Sensitivity and specificity

• The sensitivity of a test, in statistics, measures the ability of a test to give a positive result if the hypothesis is true.


• The specificity of a test, in statistics, measures the ability of a test to give a negative result when the hypothesis is not verified.

Tableau 1

	Sick	Not Sick
Positive test	VP	FP
Negative test	FN	VN

 

Table 1 shows the possible results when measuring the intrinsic validity of a test. In this table, we observe that:

• VP (true positives) represents the number of sick individuals with a positive test,


• FP (false positives) represents the number of non-sick individuals with a positive test,


• FN (false negatives) represents the number of sick individuals with a negative test,


• VN (true negatives) represents the number of non-sick individuals with a negative test.

 

Sensitivity, or the likelihood of a positive test if disease is present, is measured in patients only. It is given by:

A measure of sensitivity is always accompanied by a measure of specificity. The latter is measured in non-patients only. Thus, the specificity, or the probability of obtaining a negative test in non-patients, is given by:



The sensitivity and specificity of a test provide an appreciation of its intrinsic validity. Taken separately, they mean nothing. We will add that a very sensitive test (close to 100%) is of no interest if its specificity is very low.

Predictive value

• Positive predictive value is the likelihood that the disease is present when the test is positive.


• Negative predictive value is the likelihood that the disease is not present when the test is negative.

In Table 1, the positive predictive value is:



The negative predictive value is:


The concept of predictive validity is very important since in a clinical situation, it is the result of the test that is available and it is from this that the doctor must assess whether the disease is present or not.

The predictive values ​​depend on the prevalence of the disease in the population.
Thus, for the same sensitivity and specificity, the negative predictive value of a given test will improve as the disease is rare (not very prevalent) and the positive predictive value of the same test will improve as the disease is frequent.

When a test has a good positive predictive value, it is especially when the result is positive that it is reliable.
Likewise, a test with a good negative predictive value is reliable when its result is negative. For example, a test with a good negative predictive value and a bad positive predictive value gives valid information if it is negative but is difficult to interpret if its result is positive (For example negative D-dimers and absence of thrombosis, few values ​​so positive because frequent elevations of inflammatory syndromes).