Title: A Perspective on Standardizing the Predictive Power of Noninvasive Cardiovascular Tests by Likelihood Ratio Computation: 1. Mathematical Principles
Abstract: 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(l- Sp) and (-)LR = Sp/(I- 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 (+)PVO d 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. 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(l- Sp) and (-)LR = Sp/(I- 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 (+)PVO d 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. A Perspective on Standardizing the Predictive Power of Noninvasive Cardiovascular Tests by Likelihood Ratio Computation: 2. Clinical ApplicationsMayo Clinic ProceedingsVol. 74Issue 11PreviewLikelihood ratio measures may be used as a standard for expressing the predictive power of noninvasive cardiovascular tests, calculated from sensitivity and specificity measures or as ratios of the predictive value odds to pretest odds for positive and negative test results. The positive likelihood ratio, (+)LR, expresses the power of a positive test result to augment an estimate of disease probability independent of the pretest prevalence of disease in a given population; the negative likelihood ratio, (-)LR, expresses the power of a negative test result to augment an estimate of the probability of no disease independent of the pretest prevalence of no disease in the same population. Full-Text PDF The Wizard of Odds: Bayes' Theorem and Diagnostic TestingMayo Clinic ProceedingsVol. 74Issue 11Preview ‘Tis with our judgements as our watches, none go just alike, yet each believes his own.Alexander Pope Full-Text PDF
Publication Year: 1999
Publication Date: 1999-11-01
Language: en
Type: article
Indexed In: ['crossref', 'pubmed']
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Cited By Count: 24
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