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Sensitivity, or recall rate, is a statistical measure of how well a binary classification test correctly identifies a condition, whether this is medical screening tests picking up on a disease, or quality control in factories deciding if a new product is good enough to be sold. Binary classification is the task of classifying the members of a given set of objects into two groups on the basis of whether they have some Property or

The results of the screening test are compared to some absolute (Gold standard); for example, for a medical test to determine if a person has a certain disease, the sensitivity to the disease is the probability that if the person has the disease, the test will be positive.

The sensitivity is the proportion of true positives of all diseased cases in the population. In Statistics, the terms Type I error (also α error, or false positive) and type II error ( β error, or a false negative It is a parameter of the test.

High sensitivity is required when early diagnosis and treatment is beneficial, and when the disease is infectious.

Contents

Worked example

Relationships among terms
Condition
(as determined by "Gold standard")
True False
Test
outcome		 Positive True Positive False Positive
(Type I error, P-value)		 → Positive predictive value
Negative False Negative
(Type II error)		 True Negative → Negative predictive value
↓
Sensitivity		 ↓
Specificity
A worked example
the Fecal occult blood (FOB) screen test is used in 203 people to look for bowel cancer:
Patients with bowel cancer
(as confirmed on endoscopy)
True False  ?
FOB
test		 Positive TP = 2 FP = 18 = TP / (TP + FP)
= 2 / (2 + 18)
= 2 / 20 ≡ 10%
Negative FN = 1 TN = 182 = TN / (TN + FN)
182 / (1 + 182)
= 182 / 183 ≡ 99. In Medicine, a gold standard test or criterion standard test is a Diagnostic test or benchmark that is regarded as definitive In Statistics, the terms Type I error (also α error, or false positive) and type II error ( β error, or a false negative In statistical Hypothesis testing the p-value is the Probability of obtaining a result at least as extreme as the one that was actually observed given The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed In Statistics, the terms Type I error (also α error, or false positive) and type II error ( β error, or a false negative The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed Faecal occult blood is a term for Blood present in the Faeces that is not visibly apparent Colorectal cancer, also called colon cancer or large bowel cancer, includes Cancerous growths in the colon, Rectum and Endoscopy means looking inside and typically refers to looking inside the body for medical reasons using an instrument called an endoscope. 5%
↓
= TP / (TP + FN)
= 2 / (2 + 1)
= 2 / 3 ≡ 66. 67%		 ↓
= TN / (FP + TN)
= 182 / (18 + 182)
= 182 / 200 ≡ 91%

Related calculations

Hence with large numbers of false positives and few false negatives, a positive FOB screen test is in itself poor at confirming cancer (PPV=10%) and further investigations must be undertaken, it will though pickup 66. The power of a statistical test is the probability that the test will reject a false Null hypothesis (that it will not make a Type II error) 7% of all cancers (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have cancer (NPV=99. 5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).

Definition

{\rm sensitivity}=\frac{\rm number\ of\ True\ Positives}{{\rm number\ of\ True\ Positives}+{\rm number\ of\ False\ Negatives}}.

A sensitivity of 100% means that the test recognizes all sick people as such.

Sensitivity alone does not tell us how well the test predicts other classes (that is, about the negative cases). In the binary classification, as illustrated above, this is the corresponding specificity test, or equivalently, the sensitivity for the other classes.

Sensitivity is not the same as the positive predictive value (ratio of true positives to combined true and false positives), which is as much a statement about the proportion of actual positives in the population being tested as it is about the test. The positive predictive value, or precision rate, or post-test probability of disease, is the proportion of patients with positive test results who are correctly diagnosed

The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, the options are to exclude indeterminate samples from analyses (but the number of exclusions should be stated when quoting sensitivity), or, alternatively, indeterminate samples can be treated as false negatives (which gives the worst-case value for sensitivity and may therefore underestimate it).

Terminology in information retrieval

In information retrieval positive predictive value is called precision, and sensitivity is called recall. Information retrieval ( IR) is the science of searching for documents for Information within documents and for metadata about documents as well as that

The F-measure can be used as a single measure of performance of the test. Information retrieval ( IR) is the science of searching for documents for Information within documents and for metadata about documents as well as that The F-measure is the harmonic mean of precision and recall:

F = 2 \times ({\rm precision} \times {\rm recall}) / ({\rm precision} + {\rm recall}).

In the traditional language of statistical hypothesis testing, the sensitivity of a test is called the statistical power of the test, although the word power in that context has a more general usage that is not applicable in the present context. In Mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of Average. A statistical hypothesis test is a method of making statistical decisions using experimental data The power of a statistical test is the probability that the test will reject a false Null hypothesis (that it will not make a Type II error) A sensitive test will have fewer Type II errors. In Statistics, the terms Type I error (also α error, or false positive) and type II error ( β error, or a false negative

See also

Online Calculators

References

External links

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