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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.
The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
Diagram relating pre- and post-test probabilities, with the green curve (upper left half) representing a positive test, and the red curve (lower right half) representing a negative test, for the case of 90% sensitivity and 90% specificity, corresponding to a likelihood ratio positive of 9, and a likelihood ratio negative of 0.111.
In medical diagnosis, test sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), whereas test specificity is the ability of the test to correctly identify those without the disease (true negative rate). If 100 patients known to have a disease were tested, and 43 test positive, then the test has ...
In medical testing with binary classification, the diagnostic odds ratio (DOR) is a measure of the effectiveness of a diagnostic test. [1] It is defined as the ratio of the odds of the test being positive if the subject has a disease relative to the odds of the test being positive if the subject does not have the disease.
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.
The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that the degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test.
The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based. [4] The general formula for Pearson's chi-squared test statistic is