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

Schlüssel-Wörter

Diagnostischer Prozeß - Fehlerforschung - Statistische Analyse - Beweisgewicht

• References

• 1 Boyle J. A, Greig WR, Franklin D. A, Harden R. McG, Buchanan W. W, Mcgirr 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 16 1967; 185-210.
• 3 card W. I, GOOD I. J. The estimation of the implicit utilities of medical consultants. Math. BioscL 06 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 psydiometric 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 tbe analysis of time-series«. by Bartlett M. S. Symposium on Information Theory, Ministry of Supply, 1950. 180 Reprinted in Trans. 1.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 pp. 20–36. Liverpool: University Press; 1954
• 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. 125-136 London: Butterworths; 1961
• 15 Good I. J. How rational should a manager be?. Management Sei 08 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. 391-404 New York, London, Sydney: Wiley; 1964
• 18 Good I. J. The Estimation of Probabilities: An Essay on Modem 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. 115-128 London: HMSO 1965);
• 20 Good I. J. How to estimate probabilities. J. Inst. math. Applic 02 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 26 1967; 206-208.
• 22 Good I. J. Some statistical methods in machine-intelli- gence research. Virginia J. Sei 19 1968; 101-110.
• 23 Good I. J. Corroboration, explanation, evolving probability, simplicity, and a sharpened razor. Brit. J, philos. Sei 29 1968; 123-143.
• 24 Good I. J. Utility of a distribution. Nature 229 1968; 1392.
• 25 Good I. J. A five-year plan for automatic chess. In Dale E, Michie D. (Eds): jMachine 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, 183-203 New York: Academic Press; 1969
• 27 Good I. J. The probabilistic explication of information, evidence, surprise, causality, explanation, and utility. Int. Statist. Symposium, Waterloo. 1970. Toronto: Holt, Reinhart and Winston; 1971
• 28 Good I. J. Information, rewards, and quasi-utilities. To appear in Leach J. J. 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 Gorry G. A. A system for computer-aided diagnosis. Project MAC, Massachusetts Institute of Technology. Thesis. 1967
• 30a Grew N. Cosmologia Sacra; or, a Discourse of the Universe, as it is the Creature and Kingdom of God, p. 66. London: W. Rogers, S. Smith, and B. Walford; 1701
• 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 for the prior probability in estimation problems. Proc, roy. Soc. A 186 1946; 453-461.
• 34 Kerridge 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 230 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. Games 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 07 1969; 435-445.
• 42 Minsky M. L, Selfridge O. G. Learning in random nets. In Cherry C. (Ed.): Information Theory. 335-347 London: Butterworths; 1961
• 43 Nacke O, Wagner G. Bibliography on the topic »The role of error in medicine; quality control as a task of medical documentation«. Meth. Inform. Med 03 1964; 133-150.
• 44 Neumann J. von, Morgenstern 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 02 1958; 320-325.
• 46 Peirce C. S. The probability of induction. Popular Science Monthly 22. 1878: 705-718 Reprinted in C. Hartshorne and P. Weiss (Eds.): Collected Papers of Charles Saunders Peirce, Vol. 2, 4th ed., pp. 415–423. (Cambridge/Mass.: The Belknap Press of Harvard University Press); Reprinted in J. R. Newman (Ed.): The World of Mathematics, Vol. 2, pp. 1341–1354. (New York: Simon and Schuster 1956).‘
• 47 Rényi A. On measures of entropy and information. Proc. Fourth Berkeley Sympos. Math. Statist, and Prob. vol. 1. 547-561 Berkeley, Calif: Univ. Calif. Press; 1961
• 48 Samuel A. L. Some studies in machine learning using the game of checkers. IBM J. Res. Dev 03 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. 64-67 London: Methuen; New York; Wiley; 1962
• 51 Shannon C, EWeaver W. The Mathematical Theory of Communication. Urbana: Univ: Illinois Press 1949;
• 52 Tribus M. Rational Descriptions, Decisions and Designs. New York: Pergamon; 1969
• 53 Vickery B. C. Faceted Classification. London: ASLIB; 1960
• 54 Woodward P. M. Probability and Information Theory, with Applications to Radar. London: Pergamon; 1953
• 55 Yenusnalmy J. Reliability of chest radiography in the diagnosis of pulmonary lesions. Amer. J. Surg 89 1955; 231-240.