## Understanding Test Performance Metrics ### Given Data - True Positives (TP) = 95 (correctly identified TB patients) - Total TB patients = 100 - True Negatives (TN) = 891 (correctly identified non-TB individuals) - Total non-TB individuals = 900 - Total population = 1000 - False Positives (FP) = 900 − 891 = 9 ### Calculating Each Metric **Sensitivity** = $\frac{TP}{TP+FN} = \frac{95}{100} = 95\%$ ✓ (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)** = $\frac{TN}{TN+FN} = \frac{891}{891+5} = \frac{891}{896} ≈ 99.4\%$ (Note: FN = 100 − 95 = 5) Option 3 states NPV ≈ 98.9%, which is **incorrect** — the actual NPV is ~99.4%. **Positive Predictive Value (PPV)** = $\frac{TP}{TP+FP} = \frac{95}{95+9} = \frac{95}{104} ≈ 91.3\%$ (Not 95%) Option 4 is also technically incorrect, but Option 3 contains the more obvious mathematical error. ### Key Point: **Sensitivity and specificity are test characteristics independent of disease prevalence**, whereas **PPV and NPV are population-dependent and vary with prevalence**. ### High-Yield: When evaluating diagnostic test performance: - **Sensitivity & Specificity** = intrinsic test properties (disease-dependent, not prevalence-dependent) - **PPV & NPV** = predictive values (highly dependent on disease prevalence in the population tested) ### Mnemonic: **SNOUT & SPIN** - **SNout**: Sensitivity rules OUT disease (high sensitivity = few false negatives) - **SPIn**: Specificity rules IN disease (high specificity = few false positives) ### Clinical Pearl: A test with 95% sensitivity and 99% specificity is excellent for ruling out TB (high sensitivity) but the PPV of ~91% means about 1 in 11 positive tests will be false positives — important for counseling patients in low-prevalence settings.
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