Statistics Notes

Diagnostic tests 4: likelihood ratios

BMJ 2004; 329 doi: http://dx.doi.org/10.1136/bmj.329.7458.168 (Published 15 July 2004)
Cite this as: BMJ 2004;329:168

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  1. Jonathan J Deeks (Jon.Deeks@cancer.org.uk), senior research biostatistician1,
  2. Douglas G Altman, professor of statistics in medicine2
  1. 1 Screening and Test Evaluation Program, School of Public Health, University of Sydney, NSW 2006, Australia
  2. 2 Cancer Research UK/NHS Centre for Statistics in Medicine, Institute for Health Sciences, Oxford OX3 7LF
  1. Correspondence to: Mr Deeks

    The properties of a diagnostic or screening test are often described using sensitivity and specificity or predictive values, as described in previous Notes.1 2 Likelihood ratios are alternative statistics for summarising diagnostic accuracy, which have several particularly powerful properties that make them more useful clinically than other statistics.3

    Each test result has its own likelihood ratio, which summarises how many times more (or less) likely patients with the disease are to have that particular result than patients without the disease. More formally, it is the ratio of the probability of the specific test result in people who do have the disease to the probability in people who do not.

    A likelihood ratio greater than 1 indicates that the test result is associated with the presence of the disease, whereas a likelihood ratio less than 1 indicates that the test result is associated with the absence of disease. The further likelihood ratios are from 1 the stronger the evidence for the presence or absence of disease. Likelihood ratios above 10 and below 0.1 are considered …

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