Explain how to use Bayesian reasoning to update disease probability after a diagnostic test with a given likelihood ratio.

• A. Convert pretest probability to odds, multiply by the test's likelihood ratio to get post-test odds, then convert back to probability.
• B. Multiply pretest probability by the likelihood ratio.
• C. Add the likelihood ratio to the pretest probability.
• D. Use the pretest probability as the post-test probability regardless of result.

Answer: (A)

Bayesian updating uses odds because the likelihood ratio multiplies what you already believe in a consistent way. Start with your pretest probability, convert it to pretest odds with odds = P/(1−P). Then multiply by the appropriate likelihood ratio to get post-test odds: post-test odds = pretest odds × LR. Finally convert back to probability: post-test probability = post-test odds / (1 + post-test odds).

For example, if the pretest probability is 30% (0.30), the pretest odds are 0.30/0.70 ≈ 0.4286. If the test result is positive and the LR is 4, the post-test odds are 0.4286 × 4 ≈ 1.714, giving a post-test probability of 1.714/(1+1.714) ≈ 0.63 (about 63%). If the result is negative and the LR is 0.2, the post-test odds are 0.4286 × 0.2 ≈ 0.0857, with a post-test probability of 0.0857/(1+0.0857) ≈ 0.079 (about 8%).

Remember: LR+ > 1 increases the probability; LR− < 1 decreases it; LR = 1 leaves it unchanged. If you only know sensitivity and specificity, you can compute LR+ = sensitivity/(1−specificity) and LR− = (1−sensitivity)/specificity to use this same approach.