What is Sensitivity (test)?

Information about Sensitivity (test)

Sensitivity, or recall rate, is a statistical measure of how well a binary classification test correctly identifies a condition, whether this be medical screening tests picking up on a disease, or quality control in factories deciding if a new product is good enough to be sold.

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. It is a parameter of the test.

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

Worked example

Relationships among terms:
Condition
(as determined by "Gold standard")
TrueFalse
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)
TrueFalse?
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 ≡ 99.5%
↓
= TP / (TP + FN)
= 2 / (2 + 1)
= 2 / 3 ≡ 66.67%		 ↓
= TN / (FP + TN)
= 182 / (18 + 182)
= 182 / 200 ≡ 91%
Related calculations
  • False positive rate (α) = FP / (FP + TN) = 18 / (18 + 182) = 9% = 1 - specificity
  • False negative rate (β) = FN / (TP + FN) = 1 / (2 + 1) = 33% = 1 - sensitivity
  • Power = 1 − β

Definition



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 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.

F-measure: can be used as a single measure of performance of the test. The F-measure is the harmonic mean of precision and 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. A sensitive test will have fewer Type II errors.

See also

External link

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 not. Some typical binary classification tasks are

..... Read more.
Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors.

Statistical error vs.


..... Read more.
gold standard test or criterion standard test is a diagnostic test or benchmark that is regarded as definitive. This can refer to diagnosing a disease process, or the criteria by which scientific evidence is evaluated.
..... Read more.
In statistical hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as a given data point, assuming the data point was the result of chance alone.
..... Read more.
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 positive predictive value must exceed the prevalence.
..... Read more.
The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed.

Worked example

Relationships among terms:

Condition
(as determined by "Gold standard")
True False
..... Read more.
The specificity is a statistical measure of how well a binary classification test correctly identifies the negative cases, or those cases that do not meet the condition under study.
..... Read more.
MeSH D009780 Fecal occult blood is a term for blood present in the feces that is not visibly apparent. In medicine, a fecal occult blood test is a check for hidden (occult) blood in the stool (feces). Conventional fecal occult blood tests look for heme.
..... Read more.
Colorectal cancer
Classification & external resources

Diagram of the stomach, colon, and rectum
ICD-10 C 18. -C 20.
ICD-9 153.0 - 154.1
ICD-O: M 8140/3 (95% of cases)
OMIM 114500
DiseasesDB 2975
MedlinePlus 000262
..... Read more.
Endoscopy means looking inside and typically refers to looking inside the human body for medical reasons using an instrument called an endoscope. Endoscopy can also refer to using a borescope in technical situations where direct line-of-sight observation is not
..... Read more.
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). As power increases, the chances of a Type II error decrease, and vice versa. The probability of a Type II error is referred to as β.
..... Read more.
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 positive predictive value must exceed the prevalence.
..... Read more.
Information retrieval (IR) is the science of searching for information in documents, searching for documents themselves, searching for metadata which describe documents, or searching within databases, whether relational stand-alone databases or hypertextually-networked databases
..... Read more.
In mathematics, the harmonic mean (formerly sometimes called the subcontrary mean) is one of several kinds of average. Typically, it is appropriate for situations when the average of rates is desired.
..... Read more.
statistical hypothesis test, or more briefly, hypothesis test, is an algorithm to state the alternative (for or against the hypothesis) which minimizes certain risks.

This article describes the commonly used frequentist treatment of hypothesis testing.
..... Read more.
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). As power increases, the chances of a Type II error decrease, and vice versa. The probability of a Type II error is referred to as β.
..... Read more.
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 not. Some typical binary classification tasks are

..... Read more.
The negative predictive value is the proportion of patients with negative test results who are correctly diagnosed.

Worked example

Relationships among terms:

Condition
(as determined by "Gold standard")
True False
..... Read more.
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 positive predictive value must exceed the prevalence.
..... Read more.
receiver operating characteristic (ROC), or simply ROC curve, is a graphical plot of the sensitivity vs. (1 - specificity) for a binary classifier system as its discrimination threshold is varied.
..... Read more.
The word selectivity has several meanings:
  • Selectivity, the ability to notice/distinguish small differences. Also the words selectiveness, refinement and discrimination are used. Discrimination is also a cultural term.

..... Read more.
In statistics, a result is called significant if it is unlikely to have occurred by chance. "A statistically significant difference" simply means there is statistical evidence that there is a difference; it does not mean the difference is necessarily large, important or significant
..... Read more.
Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors.

Statistical error vs.


..... Read more.
Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors.

Statistical error vs.


..... Read more.
Type I errors (or α error, or false positive) and type II errors (β error, or a false negative) are two terms used to describe statistical errors.

Statistical error vs.


..... Read more.

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