Likelihood Ratios

LRs are also calculated using the sensitivity and specificity of a diagnostic test. The positive LR (LR+) is the ratio of the probability of a positive test in diseased patients to the probability of a positive test in patients who are not diseased. Mathematically, this is expressed as follows:

The negative LR (LR-) is the ratio of the probability of a negative test in patients with the disease to the probability of a negative test in patients who are not diseased. Mathematically, the LR- is expressed as follows:

LR Specificity (31)

Fig. 3-8. A stylized ROC curve. Sensitivity is plotted on the y-axis and 1-specificity is plotted on the x-axis. The points on curve A should be above the dashed 45° line B for the test to have diagnostic utility as shown here.

LRs are less dependent on prevalence than predictive values. As an assessment of the utility of a diagnostic test, the greater either LR is from 1, the better is the ability of the test to discriminate between patients with and without the disease. The LR+ should be greater than 1. This suggests that it is more likely to find a positive test in a patient with the disease than in a patient without the disease. The LR- should be less than 1, which suggests that a negative test is less likely to be found in a patient with the disease than in a patient without the disease.

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