Sensitivity (tests)

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Sensitivity 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.

Contents

[edit] 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
= 0.1
= 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

[edit] 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 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).

[edit] 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:

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. A sensitive test will have fewer Type II errors.

[edit] See also

[edit] External link

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