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In evidence-based medicine, likelihood ratios are used for assessing the value of performing a diagnostic test.They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition (such as a disease state) exists.
Likelihood ratio is calculated from sensitivity and specificity of the test, and thereby it does not depend on prevalence in the reference group, [2] and, likewise, it does not change with changed pre-test probability, in contrast to positive or negative predictive values (which would change).
is the sensitivity; is the specificity; is disease prevalence; Of note, the denominator of the above equation is the natural logarithm of the positive likelihood ratio (LR+). Also, note that a critical assumption is that the tests must be independent.
Sensitivity and specificity are prevalence-independent test characteristics, as their values are intrinsic to the test and do not depend on the disease prevalence in the population of interest. [6] Positive and negative predictive values , but not sensitivity or specificity, are values influenced by the prevalence of disease in the population ...
The log diagnostic odds ratio can also be used to study the trade-off between sensitivity and specificity [5] [6] by expressing the log diagnostic odds ratio in terms of the logit of the true positive rate (sensitivity) and false positive rate (1 − specificity), and by additionally constructing a measure, :
Negative likelihood ratio = (1 − sensitivity) / specificity ≈ (1 − 0.67) / 0.91 ≈ 0.37 ... This template is used as a portion of the articles on sensitivity ...
The importance of specificity can be seen by showing that even if sensitivity is raised to 100% and specificity remains at 80%, the probability that someone who tests positive is a cannabis user rises only from 19% to 21%, but if the sensitivity is held at 90% and the specificity is increased to 95%, the probability rises to 49%.
Youden's J statistic is = + = + with the two right-hand quantities being sensitivity and specificity.Thus the expanded formula is: = + + + = (+) (+) In this equation, TP is the number of true positives, TN the number of true negatives, FP the number of false positives and FN the number of false negatives.