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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 to provide strong evidence to rule in or rule out diagnoses respectively in most circumstances. 4 When tests report results as being either positive or negative the two likelihood ratios are called the positive likelihood ratio and the negative likelihood ratio.
The table shows the results of a study of the value of a history of smoking in diagnosing obstructive airway disease. 5 Smoking history was categorised into four groups according to pack years smoked (packs per day x years smoked). The likelihood ratio...