Likelihood ratio interpretation of the relative risk

Abstract

Interpreting diagnostic test results in medicine The likelihood ratio (LR) is today commonly used in medicine for diagnostic inference. Historically, it was preceded by introduction, in 1966, of the predictive value of a diagnostic test in Medicine1 and within a decade of the latter, it was realised that the true-positive to false-positive ratio2 3 also then called the likelihood value4 was the main driver of the change from prior probabilities to posterior predictive values. The latter were also called posttest likelihoods and this ratio became known as the LR in Medicine. The change from prior probabilities to posterior predictive values was formulated using Bayes’ theorem5 and represented a more versatile approach to predictive values. The reason this is considered more versatile is that Bayes’ theorem allows a physician to compute the predictive value (probability) of a diagnosis conditional on a specific test result. For example, if we denote test status as +ve (positive) and –ve (negative) and the gold standard (eg, underlying diagnosis) as D (diagnosed) and nD (not diagnosed), respectively, then from Bayes’ theorem,5 the posterior (after the test result) probability (expressed in odds form) of the diagnosis can be derived from test sensitivity and specificity as follows