Recently I received an email seeking guidance on calculating sensitivity of a screening test. I suspect the poser was confused by the question, as it was ambiguous in some aspects.
Nevertheless, the question and my answer are provided below.
Q: In a screening test done on 1000 people 90 were found to be positive and on using gold standard test out of 1000, 100 were found positive, what is the sensitivity of the screening test?
A: Sensitivity refers to the ability of a screening test to correctly identify those who actually (truly) have the disease.
Screening tests are always compared with a gold standard test (the best possible test available at the time, not necessarily a perfect test). The results of the gold standard test are assumed to be absolutely correct. Results of a screening test are compared with the gold standard to determine the usefulness (validity) of the screening test. This means that each person must be subjected to both tests- gold standard test; and the screening test.
When both screening test and gold standard test agree that a person is positive for the condition, the screening test result is termed ‘True Positive’, and entered in cell ‘a’.
When both screening test and gold standard test agree that a person is negative for the condition, the screening test result is termed ‘True Negative’, and entered in cell ‘d’.
When the screening test result claims the person has the condition under study (screening test result is positive), but in reality the person doesn’t have the condition (disease status is negative), the screening test result is termed ‘False Positive’, and entered in cell ‘b’.
When the screening test result claims the person does not have the condition under study (screening test result is negative), but in reality the person has the condition (disease status is positive), the screening test result is termed ‘False Negative’, and entered in cell ‘c’.
In a 2*2 contingency table, values may be entered as follows:
In the given problem, the total number of people with disease (positive on the gold standard test) is 100. Typically, all those positive on the screening test would not be True Positive. However, in this case, since no other information is provided, one has to assume that the number 90 refers to True Positive persons.
Sensitivity tries to answer the question, ‘Out of all those having the disease/ condition, how many did the screening test correctly identify as having disease/ condition?’. It is given by the formula:
Sensitivity = (True Positive/ Total diseased )* 100 (%)
Substituting, we have:
Sensitivity = (a/(a+c))*100 (%)
Sensitivity = (90/100)*100 (%) = 90%
This is interpreted as: ‘The screening test correctly identifies 90% of those who have the disease’.
Note: For any combination of screening test and Gold standard test, sensitivity is fixed. For example, if the sensitivity of Widal test to detect typhoid (compared to blood culture) is 70% (say), then the sensitivity will remain 70% regardless of the location/ population Widal test is applied in.
Therefore, the sensitivity will not change if the prevalence of typhoid varies, or the geographical setting in which the test is administered varies (India versus Bangladesh, for instance).