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

Pre-test Probability
0.00%
Prevalence
Likelihood Ratio
0.0000
LR
Post-test Probability
0.00%
Final result
Pre-test Odds
1:Infinity
Post-test Odds
1:Infinity

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

Pre-test Probability

Disease prevalence before testing

Also called prevalence

LR

Likelihood Ratio

How test changes probability

LR+ for positive, LR- for negative

Post

Post-test Probability

Disease probability after testing

Updated probability

Formula Reference

Pre-test odds = prevalence / (1 - prevalence)
Post-test odds = pre-test odds × LR
Post-test prob = post-test odds / (1 + post-test odds)

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.