## Understanding False-Positive Results in Screening ### Definition and Epidemiology A false-positive result occurs when a screening test is positive but the disease is actually absent. The frequency of false positives in a screening program is directly determined by the **specificity** of the test and the **prevalence** of disease in the population. ### Mathematical Relationship **Key Point:** The positive predictive value (PPV) — the probability that a positive test truly indicates disease — is given by: $$PPV = \frac{TP}{TP + FP} = \frac{\text{Sensitivity} \times \text{Prevalence}}{\text{Sensitivity} \times \text{Prevalence} + (1 - \text{Specificity}) \times (1 - \text{Prevalence})}$$ False positives = $(1 - \text{Specificity}) \times (1 - \text{Prevalence}) \times N$ ### Why Low Specificity Is the Answer | Factor | Effect on False Positives | Explanation | |--------|---------------------------|-------------| | **Low specificity** | **Directly increases** | A test with low specificity incorrectly identifies healthy individuals as diseased | | Low sensitivity | Increases false negatives (not false positives) | Misses true cases; does not create false positives | | High prevalence | Decreases false positives (relatively) | When disease is common, positive tests are more likely to be true positives | | Poor compliance | Affects follow-up, not the test result itself | Does not determine initial screening accuracy | **High-Yield:** In screening programs, especially in low-prevalence populations, a test with low specificity will generate many false positives, leading to unnecessary investigations, anxiety, and healthcare costs. ### Clinical Pearl This is why screening tests are chosen to have **high specificity** (≥95%) to minimize false positives and unnecessary harm to healthy individuals, even if sensitivity is slightly lower. ### Example In tuberculosis screening with chest X-ray in a low-prevalence urban population, a non-specific finding (e.g., old fibrosis) can be falsely interpreted as active TB if specificity is poor, generating false positives.
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