A study reports a pre-test probability of 30% for coronary artery disease in a patient. The positive likelihood ratio (LR+) of the exercise stress test used is 5. What is the approximate post-test probability of disease after a positive result?
- A 68% ✓
- B 51%
- C 75%
- D 83%
Correct answer: A. 68%
Explanation
Pre-test odds = probability/(1 − probability) = 0.30/0.70 = 0.4286. Post-test odds = pre-test odds × LR+ = 0.4286 × 5 = 2.143. Post-test probability = post-test odds/(1 + post-test odds) = 2.143/3.143 ≈ 0.682 ≈ 68%. The positive likelihood ratio (LR+) = sensitivity/(1 − specificity) and indicates how much more likely a positive test is in a diseased than a non-diseased person; using Bayes theorem via odds form allows direct pre-to-post probability conversion.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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