How this instrument works
Post-test probability answers the question: after a positive test result, how likely is the condition now, starting from whatever probability you believed beforehand? That starting point, pre-test probability, doesn't have to be a population-wide prevalence figure — it can be a clinician's estimate built from a patient's symptoms, risk factors, or history, which is what makes this a genuinely different tool from a simple prevalence-based lookup.
The calculation works in odds rather than probability directly, because odds multiply cleanly under Bayes' theorem. Pre-test probability is first converted to pre-test odds, odds = probability / (1 − probability). Those odds are then multiplied by the test's positive likelihood ratio, LR+ = sensitivity / (1 − specificity) — a single number summarising how much more likely a positive result is in someone who truly has the condition versus someone who doesn't. The product is post-test odds, which converts back to post-test probability.
This odds-and-likelihood-ratio method is the standard way results get folded into clinical reasoning: a positive finding on an instrument with a strong LR+ (well above 1) shifts belief upward substantially, while a positive result on a weak instrument barely moves the needle, regardless of how the starting probability was arrived at.
- Enter your starting estimate of how likely the condition is before testing into Pre-test probability (0-1) — from population prevalence, clinical judgment, or another calculator on this site.
- Enter the test's true positive rate into Test sensitivity (0-1).
- Enter the test's true negative rate into Test specificity (0-1).
- Read Post-test probability (0-1) — the updated probability of the condition given a positive test result.
- Pre-test probability and specificity must both be below 1 — either one at 100% makes the likelihood-ratio math undefined, so the instrument will ask you to adjust the inputs.
Worked example — 10% pre-test probability, a 90%/90% test
Enter Pre-test probability = 0.1, Test sensitivity = 0.9, and Test specificity = 0.9. Pre-test odds are 0.1 / (1 − 0.1) = 0.111111. The positive likelihood ratio is LR+ = 0.9 / (1 − 0.9) = 0.9 / 0.1 = 9. Post-test odds are 0.111111 × 9 = 1.0 exactly, which converts back to a post-test probability of 1.0 / (1 + 1.0) = 0.5.
A single positive result here took a 10% starting suspicion all the way up to a 50/50 probability — a substantial shift driven by this instrument's strong likelihood ratio of 9. A weaker LR+, closer to 1, would move that same 10% starting point by far less, which is exactly the kind of comparison this instrument is built to make explicit.
Questions
How is this different from the false-positive-paradox / PPV calculator?
They compute the same underlying Bayesian update through two equivalent routes. The PPV calculator starts from population prevalence and applies Bayes' theorem directly in probability form. This calculator starts from a pre-test probability — which can be any prior estimate, not only population prevalence — and applies the same update using odds and a likelihood ratio. Set pre-test probability equal to prevalence with matching sensitivity and specificity, and both instruments return an identical answer, as this site's shared 1%-prevalence test vector confirms.
Why use odds and likelihood ratios instead of working in probability directly?
Because likelihood ratios multiply cleanly: LR+ combines a test's sensitivity and specificity into one number, and multiplying pre-test odds by that number in a single step gives post-test odds. Doing the equivalent update directly in probability terms requires the full Bayes' theorem fraction each time. The odds-form method is the version most commonly taught for quick bedside or classroom estimation, especially when combining evidence from more than one test.
Where does pre-test probability come from?
It's an estimate of how likely the condition is before the result is known — it can come from population prevalence, from a clinical prediction rule, or from a clinician's structured judgment based on a patient's specific history, symptoms, and risk factors. Because it isn't limited to a population-wide figure, the same instrument can produce very different post-test probabilities for two different patients who start from different pre-test estimates.
What does a likelihood ratio (LR+) greater than 1 mean?
LR+ = sensitivity / (1 − specificity) is greater than 1 whenever the test is at least somewhat informative — a positive result is more likely to come from someone who truly has the condition than from someone who doesn't. The further above 1, the more a positive result shifts belief upward. An LR+ of exactly 1 means a positive result carries no information at all, and post-test probability would equal pre-test probability regardless of the test having been run.
Is this a substitute for clinical decision-making?
No — it's an educational tool for understanding how results update probability estimates through Bayesian reasoning, not a diagnostic instrument. Real clinical decisions depend on validated real-world performance in the relevant population, the full clinical picture, and a qualified professional's judgment, not a single number from a calculator.