In a given set of conditions, a screening test has 90% sensitivity and 90% specificity for screening a particular disease. The prevalence of the disease at the given time in that population is 10%. Which one of the following statements regarding positive predictive value of the test is correct?
The positive predictive value is 50%.
The correct answer is 50%. PPV = True Positives ÷ (True Positives + False Positives). Take a hypothetical population of 1000. Prevalence 10% gives 100 diseased and 900 non-diseased. Sensitivity 90% gives TP = 0.90 × 100 = 90 (10 false negatives). Specificity 90% means 10% of the healthy test falsely positive, so FP = 0.10 × 900 = 90 (810 true negatives). Hence PPV = 90 ÷ (90 + 90) = 90/180 = 50%. The NPV here is 810/(810 + 10) = 98.8%.
Why the others are wrong: 90% simply repeats the sensitivity and specificity — the classic trap, since predictive value is not the same as test validity. 70% and 60% cannot be derived from these figures; PPV would climb to that range only at a substantially higher prevalence (roughly 20–25% with the same test).
Key point: Sensitivity and specificity are intrinsic to the test and independent of prevalence, but PPV rises and NPV falls as prevalence rises — which is why screening low-prevalence populations yields many false positives.
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