A disease has a prevalence of 2% in a population. A diagnostic test has 90% sensitivity and 95% specificity. If a person tests positive, what is the probability they actually have the disease?
Answer and explanation
Correct answer: A. 18/67 (approximately 26.9%)
- Step 1: In a cohort of 1000 people: 20 have the disease, 980 do not. Step 2. True positives = 20 0.90 = 18. Step 3. False positives = 980 (1 - 0.95) = 980 0.05 = 49. Step 4. Total positives = 18 + 49 = 67. Step 5. P(Disease | +) = 18 / 67 approx 26.9%. Answer: 18/67 (approximately 26.9%). Why not the others:* 90% confuses sensitivity with positive predictive value.
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