sensitivity, specificity, PPV, NPV, true positive, false positive, true negative, false negative
- related: Biostats
- tags: #literature #pulmonology
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- high sensitivity: high NPV, low false negative
- high specificity: high PPV, low false positive
The sensitivity of a test, given by TP / (TP + FN), is the probability that a patient with a given disease will have a positive result on that test; for a highly sensitive test, a negative result helps rule out a disease (SnNout). Higher sensitivity means fewer FNs. Similarly, the specificity of a test, given by TN / (TN + FP), is the probability that a patient without a given disease will have a negative test result on that test; for a highly specific test, a positive result helps rule in a disease (SpPin). Higher specificity means fewer FPs.
Positive predictive value (PPV), given by TP / (TP + FP), is the probability that a positive test correctly identifies an individual with the disease. Because higher specificity is associated with fewer FPs, higher specificity will, in the vast majority of cases, increase the PPV of the test (because FP is the denominator of PPV). In this case, the test with highest specificity (97%) is the best choice as it will most likely also has the highest PPV.
Negative predictive value (NPV) is the probability that a negative test result correctly identifies an individual who does not have the disease. A higher sensitivity leads to fewer false negatives and increases the NPV of the test. In this case, the test has a 100% sensitivity, implying no false negatives and a NPV value of 100%.
A 55-year-old patient with a history of moderate COPD is admitted to the hospital with community-acquired pneumonia that leads to ARDS requiring mechanical ventilation. No organisms were identified on laboratory testing. After 7 days on the ventilator, the patient develops a new fever. Repeat cultures are sent, along with a new fungal assay by a cross-covering colleague who quotes a 90% sensitivity and 60% specificity for the new assay from a recent multicenter cohort study of 600 immunocompromised ICU patients of whom 200 were determined to have true fungal infection by a composite gold standard. Based on this information, and knowing your patient may not be as immunocompromised as those in the referenced manuscript, which of the following statements is correct?