Core concept
- Likelihood ratios express how much a test result shifts the odds of disease -- prevalence-independent (unlike PPV/NPV), so they transfer across populations
- LR+ = sensitivity / (1 - specificity) -- how much more likely a positive result is in someone with disease vs without
- LR- = (1 - sensitivity) / specificity -- how much more likely a negative result is in someone with disease vs without
Key detail
- Applying an LR: pre-test odds x LR = post-test odds, then convert back: odds = probability / (1 - probability); probability = odds / (1 + odds)
- Rule-of-thumb magnitude of effect: LR+ >10 or LR- <0.1 produces large, often decisive shifts in post-test probability; LR close to 1 = the test result changes very little
- Trap: applying LR to a raw probability by simple multiplication -- LRs operate on odds, not probability directly; must convert probability to odds first, multiply, then convert back
Clinical relevance
- Given sensitivity and specificity in a vignette, she should compute the requested LR directly from the formula rather than trying to recall a memorised value for a named test
- A test with high sensitivity but only moderate specificity can still have a very high LR+ if specificity is close to 1 (small denominator) -- do not judge LR quality from sensitivity alone
- Choosing between two tests: compare LR+ for ruling in and LR- for ruling out -- a test can be excellent for one purpose and poor for the other
Correlations
- LR is the direct bridge between sensitivity/specificity (test properties) and PPV/NPV (prevalence-dependent, population-specific) -- see PPV/prevalence note
- SpPin/SnNout mnemonic (highly Specific test positive rules in; highly Sensitive test negative rules out) is a qualitative shortcut for the same underlying LR logic
- ROC curve threshold selection changes sensitivity and specificity simultaneously (trade-off) -- and therefore changes both LR+ and LR- at each candidate cut-off
4 of 4 sections written · drafted 2026-09-13