A nuclear stress test using a new radioisotope tracer has a sensitivity of 60% and specificity of 80% for detecting hemodynamically significant coronary artery disease, defined as coronary artery narrowing 50% by coronary angiography. In a patient with a pre-test probability for coronary artery disease of 40%, what is the positive likelihood ratio for the test?

Question

A nuclear stress test using a new radioisotope tracer has a sensitivity of 60% and specificity of 80% for detecting hemodynamically significant coronary artery disease, defined as coronary artery narrowing > 50% by coronary angiography.  In a patient with a pre-test probability for coronary artery disease of 40%, what is the positive likelihood ratio for the test?

Quizplus · Accepted Answer

The likelihood ratio (LR) is an expression of sensitivity and specificity that can be used to assess the value of a diagnostic test. The positive likelihood ratio (LR+) represents the value of a positive test result, and the negative likelihood ratio (LR-) represents the value of a negative test result. LR+ = sensitivity / (1 - specificity). It is the probability of a patient with the disease testing positive divided by the probability of a patient without the disease testing positive. It is equivalent to true positive rate / false positive rate.LR- = (1 - sensitivity) / specificity. It is the probability of a patient with the disease testing negative divided by the probability of a patient without the disease testing negative. It is equivalent to the false negative rate / true negative rate. LR+ = sensitivity / (1 - specificity). It is the probability of a patient with the disease testing positive divided by the probability of a patient without the disease testing positive. It is equivalent to true positive rate / false positive rate. LR- = (1 - sensitivity) / specificity. It is the probability of a patient with the disease testing negative divided by the probability of a patient without the disease testing negative. It is equivalent to the false negative rate / true negative rate. LRs can range from zero to infinity. A test result with an LR > 1 suggests the presence of the disease; the higher the LR, the more likely that the disease is actually present. A test result with an LR < 1 argues against the disease; the lower the LR, the less likely that the disease is actually present. General guidelines for interpretation of LRs are shown in the table. 11ec193a_972e_b1df_853d_15f7ffa59e02_MD0002_00 In this example, LR+ = sensitivity / (1 - specificity) = 0.6 / (1 - 0.8) = 3. Thus, a positive test result would provide only weak evidence for a patient having hemodynamically significant coronary artery disease. Because LRs are calculated from sensitivity and specificity, they do not change with the prevalence of the disease. Other advantages of LRs are that they can be used with tests that have more than 2 possible results, they can be used to combine the results of multiple diagnostic tests, and they can be used to calculate post-test probability for a target disorder (post-test odds = pre-test odds * LR). Educational objective: The positive likelihood ratio = sensitivity / (1 - specificity) The negative likelihood ratio = (1 - sensitivity) / specificity Positive and negative likelihood ratios, like sensitivity and specificity, are independent of disease prevalence. __________ References: How to use and interpret likelihood ratios. (http://www.ncbi.nlm.nih.gov/pubmed/10367208) Simplifying likelihood ratios. (http://www.ncbi.nlm.nih.gov/pubmed/12213147)

A Nuclear Stress Test Using a New Radioisotope Tracer Has