A perspective on standardizing the predictive power of noninvasive cardiovascular tests by likelihood ratio computation: 1. Mathematical principles

The current practice of reporting positive and negative predictive value (PV), sensitivity (Se), and specificity (Sp) as measures of the power of noninvasive cardiovascular tests has significant limitations. A test result's PV and its comparison with other test results are highly dependent on the pretest disease prevalence at which it is determined; the citation of sensitivity and specificity provides no succinct or explicit quantitation of the rule-in and rule-out power of a test. This article presents a rationale for the use of an alternative standard for expressing predictive power in the form of positive and negative likelihood ratios, (+)LR and (-)LR. The likelihood ratios are composite expressions of test power, which incorporate the Se and Sp and their respective complements [(1-Se) and (1-Sp)], thus yielding single unambiguous measures of positive and negative predictive power. The likelihood ratios are calculated as follows: (+)LR = Se/(1-Sp) and (-)LR = Sp/(1-Se). On analysis of the predictive value equations, the likelihood ratios equal the quotients of the posttest predictive value odds to the pretest prevalence odds for disease and no disease, respectively, as follows: (+)LR = (+)PVOd/POD and (-)LR = (-)PVOn/PON, where (+)PVOd is positive predictive value odds for disease, POD is prevalence odds for disease, (-)PVOn is negative predictive value odds for no disease, and PON is prevalence odds for no disease. Thus, the likelihood ratios are measures of the odds advantage in posttest probability of disease or no disease relative to pretest probability, independent of disease prevalence in the tested population. The quotients of the (+)LR or the (-)LR among test results studied in a common population are direct expressions of their relative predictive power in that population. The likelihood ratio principle is applicable to the evaluation of the predictive power of multiple tests performed in a common population and to estimating predictive power at multiple test thresholds.