## Understanding Test Utility in Low-Prevalence Populations **Key Point:** In low-prevalence populations, PPV is substantially lower than NPV, even when sensitivity and specificity are reasonable. This is the critical discriminator between ruling-in and ruling-out utility. ### Calculation of Predictive Values Given: Sensitivity = 85%, Specificity = 90%, Prevalence = 5% Using Bayes' theorem for a population of 10,000: - True Positives (TP) = 5% × 85% = 425 - False Positives (FP) = 95% × 10% = 950 - True Negatives (TN) = 95% × 90% = 8,550 - False Negatives (FN) = 5% × 15% = 75 $$PPV = \frac{TP}{TP+FP} = \frac{425}{425+950} = \frac{425}{1375} ≈ 31\%$$ $$NPV = \frac{TN}{TN+FN} = \frac{8,550}{8,550+75} = \frac{8,550}{8,625} ≈ 99\%$$ ### Likelihood Ratios $$LR+ = \frac{Sensitivity}{1-Specificity} = \frac{0.85}{0.10} = 8.5$$ $$LR- = \frac{1-Sensitivity}{Specificity} = \frac{0.15}{0.90} = 0.17$$ **Clinical Pearl:** A positive test result only increases the probability of disease to 31% (PPV). A negative test result decreases it to <1% (1 − NPV = 1%). This test is far superior for **ruling out** GDM than for **ruling it in**. **High-Yield:** In low-prevalence settings, even good tests have poor PPV. The low PPV (31%) is the distinguishing feature that limits this test's ability to confidently diagnose disease when positive. ### Why This Matters Clinically A positive screening test requires confirmatory testing (e.g., oral glucose tolerance test) because only 31% of positive screens truly have GDM. A negative test is highly reassuring (99% NPV) and effectively rules out disease. **Mnemonic:** **SnNOut, SpPIn** — High Sensitivity rules out (Negative result is reassuring); High Specificity rules in (Positive result is diagnostic). This test has moderate sensitivity (85%) and high specificity (90%), making it better for ruling out. [cite:Park 26e Ch 10]
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