Wiley; 1957
• 40 Lusted L. B. Introduction to Medical Decision Making. Springfield, Illinois: Ch. C. Thomas; 1968
• 41 Lusted L. B. Perception of the Roentgen image: applications of signal detectability theory. Radiol Clin. N. Amer. 7 1969; 435-445.
• 42 Minsky M. L, Selfridge O. G. Learning in random nets. In Cherry C. (Ed.) Information Theory. London: Butterworths; 1961: 335-347.
• 43 Nacke O, Wagner G. Bibliography on the topic »The role of error in medicine; quality control as a task of medical documentation'!. Moth lnform. Med. 3 1964; 133-150.
• 44 Neumann J. von, Mohoenstejin O. Theory of Games and Economic Behaviour, 2. ed. Princeton: University Press; 1947
• 45 Newell A, Shaw J. C, Simon H. A. Chess-playing programs and the problem of complexity. IBM J. Res. Dev. 2 1958; 320-325.
• 46 Peirce C. S. The probability of induction. Popular Science Monthly 1878; 12: 705-718.
• 46a Reprinted in Hartshorne C, Weiss P. (Eds.) Collected Papers of Charles Saunders Peirce, Vol. 2. 4th ed. Cambridge/Mass: The Belknap Press of Harvard University Press; 415-423.
• 46b Reprinted in Newman J. R. (Ed.) The World of Mathematics, Vol. 2. New York: Simon and Schuster; 1956: 1341-1354.
• 47 Rényi A. On measures of entropy and information. Proc. Fourth Berkeley Sympos. Math. Statist and Prob., Vol. 1. Berkeley, Calif: Univ. Calif. Press; 1961: 547-561.
• 48 Samuel A. L. Some studies in machine learning using the game of checkers. IBM J. Res Dev 3 1959; 211-229.
• 49 Samuel A. L. Some studies in machine learning using the game of checkers, II. IBM J. Res. Dev 11 1967; 601-617.
• 50 Savage L J. Discussion. In Barnard G. A, Cox D. R. (Eds) The Foundations of Statistical Inference. London: Methuen; New York: Wiley; 1962: 64-67.
• 51 Shannon C. E, Weaver W. The Mathematical Theory of Communication. Urbana: Univ. Illinois Press; 1949
• 52 Thibus M. Rational Descriptions, Decisions and Designs. New York: Pergamon; 1969
• 53 Vickehy B. C. Faceted Classification. London: ASLIB; 1960
• 54 Woodward P. M. Probability and Information Theory, with Applications to Radar. London: Pergamon; 1953
• 55 Yerushalmy J. Reliability of chest radiography in the diagnosis of pulmonary lesions. Amer. J. Surg. 89 1955; 231-240.