The sensitivity of a test is the probability that the test is positive when given to a group of patients with the disease. Sensitivity is sometimes abbreviated Sn.
The formula for sensitivity is
Sn = TP / (TP + FN)
where TP and FN are the number of true positive and false negative results, respectively. You can think of sensitivity as 1- the false negative rate. Notice that the denominator for sensitivity is the number of patients who have the disease. Using conditional probabilities, we can also define sensitivity as
Sn = P [ Test is positive | Patient has the disease ]
The following table summarizes these calculations.
A large sensitivity means that a negative test can rule out the disease. David Sackett coined the acronym "SnNOut" to help us remember this.
Here is an example of a sensitivity calculation.
- In a study of 5,113 subjects checked for
gastric cancer by endoscopy (Gut 1999; 44: 693-697), serum
pepsinogen concentrations were also measured. A pepsinogen I concentration
of less than 70 ng/ml and a ratio of pepsinogen I to pepsinogen II of less
than 3 was considered a positive test. There were
13 patients with gastric cancer confirmed by endoscopy.
11 of these patients were positive on
the test. The sensitivity is 11/13 = 85%.