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Arch Hellen Med, 23(2), March-April 2006, 178-205


Diagnostic probabilities. Bayes' theorem and logistic regression

Laboratory of Clinical Epidemiology, School of Nursing, University of Athens, Athens, Greece

The probability of having or not having a specified disease, given positive or negative test result, is called the diagnostic value or diagnostic probability or posttest probability of the test. The diagnostic probability, according to Bayes' theorem, depends on the diagnostic quality (likelihoods, likelihood ratio) of the test, and the prior (or pretest) probability of the disease. For very low pretest probabilities, the posttest probability is also low irrespective of the test result. Similarly, for very high pretest probabilities, the posttest probability is also high, irrespective of the test result. Thus, performing a test is, in general, most useful when the pretest probability of disease is intermediate, which indicates considerable uncertainty about the patient's true state. It is also useful when the pretest probability is close to a treatment threshold probability, because a small change in the probability of disease is sufficient to alter management. The change from pretest to posttest probability of disease, which occurs as a result of diagnostic testing, is called diagnostic gain. Following the first severe criticism of the Bayesian approach to diagnosis by Miettinen and Caro, published in 1994, a new theory was introduced in diagnostic research, which is the application of the logistic regression model.

Key words: Bayes' theorem, Concentration-reduction effect, Diagnostic gain, Diagnostic value, Logistic regression, Treatment threshold.

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