## Understanding Test Performance Metrics **Key Point:** Sensitivity and specificity are intrinsic properties of a test independent of disease prevalence, while predictive values depend on the prevalence of disease in the population being tested. ### Calculation of Test Metrics Given data: - True Positives (TP) = 95 (correctly identified TB patients) - True Negatives (TN) = 891 (correctly identified non-TB individuals) - False Negatives (FN) = 5 (TB patients missed) - False Positives (FP) = 9 (non-TB individuals incorrectly identified as TB) - Total TB patients = 100 - Total non-TB individuals = 900 **Sensitivity** = $\frac{TP}{TP+FN} = \frac{95}{95+5} = \frac{95}{100} = 95\%$ ✓ (Option 1 is correct) **Specificity** = $\frac{TN}{TN+FP} = \frac{891}{891+9} = \frac{891}{900} = 99\%$ ✓ (Option 2 is correct) **Negative Predictive Value (NPV)** = $\frac{TN}{TN+FN} = \frac{891}{891+5} = \frac{891}{896} = 99.4\%$ (NOT 98.9%) However, let me recalculate option 3: If we consider the test results among those who tested negative: - True negatives = 891 - False negatives = 5 - Total negative tests = 896 - NPV = 891/896 ≈ 99.4% Option 3 states "approximately 98.9%" which is incorrect. **Positive Predictive Value (PPV)** = $\frac{TP}{TP+FP} = \frac{95}{95+9} = \frac{95}{104} = 91.3\%$ (NOT 95%) Option 4 states "approximately 95%" which is incorrect. ### Comparison of Metrics | Metric | Formula | Value | Depends On | |--------|---------|-------|------------| | Sensitivity | TP/(TP+FN) | 95% | Test accuracy in diseased | | Specificity | TN/(TN+FP) | 99% | Test accuracy in non-diseased | | PPV | TP/(TP+FP) | 91.3% | Prevalence + test characteristics | | NPV | TN/(TN+FN) | 99.4% | Prevalence + test characteristics | **High-Yield:** PPV and NPV are heavily influenced by disease prevalence. In this population with 10% TB prevalence, the PPV (91.3%) is lower than sensitivity (95%) because many positive tests occur in the larger non-diseased population. **Clinical Pearl:** When evaluating a positive test result in clinical practice, the PPV tells you the actual probability the patient has the disease. A 91.3% PPV means about 1 in 11 positive tests will be false positives—clinically significant for TB screening. **Warning:** Do not confuse sensitivity/specificity (intrinsic test properties) with PPV/NPV (population-dependent predictive values). A test with high sensitivity and specificity can still have a low PPV in a low-prevalence population.
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