A study of a new rapid diagnostic test for malaria in a high-transmission district finds sensitivity 92%, specificity 85%. The disease prevalence in this population is 40%. What is the Positive Predictive Value (PPV) of this test?
- A Approximately 79% ✓
- B Approximately 88%
- C Approximately 92%
- D Approximately 95%
Correct answer: A. Approximately 79%
Explanation
Using Bayes' theorem: PPV = (Sensitivity × Prevalence) / [(Sensitivity × Prevalence) + (1 − Specificity) × (1 − Prevalence)]. Numerator = 0.92 × 0.40 = 0.368. Denominator = 0.368 + (0.15 × 0.60) = 0.368 + 0.09 = 0.458. PPV = 0.368/0.458 ≈ 0.803 ≈ 80%, approximately 79–80%. In high-prevalence settings PPV is good. Options C and D overestimate by ignoring false positives, and B is also too high.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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