Post-Test Probability Calculator
Free post-test probability calculator. Compute from pre-test and LR. Fagan nomogram, Bayes theorem,
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Post-Test Probability — From Pre-Test and LR to Clinical Action
Use sensitivity, specificity, and likelihood ratios with Bayes' theorem. Fagan nomogram visualization. Rule in, rule out, sequential testing.
Real-World Scenarios — Click to Load
Fagan-Style Nomogram
Visual line: Pre-test → LR → Post-test (Fagan 1975)
Pre-test vs Post-test Probability
Probability Distribution (positive test)
Fagan Nomogram Flow
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • Pre-test probability matters more than test accuracy for rare diseases — a "95% accurate" test can be wrong 90%+ of the time when prevalence is low
- • LR+ > 10 is "rule in" — strong evidence for disease; LR− < 0.1 is "rule out" — strong evidence against disease
- • Sequential testing shifts probability: each test result updates the prior for the next test
- • The Fagan nomogram (1975) provides a visual line from pre-test probability through LR to post-test probability
- • Post-test odds = Pre-test odds × LR. Convert odds to probability: P = odds / (1 + odds)
Did You Know?
Expert Tips
Use sequential testing
For borderline results, a second test updates the prior — post-test from test 1 becomes pre-test for test 2.
Consider clinical context
Numbers alone do not replace clinical gestalt — combine with history, exam, and risk factors.
LR > 10 or < 0.1
These generate large probability shifts — useful for rule-in and rule-out decisions.
Validate pre-test probability
Pre-test probability is often estimated from experience — validate with published prevalence when available.
Common Diagnostic Tests
| Test | Sensitivity | Specificity | LR+ | LR− |
|---|---|---|---|---|
| Mammography | 87% | 93% | 12.4 | 0.14 |
| Troponin (hs) | 95% | 90% | 9.5 | 0.06 |
| COVID PCR | 98% | 99% | 98 | 0.02 |
| D-dimer | 96% | 40% | 1.6 | 0.1 |
| PSA | 80% | 70% | 2.7 | 0.29 |
| Strep rapid | 86% | 95% | 17.2 | 0.15 |
| CTPA | 95% | 97% | 31.7 | 0.05 |
Frequently Asked Questions
What is post-test probability?
The probability of disease after knowing the test result. For a positive test: P(disease|positive). For a negative test: P(disease|negative). It is computed from pre-test probability and likelihood ratios via Bayes' theorem.
What is the difference between PPV and post-test probability?
PPV is post-test probability after a positive test when pre-test probability equals prevalence. Post-test probability is more general — it can use any pre-test probability (e.g., from clinical assessment).
When does LR+ "rule in" disease?
LR+ > 10 is often considered strong evidence to rule in. LR+ 5–10 is moderate; 2–5 is fair; 1–2 is poor. The exact threshold depends on the clinical context.
When does LR− "rule out" disease?
LR− < 0.1 is strong evidence to rule out. LR− 0.1–0.2 is good; 0.2–0.5 is fair; 0.5–1 is poor. D-dimer for DVT is a classic rule-out test (LR− ≈ 0.1).
Why use likelihood ratios instead of sensitivity/specificity?
LRs combine sensitivity and specificity into a single number that directly multiplies odds. They are independent of prevalence, making them portable across populations.
What is the Fagan nomogram?
A visual tool (1975) with three vertical axes: pre-test probability, likelihood ratio, and post-test probability. Draw a straight line through your values to read the result.
How do I use sequential testing?
After test 1, the post-test probability becomes the pre-test probability for test 2. Enter the first post-test probability as the new pre-test probability and apply the second test's LR.
Why does a "95% accurate" test fail for rare diseases?
When prevalence is very low, the large number of healthy people generates many false positives. Even with 95% specificity, 5% of healthy people test positive — swamping the few true positives.
By the Numbers
Official Data Sources
Medical Disclaimer: This calculator is for educational purposes only. It is not a substitute for clinical judgment, professional medical advice, or formal diagnostic protocols. Consult qualified healthcare providers for medical decisions.
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