Post-Test Probability Calculator

Post-test probability is the probability that a patient truly has a disease after accounting for the result of a diagnostic test. Unlike pre-test probability (prevalence), it incorporates how well the test performs — its sensitivity and specificity — to update the likelihood of disease. It is closely related to positive predictive value but is framed in a Bayesian context.

Post-test probability is calculated using three steps: (1) Convert pre-test probability to pre-test odds: Pre-test odds = Prevalence / (1 − Prevalence). (2) Multiply pre-test odds by the relevant likelihood ratio: Post-test odds = Pre-test odds × LR. (3) Convert back to probability: Post-test probability = Post-test odds / (1 + Post-test odds). Use the positive LR (LR+) for a positive test result and the negative LR (LR−) for a negative result.

Pre-test probability is the prevalence of the disease in the population being tested before any test is performed. It can be estimated from published epidemiological data, clinical experience, or a 2×2 contingency table as: Prevalence = (TP + FN) / (TP + FN + FP + TN), where TP = true positives, FN = false negatives, FP = false positives, and TN = true negatives.

Pre-test probability (prevalence) is expressed as a proportion between 0 and 1 (or 0–100%). Pre-test odds express the same information as a ratio of the probability of disease to the probability of no disease: Odds = Probability / (1 − Probability). For example, a prevalence of 20% corresponds to pre-test odds of 0.20 / 0.80 = 0.25. Odds are used in the Bayesian calculation because likelihood ratios multiply directly against odds.

The positive likelihood ratio (LR+) tells you how much more likely a positive test result is in someone with the disease compared to someone without it: LR+ = Sensitivity / (1 − Specificity). The negative likelihood ratio (LR−) tells you how much more likely a negative result is in someone with the disease compared to someone without: LR− = (1 − Sensitivity) / Specificity. Higher LR+ values and lower LR− values indicate a more diagnostically useful test.

Post-test odds are calculated by multiplying the pre-test odds by the appropriate likelihood ratio: Post-test odds = Pre-test odds × LR. For a positive test, use LR+; for a negative test, use LR−. Post-test odds can then be converted to post-test probability using: Post-test probability = Post-test odds / (1 + Post-test odds).

A test with sensitivity above 95% is very good at ruling out disease when the result is negative (a useful screening test). A test with specificity above 95% is very good at ruling in disease when the result is positive (a useful confirmatory test). In practice, most tests involve a trade-off between sensitivity and specificity, and the clinical usefulness depends on the pre-test probability of the disease in the population being tested.

No. Post-test probability is always between 0% and 100% because it is derived from odds that are always non-negative, and the conversion formula Post-test probability = Post-test odds / (1 + Post-test odds) always produces a value in the range [0, 1]. If you are seeing unexpected results, check that your sensitivity, specificity, and prevalence inputs are valid percentages between 0 and 100.