Post-Test Probability Calculator
The post-test probability calculator is a Bayesian tool that helps clinicians and researchers determine the probability of a disease or condition after a diagnostic test has been performed. It combines pre-test probability (prevalence) with the test's sensitivity and specificity through likelihood ratios.
How to Use
Choose between two input modes:
- Confusion Matrix — enter the number of True Positives (TP), False Negatives (FN), False Positives (FP), and True Negatives (TN).
- Direct Input — enter sensitivity, specificity, and pre-test probability directly as percentages or decimals.
Key Formulas
Sensitivity = TP / (TP + FN)
Measures how well the test detects a true positive (diseased) patient.
Specificity = TN / (FP + TN)
Measures how well the test identifies true negatives (healthy patients).
Positive Likelihood Ratio (LR+) = Sensitivity / (1 − Specificity)
How much more likely a positive result is in a diseased vs. healthy person.
Negative Likelihood Ratio (LR−) = (1 − Sensitivity) / Specificity
How much less likely a negative result is in a diseased vs. healthy person.
Pre-test Odds = Prevalence / (1 − Prevalence)
Post-test Odds (positive test) = Pre-test Odds × LR+
Post-test Probability (positive test) = Post-test Odds / (1 + Post-test Odds)
Post-test Odds (negative test) = Pre-test Odds × LR−
Post-test Probability (negative test) = Post-test Odds / (1 + Post-test Odds)
Interpreting Likelihood Ratios
- LR+ > 10 — strongly confirms the presence of the disease
- LR+ 2–10 — moderate evidence for the disease
- LR− < 0.1 — strongly rules out the disease
- LR− 0.1–0.5 — moderate evidence against the disease
Pre-test vs Post-test Probability
The pre-test probability (also called prevalence) is the probability of disease before the test is performed, based on population data or clinical judgment. The post-test probability updates this estimate after receiving the test result — either positive or negative.
Example
Suppose a disease has a 10% prevalence and a test has 80% sensitivity and 89% specificity:
- LR+ = 0.80 / (1 − 0.89) = 7.27
- Pre-test odds = 0.10 / 0.90 = 0.111
- Post-test odds (positive) = 0.111 × 7.27 = 0.808
- Post-test probability (positive) = 0.808 / 1.808 ≈ 44.7%