Sensitivity is the ability of a test to correctly identify patients with a disease. Specificity is the ability of a test to correctly identify people without the disease.
Many outcomes can be characterized as either present or absent, nonwhite or white, male or female, better or unimproved. Of course, one of these two groups is frequently chosen as the focus of attention: presence in the presence and absence classification, nonwhite in the white and nonwhite classification, and so on. We can, in general, re-label the two outcome categories as positive (+) and negative (-). An outcome is positive if the primary category is observed and is negative if the other category is observed.
Use of proportions can be found in the evaluation of screening tests or diagnostic procedures. Following these procedures, clinical observations, or laboratory techniques, people are classified as healthy or as falling into one of a number of disease categories. Such tests are important in medicine and epidemiologic studies and may form the basis of early interventions.
In the given example two rows indicate the results of the test, positive or negative and two columns indicate the actual condition of the subjects, diseased or non-diseased. In box A there are all the true positives, i.e. subjects with the disease and positive test results. In box D there falls all the true negative, i.e. is subjects do not have the disease and the test agrees.
A good test will have minimal numbers in cells B and C. Cell B identifies people who don’t have an illness yet have a ‘disease’ result from the test. This is a case of false positives. The false negatives are in Cell C.
If these results are from a population-based study, prevalence can be calculated as follows:
Sensitivity: the ability of a test to correctly identify patients with a disease. It is the probability that a test will indicate ‘disease among those which the disease
It can be calculated by given formula with reference to the table:
Specificity: the ability of a test to correctly identify people without the disease. It is the fraction of those without disease who will have a negative result:
It can be calculated by given formula with reference to the table
Examples to make it more clear.
- Suppose a population of 1,000 people, of whom 100 have the disease and 900 do not have the disease. A screening test is used to identify the 100 people who have the disease. The result is shown in the table. Sensitivity and Specificity will be calculated from the formula we just saw above as:
Sensitivity: A/(A+C) x100
=80/(80+20)x100
=80%
Similarly ;
Specificity: D/(D+B)x100
=800/(800+100)x100
= 89%
Thus, the sensitivity of the test, which is defined as the proportion of diseased people who were correctly identified as “positive” by the test, or 80% and,
The specificity of the test, which is defined as the proportion of non-diseased people who are correctly identified as “negative” by the test, is therefore 89%.
Note that to calculate the sensitivity and specificity of a test, we must know who “really” has the disease and who does not from a source other than the test we are using. We are, in fact, comparing our test results with some “gold standard” an external source of “truth” regarding the disease status of each individual in the population.
Among the major references:
- BMJ
- INTRODUCTORY BIOSTATISTICS by Chap T.Le
- PennState University