Post-Test Probability Calculator

This calculator converts diagnostic test information into a clinically interpretable post-test probability. By combining a pre-test probability with a likelihood ratio, it shows how a test result meaningfully shifts the probability of disease.

Enter the following values
Pre-test Probability (%) Estimated probability of disease before the test result
Likelihood Ratio (LR) Use LR+ for positive test, LR− for negative test

Formula

Odds-Based Calculation (Bayes' Theorem)

\( \text{Pre-test Odds} = \frac{\text{Pre-test Probability}}{1 - \text{Pre-test Probability}} \)
\( \text{Post-test Odds} = \text{Pre-test Odds} \times \text{Likelihood Ratio} \)
\( \text{Post-test Probability} = \frac{\text{Post-test Odds}}{1 + \text{Post-test Odds}} \)

Understanding Post-Test Probability

Post-test probability represents the updated probability of disease after incorporating the diagnostic test result. It bridges the gap between test characteristics (sensitivity, specificity, likelihood ratios) and clinical decision-making.

This calculation uses Bayes' theorem in odds form, which provides an intuitive way to see how diagnostic information shifts probability:

  • Pre-test probability reflects clinical suspicion before the test (based on symptoms, risk factors, prevalence)
  • Likelihood ratio quantifies the diagnostic power of the test result
  • Post-test probability is the revised probability after incorporating the test result

Clinical Interpretation

The post-test probability helps clinicians decide whether to:

  • Treat — if post-test probability exceeds the treatment threshold
  • Rule out — if post-test probability falls below the no-treat threshold
  • Perform additional testing — if post-test probability remains in an indeterminate range

A strong positive likelihood ratio (LR+ > 10) with a moderate pre-test probability can shift the post-test probability substantially, while a weak likelihood ratio near 1 provides little diagnostic information.

Specific Examples

Example 1: A patient with 30% pre-test probability of pulmonary embolism has a positive CT-PA (LR+ = 12). Post-test probability ≈ 84%, supporting treatment.

Example 2: A low-risk patient with 10% pre-test probability of DVT has a negative D-dimer (LR− = 0.1). Post-test probability ≈ 1%, safely ruling out disease.

Example 3: A patient with 50% pre-test probability has a test with LR+ = 2. Post-test probability = 67% — still indeterminate, further testing may be needed.

Assumptions & Limitations

  • Assumes the pre-test probability is accurately estimated
  • Assumes the likelihood ratio is valid for the patient population
  • Does not account for test interdependence when multiple tests are performed
  • Decision thresholds vary by clinical context and patient preferences
  • Post-test probability is only as reliable as the inputs

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