A positive test result with a likelihood ratio of 2.0 implies what about post-test odds?

A positive test result with a likelihood ratio of 2.0 implies what about post-test odds?

• A. Post-test odds are halved
• B. No change in odds
• C. Post-test odds triple
• D. Post-test odds are doubled relative to pre-test odds

Answer: (D)

The key idea is how a positive likelihood ratio updates the odds after testing. When a test result is positive, the post-test odds are obtained by multiplying the pre-test odds by the positive likelihood ratio: post-test odds = pre-test odds × LR+. With a likelihood ratio of 2.0, you multiply the pre-test odds by 2, so the post-test odds are doubled relative to the pre-test odds. If you want to see this in probability terms, convert the pre-test probability to odds, multiply by 2, then convert back to probability. For example, a pre-test probability of 30% has odds of 0.3/0.7 ≈ 0.429; doubling gives ≈0.857, which corresponds to a post-test probability of about 46%. Therefore, the post-test odds are doubled relative to the pre-test odds.

The key idea is how a positive likelihood ratio updates the odds after testing. When a test result is positive, the post-test odds are obtained by multiplying the pre-test odds by the positive likelihood ratio: post-test odds = pre-test odds × LR+. With a likelihood ratio of 2.0, you multiply the pre-test odds by 2, so the post-test odds are doubled relative to the pre-test odds.

If you want to see this in probability terms, convert the pre-test probability to odds, multiply by 2, then convert back to probability. For example, a pre-test probability of 30% has odds of 0.3/0.7 ≈ 0.429; doubling gives ≈0.857, which corresponds to a post-test probability of about 46%.

Therefore, the post-test odds are doubled relative to the pre-test odds.