Sensitivity and specificity

Let’s say a new screening test is developed to figure out if people have diabetes before they start showing symptoms. Before using the test, we have to make sure that the test works - in other words, can the test correctly identify if a person has diabetes or not? This is the test’s validity, and it has two components - sensitivity and specificity.

A test with high sensitivity will correctly identify most people who have the condition, and a test with high specificity will correctly identify most people who don’t have the disease.

So let’s say that we recruit a 1000 people - 100 people who have diabetes and 900 people who don’t to put our diabetes test to the test!

We can organize the results using a 2 by 2 table, where the true disease status, positive or negative, of the individual is on the top of the box and the results of the screening test, positive or negative, are on the side, and each of the cells is labeled a, b, c, or d. In this situation, a positive test indicates that a person has diabetes.

So let’s look at this table closer, a person who gets a positive test result and has positive disease status, so has diabetes, is called a true positive.

A person who gets a negative test result and a negative disease status, so doesn’t have diabetes, would be a true negative.

A person who gets a positive test result even though they don’t have diabetes, would be a false positive.

And lastly a person who gets a negative test result even though they have diabetes, would be a false negative.

To calculate sensitivity, we divide the number of true positives by the total number of people who have diabetes - so cell a divided by the sum of cell a and cell c.

A test with perfect sensitivity would have 100 true positives in cell a, because the test would correctly identify everyone who has diabetes, and zero false negatives in cell c.

To calculate specificity, we divide the number of true negatives by the total number of people who do not have diabetes - so cell d divided by the sum of cell d and cell b.

A test with perfect specificity would have 900 true negatives in cell d, because the test would correctly identify everyone who doesn’t have diabetes, and zero false positives, in cell b.

But no test is 100% perfect, so let’s say that cell a contains 80 true positives, cell b contains 100 false positives, cell c contains 20 false negatives, and cell d contains 800 true negatives.