Acute Gout with Comorbidities — UKMLA MCQ

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In a screening follow-up clinic, the pre-test probability of disease is 20%. A positive confirmatory test has a positive likelihood ratio of 6. What is the post-test probability of disease?

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Correct answer: B — 60.0%

First convert probability to odds: pre-test odds = p ÷ (1 − p) = 0.20 ÷ 0.80 = 0.25. Apply the likelihood ratio: post-test odds = 0.25 × 6 = 1.5. Convert odds back to probability: probability = odds ÷ (1 + odds) = 1.5 ÷ 2.5 = 0.60, or 60.0%. Option D incorrectly multiplies the 20% probability directly by an odds-based factor and then transforms inconsistently. Option E treats 6 as though it were the post-test odds without incorporating pre-test odds. The other choices reflect common odds-to-probability conversion errors. The final unit is percent probability.

Reference: NICE diagnostic-accuracy methods and Oxford CEBM likelihood-ratio resource: https://www.nice.org.uk/process/pmg30/chapter/diagnostic-accuracy ; https://www.cebm.ox.ac.uk/resources/ebm-tools/likelihood-ratios