DEFINITION OF LIKELIHOOD RATIOS (LRs)17 In the far right-hand columns of TabJeJJM, T.ab!e...,6.8.-5, Table...68-6, Iable6_8_-7, Iable 68:8, Iabje.6.8-9, Table
68-10, T.a.ble.68z11, Iab|e..68-12, Ta.bie.,...6.8.-..1..3 and Tablje...68-|4, test performance is expressed using positive and negative likelihood ratios (LRs). LRs are defined as the likelihood that a particular test result would be found in a patient with the target disorder, relative to the likelihood of that same test result occurring in a patient without the target disorder.
Likelihood ratios (LRs) are often divided into positive and negative LRs, expressed as follows: LR of a (+) test = (TPR/FPR) = [(true-positive rate)/(false-positive rate)] = [sensitivity/(1-specificity)]. LR of a (-) test = (FNR/TNR) = [(false-negative rate)/(true-negative rate)] = [(1-sensitivity)/specificity].
The formal definition of an LR(+) is simply a special case of the general definition of LRs: An LR(+) is the likelihood that a positive test result would be found in a patient with the target disorder, compared with the likelihood of a positive test result occurring in a patient without the target disorder. The definition of an LR(-) is the likelihood that a negative test result would be found in a patient with the target disorder, compared with the likelihood of a negative test result occurring in a patient without the target disorder.
INTERPRETATION OF LRs17 In general, an LR(+) of 1 to 2, or an LR(-) of 0.5 to 1, alters disease probability by a small and clinically insignificant degree. In contrast, LR(+)s >10, or LR(-)s <0.1 may have a very substantial impact on clinical decision making through meaningful revision of disease probability. LR(+)s of 2 to 10, or LR(-)s of 0.5 to 0.1 may still make some small contribution to management, depending upon their magnitude and the clinical context in which they are applied. Because LRs are odds, a diagnostic test with an LR(-) = 0.1 is as powerful as a diagnostic test with an LR(+) = 10.
CLINICAL APPLICATION OF LRs17 Likelihood ratios (LRs) combine the stability of sensitivity and specificity with the utility of predictive values, resulting in an index of test performance that can be applied directly to a particular patient at the bedside. This is done by multiplying an LR(+) or LR(-) times the pretest odds of disease, resulting, respectively, in an increased or decreased posttest odds of disease. The larger the LR(+) or the smaller the LR(-), the more powerful the test is.
The performance characteristics of the various tests shown in Table„6.8.:4, IaJ?ie__6_8:§, IaJ?ie__6_8:6, Ta_b!e__6_8:Z, Iable__68:8, Tjble__68-9_, Jable__68:10, IabJeJ81_1, Table6.8-.12, Ta.b!.e.„l.68.-.13 and Ta.b!.e.„l.68.-.14 are incorporated into the discussion of specific diagnoses below.
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