Lead-time bias — USMLE Step 3 MCQ

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HardPreventive Medicine, Epidemiology, BiostatisticsLead-time biasUSMLE Step 3

A patient has a 20% pretest probability of pulmonary embolism. A diagnostic result has a positive likelihood ratio of 8. What is the approximate posttest probability after this positive result?

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Correct answer: A — 67%

The best answer is “67%”. Convert probability to odds: 0.20/0.80 = 0.25. Multiply by the likelihood ratio: 0.25 × 8 = 2. Convert back to probability: 2/(1 + 2) = 0.667, or about 67%. Multiplying 20% directly by 8 is not Bayesian updating because likelihood ratios operate on odds, not percentages. The result is therefore lower than the superficially calculated 160% and remains a clinically interpretable probability.

Reference: American Family Physician: Applying a Clinical Decision Rule for CAD in Primary Care to Select a Diagnostic Test and Interpret the Results: https://www.aafp.org/pubs/afp/issues/2019/0501/p584.html