A screening test for a disease has a sensitivity of 95% and a specificity of 85%. In a population with a disease prevalence of 5%, what is the positive predictive value (PPV) of this test?

Explanation

## Positive Predictive Value Calculation **Key Point:** Positive Predictive Value (PPV) is the probability that a person with a positive test result actually has the disease. It depends on both the test characteristics (sensitivity and specificity) AND the disease prevalence. ### Formula and Calculation Using the formula: $$PPV = \frac{TP}{TP + FP} = \frac{Sensitivity \times Prevalence}{(Sensitivity \times Prevalence) + [(1 - Specificity) \times (1 - Prevalence)]}$$ Given: - Sensitivity = 95% = 0.95 - Specificity = 85% = 0.85 - Prevalence = 5% = 0.05 **Calculation:** $$PPV = \frac{0.95 \times 0.05}{(0.95 \times 0.05) + [(1 - 0.85) \times (1 - 0.05)]}$$ $$PPV = \frac{0.0475}{0.0475 + (0.15 \times 0.95)}$$ $$PPV = \frac{0.0475}{0.0475 + 0.1425} = \frac{0.0475}{0.19} ≈ 0.25 = 25\%$$ **High-Yield:** PPV increases with: - Higher sensitivity - Higher specificity - Higher disease prevalence PPV decreases with lower prevalence, even if the test is highly sensitive and specific. **Clinical Pearl:** This is why screening tests for rare diseases (low prevalence) have low PPV—many positive results are false positives. Conversely, screening tests for common diseases (high prevalence) have higher PPV with the same test characteristics. **Tip:** In low-prevalence populations, always calculate PPV; don't assume a "good" test (high sensitivity/specificity) will have a high PPV. [cite:Park 26e Ch 10]