# Sensitivity And Specificity Definition

## What is sensitivity and specificity?

*Sensitivity and specificity*are terms often used to describe the value of a test in medical diagnostics. The sensitivity is a measure of the "sensitivity" of the test, the specificity determines how "specifically" is the test. The sensitivity and specificity are both expressed as a fraction or percentage, such as 0.90 or 90%.

### Define sensitivity

The sensitivity of a medical test is the percentage of true positive results among the diseased people. It is the ratio between the number of persons and scored positive in whom the disease has been examined by the test actually present, and the total of all the examined individuals with the disease (including the number of persons and scored negative in whom the disease is still present ). It is thus a measure of the sensitivity of the test for the disease under investigation. The higher the sensitivity of a test, the greater the chance that someone who actually has the disease, getting a positive test result (few false negatives (low C)). A test result is positive if the posterior probability (nakans retrospect probability) associated with it is greater than the nakans that belongs to the other (negative) test result.

### Specificity definition

The specificity of a test is the percentage of true negative test results among the non-diseased individuals. The specificity of a test is the ratio between the number of true negative results (not ill, negative results), and the total of all the cases where the disease is absent. The total of all cases in which the disease was absent consists of a sum of cases where a false positive result (false alarm) is obtained, and the cases that received a correct negative result. See the formulas below. So the higher the specificity of a test, the greater the chance that someone who does not have the disease, receive a negative test result (few false positive results (small B)).

### Ideal test from the standpoint of sensitivity and specificity

A test can have a high sensitivity (sensitivity), but often strike false alarms. The test should also be specific, that is to say as far as possible to give positive reaction in the test by the disease investigated, and as little as possible in the absence of the tested disease. An ideal test should have a sensitivity of 100% (on all cases of disease is the positive test) and also a specificity of 100% (if the disease is not present, the test is negative). This 100% accurate test is the 'Gold Standard' said In reality, this is never the case, if such a test is impractical or too expensive.

### Examples

__HIV test__

A screening test for hiv in blood donors should have the highest possible sensitivity: one wants to so avoid error-negative results are. An error-negative result means that someone who is hiv-infected, the rash that he is healthy. In this case, will be considered as unjustified the blood healthy and it will infect the recipient when fed.

The sensitivity of the test can be set by sliding the threshold value, the value at which the test is regarded as positive. If bv. 5 and is considered more as a positive test result and less than 5 as a negative test result then 5 the threshold value (cut-off, English: cut-off point). As the cut-off point is higher, the number of that positive scores drop, so the reverse also applies for the sensitivity and specificity. A test with high sensitivity (low threshold) will have a lower specificity, which makes some people be considered as hiv-positive. Their blood will be unfairly denied, but this is much less serious than the reverse. One tests, however, a person who is concerned for his own health than is the reverse, and one will be a positive test (which is a good chance has unfairly positive (false positive), to be) by a further investigation always like to confirm.

In practice, one usually first use a test with high sensitivity (ELISA). If the result is negative one can reassure the patient and say that he is not infected with hiv. If the ELISA is positive one will notify the patient here, however, not yet. Given the lower specificity of the ELISA is there, after all, a substantial number of false-positive test results and there is a risk the patient wrongly to bring bad news. Instead, one will run a test on the same blood sample with high specificity: an immunoblot. If this test is positive we can with certainty that the patient is seropositive for hiv.

__Fault of a suspect__

An example of a situation where a high specificity is desired, the judicial review of the criminality of a defendant. This should have the highest possible specificity. False positive in this case means that an innocent yet is found guilty. Error-negative means that a guilty is found to be innocent. In our legal system, it is considered that it is worse to lock up an innocent than a guilty freely to let go. One wishes in condemning so as little as possible false positives. So the suspect always gets the benefit of the doubt, despite the fact that as a result, the sensitivity is lower and thus more culprits impunity.

__Feasibility__

When medical tests, a high sensitivity and specificity is often not feasible. If both 90% is considered that, in the medicine usually already as a very good test. A pregnancy test is one of the best, with a sensitivity and specificity of approximately 99%. In the so-called "test rheumatism 'both are about 80%. For the results of medical tests useful to evaluate is therefore of great importance to have a good idea of the prevalence of the disease. A positive test result in an investigation into a rare condition often has the means nothing.

### Sensitivity, specificity, and the ROC curve

In a continuous variable, it is obvious that, in a positive context, the sensitivity will increase as the cutoff point, the point at which and above which a test result as positive seeth decreasing. Is a second cut-off point lower than the first then there will be not only more ill are that score positive but there will also be more non-sick that score positive, in other words, a higher sensitivity is always coupled to a lower specificity (unless near perfect association ). One can now view the sensitivity on the y-axis of a cartesian system as a function of 1 - specificity (x-axis). The result of this operation is an ROC curve.

### History of the diagnostic interpretation

In the last century, a high sensitivity has been seen as a way to exclude the disease examined by the test, a high specificity in order to make the diagnosis. The reason was a mendasar distrust of the post-test probabilities (nakansen) and therefore predictive (predictive) values (positive predictive value = nakans with positive test results, negative predictive value is the complement of nakans with negative test result).

Sensitivity and specificity are then, by default, considered as constants. One forgets to this way of thinking that, by multiplying the number of patients with factor ignores the representativeness of the sample and that the cause is that no valid nakans can charge more. It generalizes the invalidity of the nakansen while on a representative sample of the nakansen indeed be valid charge.

This view is still widely spread in this century but a new idea is gaining ground. The value of the nakans be made first, and there is again confident. More and more accompany the sensitivity and specificity of the predictive values. Moreover, they all constructed at the end of the last century dimensions which are a combination of sensitivity and specificity, the likelihood ratios. The likelihood ratios should be used to calculate the nakans. At this nakans awarded the highest diagnostic value. So there seems to be a Copernican revolution to occur in this area: the sensitivity and specificity to the post-test probability.

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