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| {{Distinguish|Likelihood-ratio test}}
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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.
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| ==Calculation==
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| Two versions of the likelihood ratio exist, one for positive and one for negative test results.
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| Respectively, they are known as the ''likelihood ratio positive'' (LR+) and ''likelihood ratio negative'' (LR–).
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| The likelihood ratio positive is calculated as
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| :<math> LR+ = \frac{\text{sensitivity}}{1 - \text{specificity}} </math>
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| which is equivalent to
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| :<math> LR+ = \frac{\Pr({T+}|D+)}{\Pr({T+}|D-)} </math>
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| or "the probability of a person who has the disease testing positive divided by the probability of a person who does not have the disease testing positive."
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| Here "T+" or "T−" denote that the result of the test is positive or negative, respectively. Likewise, "D+" or "D−" denote that the disease is present or absent, respectively. So "true positives" are those that test positive (T+) and have the disease (D+), and "false positives" are those that test positive (T+) but do not have the disease (D−).
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| The likelihood ratio negative is calculated as<ref name=altman>{{cite book |author=Gardner, M.; Altman, Douglas G. |title=Statistics with confidence: confidence intervals and statistical guidelines |publisher=BMJ Books |location=London |year=2000 |pages= |isbn=0-7279-1375-1 |oclc= |doi= |accessdate=}}</ref>
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| :<math> LR- = \frac{1 - \text{sensitivity}}{\text{specificity}} </math>
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| which is equivalent to<ref name=altman/> | |
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| :<math> LR- = \frac{\Pr({T-}|D+)}{\Pr({T-}|D-)} </math>
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| or "the probability of a person who has the disease testing negative divided by the probability of a person who does not have the disease testing negative."
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| The [[pretest odds]] of a particular diagnosis, multiplied by the likelihood ratio, determines the [[post-test odds]]. This calculation is based on [[Bayes' theorem]]. (Note that odds can be calculated from, and then converted to, [[probability]].)
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| ==Application to medicine==
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| A likelihood ratio of greater than 1 indicates the test result is associated with the disease. A likelihood ratio less than 1 indicates that the result is associated with absence of the disease. | |
| Tests where the likelihood ratios lie close to 1 have little practical significance as the post-test probability (odds) is little different from the pre-test probability. In summary, the pre-test probability refers to the chance that an individual has a disorder or condition prior to the use of a diagnostic test. It allows the clinician to better interpret the results of the diagnostic test and helps to predict the likelihood of a true positive (T+) result.<ref>{{cite journal | doi = 10.1001/jama.247.18.2543 | author = Harrell F, Califf R, Pryor D, Lee K, Rosati R | year = 1982 | title = Evaluating the Yield of Medical Tests | url = | journal = JAMA | volume = 247 | issue = 18| pages = 2543–2546 | pmid = 7069920 }}</ref>
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| Research suggests that physicians rarely make these calculations in practice, however,<ref name="pmid9576412">{{cite journal |author=Reid MC, Lane DA, Feinstein AR |title=Academic calculations versus clinical judgments: practicing physicians’ use of quantitative measures of test accuracy |journal=Am. J. Med. |volume=104 |issue=4 |pages=374–80 |year=1998 |pmid=9576412| doi = 10.1016/S0002-9343(98)00054-0}}</ref> and when they do, they often make errors.<ref name="pmid11934776">{{cite journal |author=Steurer J, Fischer JE, Bachmann LM, Koller M, ter Riet G |title=Communicating accuracy of tests to general practitioners: a controlled study |journal=BMJ |volume=324 |issue=7341 |pages=824–6 |year=2002 |pmid=11934776 |pmc=100792| doi = 10.1136/bmj.324.7341.824}}</ref> A [[randomized controlled trial]] compared how well physicians interpreted diagnostic tests that were presented as either [[sensitivity (tests)|sensitivity]] and [[specificity (tests)|specificity]], a likelihood ratio, or an inexact graphic of the likelihood ratio, found no difference between the three modes in interpretation of test results.<ref name="pmid16061916">{{cite journal |author=Puhan MA, Steurer J, Bachmann LM, ter Riet G |title=A randomized trial of ways to describe test accuracy: the effect on physicians' post-test probability estimates |journal=Ann. Intern. Med. |volume=143 |issue=3 |pages=184–9 |year=2005 |pmid=16061916 |doi=}}</ref>
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| ==Example==
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| A medical example is the likelihood that a given test result would be expected in a patient with a certain disorder compared to the likelihood that same result would occur in a patient without the target disorder.
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| Some sources distinguish between LR+ and LR−.<ref name="urlLikelihood ratios">{{cite web |url=http://www.poems.msu.edu/InfoMastery/Diagnosis/likelihood_ratios.htm |title=Likelihood ratios |work= |accessdate=2009-04-04}}</ref> A worked example is shown below.
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| {{SensSpecPPVNPV}}
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| [[Confidence intervals]] for all the predictive parameters involved can be calculated, giving the range of values within which the true value lies at a given confidence level (e.g. 95%).<ref>[http://www.medcalc.org/calc/diagnostic_test.php Online calculator of confidence intervals for predictive parameters]</ref>
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| ==Estimation of pre- and post-test probability==
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| {{Further|Pre- and post-test probability}}
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| The likelihood ratio of a test provides a way to estimate the [[pre- and post-test probabilities]] of having a condition.
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| With ''pre-test probability'' and ''likelihood ratio'' given, then, the ''post-test probabilities'' can be calculated by the following three steps:<ref>[http://www.cebm.net/index.aspx?o=1043 Likelihood Ratios], from CEBM (Centre for Evidence-Based Medicine). Page last edited: 1 February 2009</ref>
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| *Pretest odds = (Pretest probability / (1 - Pretest probability)
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| *Posttest odds = Pretest odds * Likelihood ratio
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| In equation above, ''positive post-test probability'' is calculated using the ''likelihood ratio positive'', and the ''negative post-test probability'' is calculated using the ''likelihood ratio negative''.
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| *Posttest probability = Posttest odds / (Posttest odds + 1)
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| In fact, ''post-test probability'', as estimated from the ''likelihood ratio'' and ''pre-test probability'', is generally more accurate than if estimated from the ''positive predictive value'' of the test, if the tested individual has a different ''pre-test probability'' than what is the ''prevalence'' of that condition in the population.
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| ===Example===
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| Taking the medical example from above (20 true positives, 10 false negatives, and 2030 total patients), the ''positive pre-test probability'' is calculated as:
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| *Pretest probability = (20 + 10) / 2030 = 0.0148
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| *Pretest odds = 0.0148 / (1 - 0.0148) =0.015
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| *Posttest odds = 0.015 * 7.4 = 0.111
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| *Posttest probability = 0.111 / (0.111 + 1) =0.1 or 10%
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| As demonstrated, the ''positive post-test probability'' is numerically equal to the ''positive predictive value''; the ''negative post-test probability'' is numerically equal to (1 - ''negative predictive value'').
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| ==References==
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| <references/>
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| {{Medical research studies}}
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| [[Category:Medical statistics]]
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| [[Category:Evidence-based medicine]]
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| [[Category:Summary statistics for contingency tables]]
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Most of the trophies from all in the members in your group get added up and as well , divided by 2 find out your clans overall medals. Playing many different kinds of games sells your gaming time more enjoyment. and your league also determines any battle win bonus. 5 star rating and is known to be unbelievably addictive as players can devote several hours enjoying the game. She focuses primarily on beauty salon business manufacturing and client fascination.
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