Post-Test Probability Calculator
Calculate post-test probability using Bayes' theorem, prevalence, and likelihood ratios for diagnostic testing
Calculate Post-Test Probability
Prevalence (Pre-test Probability)
Likelihood Ratio
Results
Example Calculation
COVID-19 Rapid Test Example
Scenario: Patient presents with COVID-19 symptoms
Pre-test probability: 30% (prevalence in symptomatic patients)
Test sensitivity: 85%
Test specificity: 95%
Test result: Positive
Positive LR: 0.85 / (1 - 0.95) = 17
Pre-test odds: 0.30 / 0.70 = 0.429
Post-test odds: 0.429 × 17 = 7.29
Post-test probability: 7.29 / (1 + 7.29) = 87.9%
Key Concepts
Pre-test Probability
Disease prevalence before testing
Also called prevalence
Likelihood Ratio
How test changes probability
LR+ for positive, LR- for negative
Post-test Probability
Disease probability after testing
Updated probability
Formula Reference
Test Performance
Sensitivity
TP / (TP + FN)
Specificity
TN / (TN + FP)
LR+ = Sens / (1 - Spec)
LR- = (1 - Sens) / Spec
Understanding Post-Test Probability
What is Post-Test Probability?
Post-test probability is the probability that a patient has a disease after a diagnostic test has been performed. It combines the pre-test probability (prevalence) with the test's performance characteristics using Bayes' theorem.
Clinical Applications
- •Medical diagnosis and screening
- •Treatment decision making
- •Risk assessment
- •Patient counseling
Calculation Steps
Step 1: Calculate Pre-test Odds
odds = prevalence / (1 - prevalence)
Step 2: Apply Likelihood Ratio
post-test odds = pre-test odds × LR
Step 3: Convert to Probability
probability = odds / (1 + odds)
Important: Post-test probability depends heavily on pre-test probability. The same test can have very different implications in different populations.
Understanding Likelihood Ratios
Positive Likelihood Ratio (LR+)
How much more likely is a positive test in someone with the disease vs. someone without it?
LR+ = Sensitivity / (1 - Specificity)
Negative Likelihood Ratio (LR-)
How much more likely is a negative test in someone with the disease vs. someone without it?
LR- = (1 - Sensitivity) / Specificity
Interpretation Guidelines
High Probability (>85%)
Disease very likely. Consider treatment or further confirmatory testing.
Intermediate (15-85%)
Uncertain. Consider additional testing or clinical assessment.
Low Probability (<15%)
Disease unlikely. Consider alternative diagnoses or reassurance.