Concept Architecture
Concept
Theoretically, Post-Test Probability is the probability that a hypothesis or condition is true after incorporating the results of a diagnostic test or other new evidence. It represents the updated probability obtained through Bayesian inference by combining the pre-test probability with the evidential strength of the observed result. The concept is founded on conditional probability and Bayes' Theorem and exists to support evidence-based clinical and health economic decision-making under uncertainty.
Mathematically, Post-Test Probability is derived by first converting the pre-test probability into pre-test odds, multiplying these odds by the appropriate likelihood ratio and then converting the resulting posterior odds back into probability. This process provides a mathematically rigorous method for updating disease probability following positive or negative diagnostic test results.
In practice, Post-Test Probability is estimated using pre-test disease prevalence or clinical judgement together with Positive or Negative Likelihood Ratios obtained from diagnostic accuracy studies. It is widely applied in diagnostic testing, health technology assessment, clinical guideline development and decision-analytic modelling to determine whether additional investigation or treatment is justified.
Purpose
Used to estimate the probability of disease after diagnostic testing, support Bayesian clinical reasoning, guide treatment decisions and improve diagnostic and health economic decision-making.
Mathematical Formulae
Primary Formula
Post-test Probability = Post-test Odds / (1 + Post-test Odds)
Supporting Formulae
Pre-test Odds = Pre-test Probability / (1 ? Pre-test Probability)
Post-test Odds = Pre-test Odds ? Likelihood Ratio
Likelihood Ratio = LR? for a positive test result
Likelihood Ratio = LR? for a negative test result
where:
- LR? = positive likelihood ratio
- LR? = negative likelihood ratio
Related Mathematical Methods
- Bayes' Theorem
- Prior Probability
- Posterior Probability
- Prior Odds
- Posterior Odds
- Positive Likelihood Ratio
- Negative Likelihood Ratio
- Diagnostic Testing
Example
A patient has a pre-test probability of disease of 25%.
Pre-test Odds:
Pre-test Odds = 0.25 / (1 ? 0.25) = 0.333
A diagnostic test produces a positive result with a Positive Likelihood Ratio of 6.
Post-test Odds:
Post-test Odds = 0.333 ? 6 = 2.00
Post-test Probability:
Post-test Probability = 2.00 / (1 + 2.00) = 0.667
Following the positive test result, the estimated probability of disease increases from 25% to approximately 66.7%.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Division | =B2/(1-B2) | Converts pre-test probability into pre-test odds. |
| Multiplication | =C2*D2 | Calculates post-test odds using the appropriate likelihood ratio. |
| Division | =E2/(1+E2) | Converts post-test odds into post-test probability. |
| IF | =IF(F2>0.80,"Treat","Consider additional testing") | Applies clinical decision thresholds using post-test probability. |
VBA (Optional)
A VBA macro can automatically calculate post-test probabilities for multiple diagnostic scenarios using user-defined pre-test probabilities and likelihood ratios.
Sources
- Bayes T. An Essay towards Solving a Problem in the Doctrine of Chances. 1763.
- Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329:168?169.
- McGee S. Simplifying likelihood ratios. Journal of General Internal Medicine. 2002;17(8):646?649.
- Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian Approaches to Clinical Trials and Health-Care Evaluation.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is post-test probability?
The updated probability that a patient has a condition after a diagnostic test result is known, combining pre-test probability with the likelihood ratio.
Source: Sackett et al. 1991
What does post-test probability tell a clinician after a result?
Post-test probability is the chance a patient has a condition once a diagnostic test result is known, arrived at by updating the pre-test probability with the test's likelihood ratio. It tells a clinician where the patient now stands after the test, which is what should guide the next step, whether to treat, to test further, or to reassure. Because it accounts for both the prior likelihood and the test's strength, it is more informative than the result alone. The revised chance of disease is what it gives. Sackett and colleagues (1991) describe this.
Source: Sackett et al. 1991
How is post-test probability calculated?
Post-test probability is calculated by converting the pre-test probability to pre-test odds, multiplying by the likelihood ratio for the observed test result to get the post-test odds, and converting those back to a probability. Tools such as nomograms can perform this without explicit calculation. So post-test probability is calculated through Bayesian updating on the odds scale, using the likelihood ratio to move from the pre-test to the post-test probability, which gives the revised probability of disease after the test, combining the patient's starting probability with the evidence the result provides in a single, coherent estimate.
Source: Sackett et al. 1991
How does post-test probability relate to pre-test probability?
Post-test probability relates to pre-test probability as its updated value after a test result: the pre-test probability is the estimate before testing, and applying the test's likelihood ratio yields the post-test probability afterward. The pre-test probability is the starting point, and the test result revises it upward or downward. So post-test probability and pre-test probability are the before and after of diagnostic updating, linked by the likelihood ratio, so that a result with a large likelihood ratio produces a big change from pre-test to post-test probability, while a result with a likelihood ratio near one leaves the probability little altered.
Source: Sackett et al. 1991
Why is post-test probability important?
Post-test probability is important because it gives the revised probability of disease that should guide clinical decisions after a test, such as whether to treat, reassure, or test further, rather than relying on the test result alone. It accounts for both the starting probability and the test's evidence. So post-test probability matters for sound diagnostic decision-making, since a test result is meaningful only in relation to the pre-test probability, and the post-test probability integrates the two, preventing errors that arise from interpreting a result without regard to how likely the condition was beforehand, especially for rare conditions.
Source: Sackett et al. 1991
How is post-test probability used in decision-making?
Post-test probability is used in decision-making by comparing it against thresholds for action: if it is high enough, treatment may be warranted; if low enough, the condition may be ruled out; and if intermediate, further testing may be needed. It thus determines the next step after a test. So post-test probability is used to guide what to do after a test result, since decisions depend on how probable the condition is once the result is known, and framing the result as a post-test probability, rather than as a bare positive or negative, supports more rational and individualised clinical choices.
Source: Sackett et al. 1991
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British health economist
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Verification date: 10 Dec 2025
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