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likelihood ratios: the only diagnostic maths worth learning

a clinician-friendly way to use lr+ and lr−, convert pre-test to post-test probability, and stop confusing sensitivity with certainty.

The Bottom Line

  • Likelihood ratios tell you how much a test result shifts probability.
  • Think in zones: big shift (useful), small shift (noise), and direction (rule in vs rule out).
  • Exam wins come from interpretation, not memorising formulas.
EBM questions often punish one specific confusion: mixing up test characteristics (sensitivity/specificity) with what you actually want (post-test probability). Likelihood ratios bridge that gap. Learn a simple workflow and you’ll pick up reliable marks in AKT/MSRA/undergrad EBM blocks.

What an LR actually means (plain English)

A likelihood ratio compares how often a result occurs in people with the disease versus without it. Values far from 1 create meaningful shifts; values close to 1 barely move probability.
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Step 1 — Set a pre-test probability (don’t overthink)

Use the vignette. If it’s a classic presentation in a high-risk group, pre-test probability is higher. If it’s a screening scenario or vague symptoms, it’s lower. You’re rarely expected to be perfect — just directionally correct.
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Step 2 — Apply the LR (use zones, not calculus)

Rule of thumb zones: LR+ >10 rules in strongly, 5–10 moderate, 2–5 small. LR− <0.1 rules out strongly, 0.1–0.2 moderate, 0.2–0.5 small. Values near 1 are weak. This lets you answer most SBA questions quickly.
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Step 3 — Translate into action

Exams care about decisions: ‘Does this cross a treatment threshold?’, ‘Do we need further testing?’, ‘Can we stop investigating?’ Tie the LR shift to a sensible next step.
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Step 4 — Avoid the classic trap

High sensitivity does *not* mean a positive test rules in. High specificity does *not* mean a negative test rules out. LRs handle direction and magnitude properly.

LR quick reference (memorise once)

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Exam-grade phrasing (use this wording)

“A positive result increases the likelihood of disease by X magnitude; a negative result reduces it by Y magnitude; therefore the test meaningfully changes management only if pre-test probability is in the decision zone.”
SourceDiagnostic tests: likelihood ratios (BMJ, open access via PMC)
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SourceBMJ EBM: making sense of likelihood ratios (PDF)
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SourceCochrane Handbook: reading meta-analysis outputs (context for diagnostic evidence)
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