result would occur in a patient without the target disorder. Some sources distinguish between LR+ and LR−. A worked example is shown below. Confidence intervals for all the predictive parameters involved can be calculated, giving the range of values within which the true value lies at a given confidence level (e.g. 95%). Estimation of pre- and post-test probability The likelihood ratio of a test provides a way to estimate the pre- and post-test probabilities of having a condition. With pre-test probability and likelihood ratio given, then, the post-test probabilities can be calculated by the following three steps: In equation above, positive post-test probability is calculated using the likelihood ratio positive, and the negative post-test probability is calculated using the likelihood ratio negative. Odds are converted to probabilities as follows: multiply equation (1) by (1 − probability) add (probability × odds) to equation (2) divide equation (3) by (1 + odds) hence Posttest probability = Posttest odds / (Posttest odds + 1) Alternatively, post-test probability can be calculated directly from the pre-test probability and the likelihood ratio using the equation: P' = P0 × LR/(1 − P0 + P0×LR), where P0 is the pre-test probability, P' is the post-test probability, and LR is the likelihood ratio. This formula can be calculated algebraically by combining the steps in the preceding description. In fact, post-test probability, as estimated from the likelihood ratio and pre-test probability, is generally more accurate than if estimated from the positive predictive value of the test, if the tested individual has a different pre-test probability than what is the prevalence of that condition in the population. Example Taking the medical example from above (20 true positives, 10 false negatives, and 2030 total patients), the positive pre-test probability is calculated as: Pretest probability = (20 + 10) / 2030 = 0.0148 Pretest odds = 0.0148 / (1 − 0.0148) = 0.015 Posttest odds = 0.015 × 7.4 = 0.111 Posttest probability = 0.111 / (0.111 + 1) = 0.1 or 10% As demonstrated, the positive post-test probability is numerically equal to the positive predictive value; the negative post-test probability is numerically equal to (1 − negative predictive value). Notes References External links Medical likelihood ratio repositories The Likelihood Ratio Database GetTheDiagnosis.org: A Database of Sensitivity and Specificity The NNT: LR Home Medical statistics Evidence-based medicine Summary statistics for contingency tables