A new biomarker for colorectal cancer has sensitivity 85% and specificity 80%. In a population with 2% prevalence, which calculation correctly estimates the Positive Predictive Value (PPV)?
- A PPV = TP/(TP+FP) = (0.85×0.02)/[(0.85×0.02)+(0.20×0.98)] = 7.97% ✓
- B PPV = sensitivity/(sensitivity + 1 − specificity) = 81%
- C PPV = sensitivity × specificity = 68%
- D PPV = (sensitivity × prevalence)/specificity = 2.1%
Correct answer: A. PPV = TP/(TP+FP) = (0.85×0.02)/[(0.85×0.02)+(0.20×0.98)] = 7.97%
Explanation
PPV = (sensitivity × prevalence) / [(sensitivity × prevalence) + (1 − specificity) × (1 − prevalence)]. Numerator: 0.85 × 0.02 = 0.017. Denominator: 0.017 + 0.20 × 0.98 = 0.017 + 0.196 = 0.213. PPV = 0.017/0.213 ≈ 7.97%. This illustrates how a low disease prevalence drastically reduces PPV even when sensitivity and specificity are both high. Options B and C apply incorrect formulae; option D omits the denominator correction.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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