Positive likelihood ratio — MRCPsych Paper A MCQ

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ModerateEpidemiology and research methodsPositive likelihood ratioMRCPsych Paper A

A delirium screening test has a positive likelihood ratio (LR+) of 10 in an acute hospital sample. Which statement is the most accurate interpretation of this result?

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Correct answer: C — After a positive result, the post-test odds of delirium are 10 times the pre-test odds.

Explanation lettering: E = shown as A · C = shown as B · D = shown as C · B = shown as D · A = shown as E

D is correct. A positive likelihood ratio is applied using the Bayesian relationship: post-test odds = pre-test odds x LR+. An LR+ of 10 therefore multiplies the pre-test odds of delirium by 10 and usually provides strong evidence in favour of delirium. It does not determine the post-test probability without the pre-test probability. For example, a pre-test probability of 10% gives pre-test odds of 1:9 and post-test odds of 10:9, equivalent to a post-test probability of about 53%, not certainty. A is therefore false. LR+ does not imply perfect sensitivity, so B is false, and it does not specify prevalence or pre-test probability, excluding C. E incorrectly applies a negative likelihood ratio of 0.1, which has not been provided.

Reference: Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329:168-169. https://www.bmj.com/content/329/7458/168