Post-Test Probability Calculator
Print PageA Post-Test Probability Calculator (also known as a Likelihood Ratio Calculator, Fagan Nomogram Utility, Bayesian Diagnostic Test Analyzer, or Clinical Pre-to-Post Test Odds Calculator) computes the updated probability that a patient has a specific medical condition following a positive test result (P(Disease | T+)) or a negative test result (P(Disease | T-)). By combining pre-test probability (clinical suspicion P(D)) with a test’s Positive Likelihood Ratio (LR+) or Negative Likelihood Ratio (LR–), a post-test probability calculator provides evidence-based diagnostic clarity.
In evidence-based medicine (EBM), diagnostic tests do not provide binary yes/no answers; rather, they shift a patient’s disease probability along a continuum. A strong positive test (high LR+ > 10) pushes probability above the treatment threshold, while a low negative likelihood ratio (LR- < 0.1) drops probability below the test/no-test threshold to safely rule out disease.
Our free online Post-Test Probability Calculator provides instant calculations across likelihood ratios, pre/post odds, and Bayesian probability updates:
- Pre-Test Odds Formula (Oddspre):
Oddspre = P(D) ÷ [ 1 - P(D) ]. - Positive Likelihood Ratio (LR+):
LR+ = Sensitivity ÷ (1 - Specificity) = TPR ÷ FPR. - Negative Likelihood Ratio (LR–):
LR- = (1 - Sensitivity) ÷ Specificity = FNR ÷ TNR. - Post-Test Odds Formula (Oddspost):
Oddspost+ = Oddspre · LR+andOddspost- = Oddspre · LR-. - Post-Test Probability Formula (Ppost):
P(D | T+) = Oddspost+ ÷ [ 1 + Oddspost+ ].
Master Clinical Diagnostic Likelihood Ratio & Post-Test Matrix
The table below displays the pre-test probabilities, diagnostic sensitivity/specificity, calculated likelihood ratios, and resulting positive/negative post-test probabilities across common medical screening tests:
| Clinical Diagnostic Test Scenario | Pre-Test Prob P(D) | Sens / Spec | Likelihood Ratios (LR+ / LR–) | Post-Test Prob Positive P(D | T+) | Post-Test Prob Negative P(D | T–) |
|---|---|---|---|---|---|
| Exercise Stress Test (Coronary Artery Disease) | 30.0% (Moderate Risk) | 80% Sens / 90% Spec | LR+ = 8.00 / LR– = 0.222 | 77.42% (Rule In) | 8.69% |
| D-Dimer Assay (Pulmonary Embolism PE) | 20.0% (Low/Mod Risk) | 95% Sens / 50% Spec | LR+ = 1.90 / LR– = 0.100 | 32.20% | 2.44% (Safely Ruled Out!) |
| Rapid Strep Test (Pharyngitis) | 40.0% (Sore Throat) | 85% Sens / 95% Spec | LR+ = 17.00 / LR– = 0.158 | 91.89% (Treat with Antibiotics) | 9.52% |
| Mammography (Screening Breast Cancer) | 1.0% (Asymptomatic) | 85% Sens / 92% Spec | LR+ = 10.625 / LR– = 0.163 | 9.68% (Needs Biopsy) | 0.16% (Reassuring) |
Step-by-Step Cardiac Stress Test Bayesian Calculation
To calculate the positive and negative post-test probability for a 55-year-old male with atypical chest pain (Pre-Test Probability P(D) = 30.0%) undergoing an exercise ECG stress test (Sensitivity = 80.0%, Specificity = 90.0%):
Step 1 (Calculate Pre-Test Odds): Oddspre = 0.30 ÷ (1 - 0.30) = 0.30 ÷ 0.70 = 0.428571
Step 2 (Calculate Positive Likelihood Ratio LR+): LR+ = 0.80 ÷ (1 - 0.90) = 0.80 ÷ 0.10 = 8.00
Step 3 (Calculate Negative Likelihood Ratio LR-): LR- = (1 - 0.80) ÷ 0.90 = 0.20 ÷ 0.90 = 0.222222
Step 4 (Calculate Positive Post-Test Odds & Probability): Oddspost+ = 0.428571 × 8.00 = 3.428571 &implies; P(D|T+) = 3.428571 ÷ 4.428571 = 77.42%
Step 5 (Calculate Negative Post-Test Odds & Probability): Oddspost- = 0.428571 × 0.222222 = 0.095238 &implies; P(D|T-) = 0.095238 ÷ 1.095238 = 8.69%
Thus, a positive stress test increases disease probability from 30.0% to 77.42% (indicating angiographic follow-up), while a negative stress test drops probability to 8.69%.
Clinical Interpretation Guidelines for Likelihood Ratios
Below is a comparative reference chart based on Evidence-Based Medicine (EBM) standards for evaluating diagnostic test power:
| Likelihood Ratio Value Range | Diagnostic Impact Strength | Shift in Pre-to-Post Test Probability | Clinical Decision Action |
|---|---|---|---|
| LR+ > 10.0 | Large & Conclusive Increase | Increases probability by +45% or more | Conclusively Rules In Disease |
| LR+ = 5.0 to 10.0 | Moderate Increase | Increases probability by +30% | Substantially Increases Suspicion |
| LR+ = 1.0 or LR– = 1.0 | No Diagnostic Value | 0% Change in probability | Useless Diagnostic Test |
| LR– = 0.1 to 0.2 | Moderate Decrease | Decreases probability by -30% | Substantially Reduces Suspicion |
| LR– < 0.10 | Large & Conclusive Decrease | Decreases probability by -45% or more | Conclusively Rules Out Disease |
History & Medicine: 1975 TJ Fagan & The Fagan Nomogram
1975 TJ Fagan & The NEJM Fagan Nomogram
In 1975, Dr. T. J. Fagan published Nomogram for Bayes’ Theorem in the New England Journal of Medicine (NEJM). Fagan introduced the famous 3-line graphical alignment chart (connecting pre-test probability on the left, likelihood ratio in the middle, and post-test probability on the right), allowing clinicians to perform instant Bayesian probability calculations at the bedside without algebra.
1980 David Sackett & Evidence-Based Medicine
In the 1980s, epidemiologist David Sackett and colleagues at McMaster University integrated likelihood ratios and post-test probability thresholds into modern Evidence-Based Medicine (EBM) guidelines.
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Frequently Asked Questions (FAQ)
What is Post-Test Probability?
Post-Test Probability is the updated probability that a patient has a condition after knowing the result of a diagnostic test (positive or negative).
How do you calculate Likelihood Ratio Positive (LR+)?
Calculate LR+ = Sensitivity ÷ (1 - Specificity). An LR+ > 10 conclusively rules in disease.
How do you calculate Likelihood Ratio Negative (LR-)?
Calculate LR- = (1 - Sensitivity) ÷ Specificity. An LR- < 0.10 conclusively rules out disease.