Translate Likelihood Ratios into Post-Test Probability

Specify the diagnostic question

Record the target condition, test threshold, clinical setting, and population before using a likelihood ratio. A result for one threshold or selected research sample may not transfer to another setting. The source should make clear how the condition was established and which patients were evaluated.

Deeks and Altman's methodological note on likelihood ratios describes updating pretest odds using the likelihood ratio for the observed result. This is a mathematical update based on inputs; it does not independently establish those inputs or make a clinical decision.

Keep probabilities and odds separate

Convert pretest probability p to odds using p/(1 − p). Multiply those odds by the applicable likelihood ratio. Convert the resulting odds o back to probability using o/(1 + o). Multiplying probability directly by the likelihood ratio skips the required transformation and can produce an invalid answer.

For a binary test, LR+ equals sensitivity divided by one minus specificity. LR− equals one minus sensitivity divided by specificity. Use proportions consistently, and match the chosen ratio to a positive or negative test result. A negative likelihood ratio is a nonnegative number, not a value with a minus sign.

Check a fictional example

Suppose sensitivity and specificity are both 80%, giving LR+ = 4 and LR− = 0.25. With an assumed pretest probability of 20%, pretest odds are 0.20/0.80 = 0.25.

A positive result produces odds of 1 and probability of 50%. A negative result produces odds of 0.0625 and probability of approximately 5.8824%. The post-test probability tool can reproduce these fictional scenarios. Neither result proves the condition present or absent.

Test the transfer assumptions

Write down where the pretest probability came from and whether it fits the setting before the test result was known. Do not use the test result to choose a pretest estimate and then count that information again through the likelihood ratio.

Repeat the calculation across plausible pretest values and, where available, the uncertainty around the likelihood ratio. Label these as scenarios rather than a formal interval unless an appropriate uncertainty method was used. Avoid multiplying several likelihood ratios as though correlated tests supplied independent evidence.

Save the source study, threshold, inputs, result direction, and assumptions with the output. Interpretation still needs the consequences of false positives and false negatives, available alternatives, and qualified clinical judgment. A calculator supplies arithmetic for research understanding, not an individualized diagnosis or treatment recommendation.

Source checked on 31 October 2026; fictional arithmetic independently recalculated.