A rapid diagnostic test for COVID-19 (RT-PCR) in symptomatic patients has sensitivity 95% and specificity 98%. In a high-prevalence setting (20% disease prevalence), which diagnostic parameter best distinguishes this test's ability to confirm infection when positive versus exclude infection when negative?

Explanation

## Predictive Values in High-Prevalence Settings **Key Point:** In high-prevalence populations, PPV becomes clinically meaningful and approaches sensitivity, while NPV remains high. PPV is the key parameter distinguishing the test's ability to **confirm** disease when positive. ### Calculation of Predictive Values Given: Sensitivity = 95%, Specificity = 98%, Prevalence = 20% For a population of 10,000: - True Positives (TP) = 20% × 95% = 1,900 - False Positives (FP) = 80% × 2% = 160 - True Negatives (TN) = 80% × 98% = 7,840 - False Negatives (FN) = 20% × 5% = 100 $$PPV = \frac{TP}{TP+FP} = \frac{1,900}{1,900+160} = \frac{1,900}{2,060} ≈ 92.2\%$$ $$NPV = \frac{TN}{TN+FN} = \frac{7,840}{7,840+100} = \frac{7,840}{7,940} ≈ 98.7\%$$ ### Likelihood Ratios $$LR+ = \frac{Sensitivity}{1-Specificity} = \frac{0.95}{0.02} = 47.5$$ $$LR- = \frac{1-Sensitivity}{Specificity} = \frac{0.05}{0.98} ≈ 0.051$$ **Clinical Pearl:** A positive test result increases disease probability to ~92%, providing strong diagnostic confirmation. A negative test result decreases it to ~1.3%, providing excellent exclusion. Both are clinically useful, but PPV is the distinguishing metric for ruling **in** disease. **High-Yield:** In high-prevalence settings, PPV improves substantially (compare 92% here vs. 31% in the low-prevalence GDM example). This is why the same test performs differently across populations. ### Comparison Table: Low vs. High Prevalence | Parameter | Low Prevalence (5%) | High Prevalence (20%) | Interpretation | | --- | --- | --- | --- | | PPV | 31% | 92% | Test much better at confirming in high-prevalence populations | | NPV | 99% | 99% | Test equally good at excluding across populations | | LR+ | 8.5 | 47.5 | Stronger evidence for disease when positive in high prevalence | | LR− | 0.17 | 0.05 | Stronger evidence against disease when negative in high prevalence | **Mnemonic:** **PreTest → PostTest Probability** — PPV directly answers "If my test is positive, what is the probability I actually have the disease?" This is the clinician's most common question when a positive result appears. [cite:Park 26e Ch 10]