出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2016/06/19 20:18:29」(JST)
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 first description of the use of likelihood ratios for decision rules was made at a symposium on information theory in 1954.[1] In medicine, likelihood ratios were introduced between 1975 and 1980.[2][3][4]
Two versions of the likelihood ratio exist, one for positive and one for negative test results. Respectively, they are known as the positive likelihood ratio (LR+, likelihood ratio positive, likelihood ratio for positive results) and negative likelihood ratio (LR–, likelihood ratio negative, likelihood ratio for negative results).
The positive likelihood ratio is calculated as
which is equivalent to
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." 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−).
The negative likelihood ratio is calculated as[5]
which is equivalent to[5]
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."
The calculation of likelihood ratios for tests with continuous values or more than two outcomes is similar to the calculation for dichotomous outcomes; a separate likelihood ratio is simply calculated for every level of test result and is called interval or stratum specific likelihood ratios.[6]
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.)
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.[7]
Research suggests that physicians rarely make these calculations in practice, however,[8] and when they do, they often make errors.[9] A randomized controlled trial compared how well physicians interpreted diagnostic tests that were presented as either sensitivity and specificity, a likelihood ratio, or an inexact graphic of the likelihood ratio, found no difference between the three modes in interpretation of test results.[10]
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Use this table to estimate how the likelihood ratio changes the probability without needing a calculator.
| Likelihood Ratio | Approximate* Change
in Probability[11] |
Effect on Posttest
Probability of disease[12] |
|---|---|---|
| Values between 0 and 1 decrease the probability of disease | ||
| 0.1 | - 45% | Large decrease |
| 0.2 | - 30% | Moderate decrease |
| 0.5 | - 15% | Slight decrease |
| 1 | - 0% | None |
| Values greater than 1 increase the probability of disease | ||
| 1 | + 0% | None |
| 2 | + 15% | Slight increase |
| 5 | + 30% | Moderate increase |
| 10 | + 45% | Large increase |
*These estimates are accurate to within 10% of the calculated answer for all pretest probabilities between 10% and 90%. The average error is only 4%.
An easy way to recall this is by simply remembering that the three specific LRs—2, 5, and 10—correspond with the first three multiples of 15 (i.e., 15, 30, and 45). An LR of 2 increases probability 15%, one of 5 increases it 30%, and one of 10 increases it 45%. For those LRs between 0 and 1, you can simply invert 2, 5, and 10 (i.e., 1/2 = 0.5, 1/5 = 0.2, 1/10 = 0.1). For any LR in between, the percent change can be estimated.
These estimates are independent of pretest probability and are accurate as long as the pretest probability is between 10% and 90%. For polar extremes of probability >90% and <10%, this usually indicates diagnostic certainty for most clinical problems, making it unnecessary to order further tests (and apply additional LRs).
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.
Some sources distinguish between LR+ and LR−.[13] A worked example is shown below.
| Patients with bowel cancer (as confirmed on endoscopy) |
||||
| Condition positive | Condition negative | |||
| Fecal occult |
Test outcome |
True positive (TP) = 20 |
False positive (FP) = 180 |
Positive predictive value
= TP / (TP + FP)
= 20 / (20 + 180) |
| Test outcome |
False negative (FN) = 10 |
True negative (TN) = 1820 |
Negative predictive value
= TN / (FN + TN)
= 1820 / (10 + 1820) |
|
| Sensitivity
= TP / (TP + FN)
= 20 / (20 + 10) |
Specificity
= TN / (FP + TN)
= 1820 / (180 + 1820) |
|||
Related calculations
Hence with large numbers of false positives and few false negatives, a positive screen test is in itself poor at confirming the disorder (PPV = 10%) and further investigations must be undertaken; it did, however, correctly identify 66.7% of all cases (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have the disorder (NPV = 99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).
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%).[14]
The likelihood ratio of a test provides a way to estimate the pre- and post-test probabilities of having a condition.
With pre-test probability and likelihood ratio given, then, the post-test probabilities can be calculated by the following three steps:[15]
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.
Alternatively, post-test probability can be calculated directly from the pre-test probability and the likelihood ratio using the equation:
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.
Taking the medical example from above (20 true positives, 10 false negatives, and 2030 total patients), the positive pre-test probability is calculated as:
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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| リンク元 | 「陽性尤度比」「LR+」 |
| 関連記事 | 「likelihood」「rat」「positive」「ratio」 |
| 疾患あり | 疾患なし | |
| 検査陽性 | a 真陽性 |
b 偽陽性 |
| 検査陰性 | c 偽陰性 |
d 真偽性 |
[★] 陽性尤度比, positive likelihood ratio