In a screening programme for type-2 diabetes, a test has sensitivity 80% and specificity 90%. The prevalence of disease in the population is 10%. Using Bayes' theorem, the Positive Predictive Value (PPV) of this test is:

• A 61.5%
• B 72.0%
• C 88.9%
• D 47.1% ✓

Explanation

PPV = (Sensitivity × Prevalence) / [(Sensitivity × Prevalence) + (1 − Specificity)(1 − Prevalence)]. Numerator = 0.80 × 0.10 = 0.08. Denominator = 0.08 + (0.10 × 0.90) = 0.08 + 0.09 = 0.17. PPV = 0.08 / 0.17 = 47.1%. Low prevalence drastically reduces PPV even with decent sensitivity and specificity.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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