Clinical utility of likelihood ratios

Abstract

Test-performance characteristics can be derived from a simple 2x2 table displaying the dichotomous relationship between a positive or negative test result and the presence or absence of a target disorder. Sensitivity and specificity, including a summary display of their reciprocal relationship as a receiver operating characteristics curve, are relatively stable test characteristics. Unfortunately, they represent an inversion of customary clinical logic and fail to tell us precisely what we wish to know. Predictive values, on the other hand, provide us with the requisite information but - because they are vulnerable to variation in disease prevalence - are numerically unstable. Likelihood ratios (LRs), in contrast, combine the stability of sensitivity and specificity to provide an omnibus index of test performance far more useful than its constituent parts. Application of Bayes' theorem to LRs produces the following summary equation: Clinically estimated pretest odds of diseasexLR=Posttest odds of disease. This simple equation illustrates a concordance between the mathematical properties of likelihood ratios and the central strategy underlying diagnostic testing: the revision of disease probability.