Pre- and Post-test Probability & Odds
The chance of disease before a test, updated by the result into the chance after it.
The pre-test probability is the chance of disease before testing — roughly the prevalence in your population tempered by clinical judgement. Apply the test result’s likelihood ratio to update it to the post-test probability (Bayesian reasoning). Probability and odds interconvert — odds = p ÷ (1 − p) — and formally post-test odds = pre-test odds × LR. The Fagan nomogram does this graphically.
Pre-test 20% → through LR+ 10 → post-test ≈ 70%
The same positive result moves different starting points to different finishing points. Here a 20% pre-test probability, pivoted through an LR+ of 10, lands near 70%. Anchor a lower pre-test value and the same LR lands far lower — the result has not changed; the starting odds have.
Fix the pre-test probability on the left axis, pivot the straight line through the result’s LR in the middle, and read the post-test probability on the right. Behind the picture is pure arithmetic: convert the pre-test probability to odds, multiply by the LR, convert the resulting post-test odds back to a probability.
Test results are never interpreted in a vacuum — only against where the patient started. Quantifying the pre-test probability and updating it is the formal version of “clinical gestalt”, and it is the reason the same result rules disease in for one patient yet barely shifts another.
odds = p ÷ (1 − p)·p = odds ÷ (1 + odds)post-test odds = pre-test odds × LR- Pre-test probability ≈ prevalence / clinical judgement
Wells score + D-dimer for PE — the same D-dimer is interpreted against the pre-test probability the score sets. In a “PE-unlikely” patient (Wells ≤4, low pre-test probability) a negative D-dimer drops the post-test probability of PE below roughly 2% and safely rules it out; in a “PE-likely” patient the identical negative D-dimer leaves too much residual risk, so CTPA is still required (Wells et al., Ann Intern Med 2001; Christopher Study, JAMA 2006). One result, two destinations: D-dimer only rules out PE when the pre-test probability is already low — apply it at a high pre-test probability and a negative result is falsely reassuring.
- Base-rate neglect — judging a result without anchoring the pre-test probability.
- Confusing odds with probability (they only coincide when both are small).
- Using a test outside the pre-test probability range it was validated in.
Quick check
The same positive result in a low-risk and a high-risk patient — same post-test probability?
Answer: No — it depends on the pre-test probability. The LR shifts the odds by the same factor, but from different starting points it lands at very different post-test probabilities.
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