What is post-test probability?
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. See also our calculate False Positive Rate, False Positives (count) & True Negatives (count) — False Positive.
How do I calculate post-test probability?
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.
How do I calculate pre-test probability (prevalence)?
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.
What's the difference between pre-test odds and pre-test probability?
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. You might also find our AUC Calculator (Area Under Curve) useful.
What are positive and negative likelihood ratios?
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.
How do I calculate post-test odds?
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).
What sensitivity and specificity values make a test clinically useful?
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.
Can post-test probability exceed 100% or be negative?
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.