posttestprobabilitet

The term posttestprobabilitet, often translated as posterior probability in English, denotes the probability of a hypothesis after observing test data. In Bayesian statistics, it is obtained by updating a prior belief with the likelihood of the observed results. The usual setting is a diagnostic test: H is the presence of a condition, E is the result of the test.

Bayes' theorem expresses this update as P(H|E) = [P(E|H) P(H)] / [P(E|H) P(H) + P(E|¬H) P(¬H)]. This gives the probability that the condition is present given the test result. When using two outcomes (positive or negative), the same formula applies for each case. An alternative presentation uses odds: post-test odds = pre-test odds × likelihood ratio, with LR+ = P(E|H) / P(E|¬H).

Example: suppose the pretest probability (prior) of a disease is 0.2, the test has sensitivity 0.9 and specificity 0.9, and the result is positive. Then P(H|positive) = (0.9 × 0.2) / [(0.9 × 0.2) + (0.1 × 0.8)] ≈ 0.69. Thus the posttestprobabilitet increases from 0.2 to about 0.69 after a positive result.

Posttestprobabilitet depends on the test’s accuracy and the prior probability, and it is central to probabilistic reasoning and decision making in diagnostics. It requires reliable estimates of sensitivity and specificity and differs in interpretation from frequentist measures such as p-values.