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Qualitative research
A qualitative approach to Bayes' theorem
  1. Mitchell A Medow1,
  2. Catherine R Lucey2
  1. 1Section of General Internal Medicine, Boston University School of Medicine, Boston, Massachusetts, USA
  2. 2Internal Medicine, The Ohio State University College of Medicine, Columbus, Ohio, USA
  1. Correspondence to: Dr Mitchell A Medow
    Section of General Internal Medicine, Boston University School of Medicine, Crosstown Center Building, 2nd Floor, 801 Massachusetts Avenue, Boston, MA 02118, USA; mitchell.medow{at}

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While decisions made according to Bayes' theorem are the academic normative standard, the theorem is rarely used explicitly in clinical practice. Yet the principles can be followed without intimidating mathematics. To do so, one can first categorise the prior-probability of the disease being tested for as very unlikely (less likely than 10%), unlikely (10–33%), uncertain (34–66%), likely (67–90%) or very likely (more likely than 90%). Usually, for disorders that are very unlikely or very likely, no further testing is needed. If the prior probability is unlikely, uncertain or likely, a test and a Bayesian-inspired update process incorporating the result can help. A positive result of a good test increases the probability of the disorder by one likelihood category (eg, from uncertain to likely) and a negative test decreases the probability by one category. If testing is needed to escape the extremes of likelihood (eg, a very unlikely but particularly dangerous condition or in the circumstance of population screening, or a very likely condition with a particularly noxious treatment), two tests may be needed to achieve. Negative results of tests with sensitivity ≥99% are sufficient to rule-out a diagnosis; positive results of tests with specificity ≥99% are sufficient to rule-in a diagnosis. This method overcomes some common heuristic errors: ignoring the base rate, probability adjustment errors and order effects. The simplicity of the method, while still adhering to the basic principles of Bayes' theorem, has the potential to increase its application in clinical practice.

Bayes' theorem1 remains the normative standard for diagnosis, but it is often violated in clinical practice. Attempts to simplify its application with diagnostic computer programs,2 3 nomograms,4 rulers5 or internet calculators6 have not helped to increase its use. Bayes' theorem helps overcome many well-known cognitive errors in diagnosis, such as …

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  • Competing interests None.