Each candidate diagnosis starts at its pretest probability — the
prevalence expected from this patient's age, sex and risk factors. Ordering
a test reveals a positive or negative result whose likelihood ratio (LR)
says how much more (or less) likely that result is under each diagnosis.
Bayes' theorem converts pretest odds into posttest odds, which are
renormalised back into a probability for every candidate — exactly what a
Fagan nomogram does graphically with a straight edge.
posttest odds = pretest odds × LR
P(dx | result) ∝ P(dx) × P(result | dx) (renormalised over all candidates)
- ECG — ST-segment changes: LR+ ≈ 9, LR− ≈ 0.3 for myocardial infarction.
- Troponin — myocardial injury marker: LR+ ≈ 20, LR− ≈ 0.1 for MI.
- D-dimer — very sensitive, poorly specific: LR+ ≈ 1.7, LR− ≈ 0.1 for pulmonary embolism (its real value is ruling PE out when negative).
- CT pulmonary angiography — near gold-standard for PE: LR+ ≈ 20, LR− ≈ 0.1.
A diagnosis is ruled in once its posterior climbs past ~85% and
ruled out once it falls below ~5% — the thresholds clinicians use to
stop testing and commit to (or abandon) a diagnosis.