PUBLIC LIBRARY / CALCULATOR

Post-test probability (Bayes’ theorem)

Converts a disease’s pretest probability to probability after a test result using that result’s likelihood ratio.

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Check the population, units and version. The result shows the formula or classification; it does not make an automatic treatment decision.

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Method · Limits of application

Bayes odds: Fagan 1975; pretest odds×LR, posttest conversion; Deeks–Altman 2004 likelihood ratios

Pre-test probability must represent the population and clinical context assessed; the likelihood ratio must correspond to the test and result category. Probability and odds are different quantities: updating multiplies odds by the likelihood ratio and only then converts back to probability. Predictive values vary with prevalence and do not transfer automatically between studies and services. The calculation updates an estimate; it does not independently confirm or exclude a disease.

Conditions of use

Check the population, units, inclusion and exclusion criteria, and version in the original source. A result alone does not establish a diagnosis, discharge decision or prescription.

Documented parameters

Pretest probability (prevalence or clinical estimate) · %
Likelihood ratio of the result (LR+ if positive, LR− if negative)

3/3 reference cases checked. Numerical tests are not clinical validation.

Sources and documentation

Documented formula

Transcribed from the source or a recorded revision; this is not a clinical recommendation.

Pretest odds = p / (1 − p) · Posttest odds = Pretest odds × LR · Posttest probability = Posttest odds / (1 + Posttest odds).

This is the odds form of Bayes theorem, solved graphically by the Fagan nomogram.

References

Identifier: probabilidade-pos-teste

Original clinical content: Brazilian Portuguese.

Method version

Bayes odds: Fagan 1975; pretest odds×LR, posttest conversion; Deeks–Altman 2004 likelihood ratios

probabilidade-pos-teste@native-2026-10-03+10aa4c06ce14

Source for the active edition

The bibliographic edition identifies the source. By itself, it proves neither full conformity of the formula nor clinical approval.

Synthetic cases checked (3)

Synthetic cases for checking the implementation, with no patient data.

Case 1

reference-001

Inputs

Pretest probability (prevalence or clinical estimate): 25 %
Likelihood ratio of the result (LR+ if positive, LR− if negative): 8

{
  "pre": 25,
  "rv": 8
}

Expected result

{
  "post": 72.73,
  "oddsPost": 2.667
}

Actual result

{
  "post": 72.72727272727273,
  "oddsPre": 0.3333333333333333,
  "oddsPost": 2.6666666666666665
}

Case 2

reference-002

Inputs

Pretest probability (prevalence or clinical estimate): 50 %
Likelihood ratio of the result (LR+ if positive, LR− if negative): 0.1

{
  "pre": 50,
  "rv": 0.1
}

Expected result

{
  "post": 9.09
}

Actual result

{
  "post": 9.090909090909092,
  "oddsPre": 1,
  "oddsPost": 0.1
}

Case 3

reference-003

Inputs

Pretest probability (prevalence or clinical estimate): 10 %
Likelihood ratio of the result (LR+ if positive, LR− if negative): 1

{
  "pre": 10,
  "rv": 1
}

Expected result

{
  "post": 10
}

Actual result

{
  "post": 10,
  "oddsPre": 0.11111111111111112,
  "oddsPost": 0.11111111111111112
}

Code and reproducibility

This tool’s code on GitHub

Download code and tests

Sources, version and reproduction instructions

The code tests are technical checks. Clinical approval and professional translation review are recorded separately.

Relationship with cancer research

Support for research — context required

A general method for post-test probability. It requires pre-test probability and test performance applicable to the population; it is not a cancer detector.

Applications: Early detection and risk assessment · Clinical trials and methods