In a study of 200 patients, the sensitivity of a diagnostic test is 80% and specificity is 90%. The prevalence of disease in this population is 10%. Using Bayes' theorem, the Positive Predictive Value (PPV) of this test is closest to:
- A 61%
- B 47% ✓
- C 72%
- D 89%
Correct answer: B. 47%
Explanation
PPV = (Sensitivity × Prevalence) / [(Sensitivity × Prevalence) + (1 − Specificity) × (1 − Prevalence)]. Substituting: (0.80 × 0.10) / [(0.80 × 0.10) + (0.10 × 0.90)] = 0.08 / (0.08 + 0.09) = 0.08 / 0.17 ≈ 47%. This illustrates that even with high sensitivity and specificity, PPV is low when disease prevalence is low.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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