Understanding diagnostic tests 2: likelihood ratios, pre- and post-test probabilities and their use in clinical practice

Authors

  • Anthony K. Akobeng

    1. Department of Paediatric Gastroenterology, Central Manchester and Manchester Children's University Hospitals, Booth Hall Children's Hospital, Manchester, UK
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Correspondence
Dr A. K. Akobeng, Department of Paediatric Gastroenterology, Central Manchester and Manchester Children's University Hospitals, Booth Hall Children's Hospital, Charlestown Road, Blackley, Manchester M9 7AA, United Kingdom. Tel: 0161 918 5458 | Fax: 0161 918 5072 | Email: tony.akobeng@cmmc.nhs.uk

Abstract

The sensitivity and specificity of a test cannot be used to estimate probability of disease in individual patients. They can, however, be combined into a single measure called the likelihood ratio which is, clinically, more useful than sensitivity or specificity. Likelihood ratios provide a summary of how many times more (or less) likely patients with a disease are to have a particular result than patients without the disease. Using the principles of the Bayes theorem, likelihood ratios can be used in conjunction with pre-test probability of disease to estimate an individual's post-test probability of disease, that is his or her chance of having disease once the result of a test is known. The Fagan's nomogram is a graphical tool which, in routine clinical practice, allows one to combine the likelihood ratio of a test with a patient's pre-test probability of disease to estimate post-test probability.

Conclusion: Likelihood ratios summarize information about a diagnostic test by combining sensitivity and specificity. The Fagan's nomogram is a useful and convenient graphical tool that allows likelihood ratios to be used in conjunction with a patient's pre-test probability of disease to estimate the post-test probability of disease.

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