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March 2007
Evidence-Based Tip
The Likelihood Ratio: What are the odds that my patient has the disease I am testing for?
Comparative studies of diagnostic tests tell us how well a particular test does, compared to the truth as best we know it, usually as determined by a "gold standard" test. The results are reported as sensitivity (percentage of patients with the disease who correctly tested positive) and specificity (percentage of patients without the disease who correctly tested negative). These are helpful numbers, but we would like to know more. We need the likelihood ratio.
The likelihood ratio is a relative measure, combining both sensitivity and specificity. A positive likelihood ratio (+LR or LRpos) gives the odds that a test result would occur in our patient with the condition we are testing for, as opposed to a patient without the condition we are testing for.
+LR = sensitivity / (1 - specificity)
positive tests with the disease / positive tests with no disease
A negative likelihood ratio (-LR or LRneg) can also be calculated.
-LR = (1 - sensitivity) / specificity
negative tests with the disease / negative tests with no disease
The likelihood ratio is important, because it is independent of the prevalence of the disease. But its value comes when it is used in conjunction with a clinician's pre-test probability for the disease. Using a nomogram, the pre-test probability is charted against the likelihood ratio to obtain a post-test probability.
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Especially in a test for influenza, knowing the prevalence of the disease at that time in the community will be very important for interpreting the results of
the test, and will impact a clinician's pretest probability. To illustrate, assume that we are seeing a patient during a mild influenza outbreak. We feel after
our clinical exam that our patient has a 75 chance of having the disease. The Vanderbilt University Medical Center article reported a sensitivity of 63% and a
specificity of 97% for the rapid flu test, which we calculate to get a +LR of 21. Charting this on the nomogram will give us a post-test probability close to 99
percent. This is made easy by online versions of the nomogram, such as the one on the left from Oxford's Centre for Evidence-Based Medicine:
www.cebm.net/nomogram.asp.
Using the positive likelihood ratio, in conjunction with our pretest probability, we are now much more confident that our patient does indeed have influenza after testing positive for the rapid flu test.
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