Pre-test and post-test probability
- Concept
Suspicion before the test, adjusted by the result, gives the probability of disease after the test.
What it is
Pre-test probability is the estimate before the result, based on prevalence and the patient's clinical picture. To update it, convert to odds, multiply by the likelihood ratio of the result and convert back to probability: Bayes' theorem applied at the bedside. The post-test probability is then compared with two thresholds: below the testing threshold further testing is not worthwhile, and above the treatment threshold treatment starts.
Key facts
- Step 1: pre-test odds = p / (1 − p).
- Step 2: post-test odds = pre-test odds × LR.
- Step 3: post-test probability = post-test odds / (1 + post-test odds).
- The Fagan nomogram does these three steps graphically.
Worked example
- Data: pre-test probability 20%; the test has LR+ 6 and LR− 0.12.
- Pre-test odds = 0.20 / 0.80 = 0.25.
- Positive result: post-test odds = 0.25 × 6 = 1.5; probability = 1.5 / 2.5 = 0.60, that is 60%.
- Negative result: post-test odds = 0.25 × 0.12 = 0.03; probability = 0.03 / 1.03 ≈ 2.9%.
- Reading: a positive raises suspicion from 20% to 60%; a negative lowers it to about 3%.
Post-test probability by pre-test probability, with LR+ of 6
| Pre-test | Pre-test odds | Post-test odds | Post-test |
|---|---|---|---|
| 5% | 0.053 | 0.32 | 24% |
| 20% | 0.25 | 1.5 | 60% |
| 50% | 1 | 6 | 86% |
Markers
- odds
- LR
- Bayes
- Fagan
In practice
- In a patient with a very low pre-test probability, a single positive may still leave the disease unlikely.
- Before ordering a test, it helps to ask whether its result could cross either decision threshold.
Common pitfalls
- Multiplying the LR directly by the probability instead of the odds.
- Forgetting to convert odds back to probability at the end.
- Using population prevalence when the patient's clinical picture has already changed the pre-test probability.
Test yourself
Think of the answer, then tap the question to see it.
Pre-test probability 50% and LR+ 4. What is the post-test probability after a positive?
Odds 1 × 4 = 4; probability = 4 / 5 = 80%.
Why is the LR not multiplied directly by the pre-test probability?
Because the LR acts on odds; multiplying the probability can give impossible values above 100%.
When is ordering a test useful according to decision thresholds?
When the probability lies between the testing and treatment thresholds, because the result can change management.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Understanding the properties of diagnostic tests - Part 2: Likelihood ratios (Perspectives in Clinical Research, 2018); Measures of Diagnostic Accuracy: Basic Definitions (EJIFCC, 2009).
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Representative model, for educational purposes only.