Fagan Post-Test Probability (likelihood ratio)

Fagan post-test probability from a pre-test probability and a likelihood ratio (or sensitivity / specificity), computed in odds space.

Open the calculator → Runs in your browser. Data leaves only if you deliberately send a problem report from the interactive tool.

Example

Input mode
Enter a likelihood ratio
Pre-test probability
20 %
Likelihood ratio
10

Result: Pre-test 20% × LR 10 → post-test 71.4%.

The tool opens with these values already filled in. Replace them with your own.

What the result means

From sens/spec
LR+ = sens/(1−spec), LR− = (1−sens)/spec; a positive test raises and a negative test lowers the probability of disease.

What you enter

  • Input mode
  • Pre-test probability (0-100, exclusive)
  • Likelihood ratio (likelihood-ratio mode)
  • Sensitivity (sens/spec mode)
  • Specificity (sens/spec mode)
How this is calculated
Formula
Pre-test odds = p/(1−p); post-test odds = pre-test odds × LR; post-test p = odds/(1+odds). Computed in odds space (no float clamp at p→0/1).

Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med. 1975;293(5):257. Read the source ↗

A reference and educational tool. Not medical, legal, or financial advice, and not a substitute for clinician judgment.

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Built by Clay Good. Source on GitHub.