Sensitivity and Specificity

Sensitivity and specificity are measures of how good a medical test, sign, or symptom is. The terms are easily confused, but refer to very different things. In this article, the word "test" will be used to include several kinds of information that help a doctor make a decision, including blood tests, X-rays, and other medical tests; signs, such as Hutchinson's sign for herpes zoster; or symptoms, such as pain in a particular pattern.

No medical test is perfect, but many of a test's attributes can be measured so that the best possible test can be chosen for a given question. Besides sensitivity and specificity, other attributes of tests used in clinical medicine include its predictive value and its accuracy.^[1]

Terminology

A positive test result means the test says the disease is present. For example, a patient's x-ray appears to show lung cancer. A true-positive test result means not only that the test says the disease is present, but that the disease really is present. The patient's symptoms, medical history, and biopsy results prove he has cancer. The x-ray was a true positive.

A negative test result means the test says the disease is not present. For example, a patient checks her blood pressure at the drugstore and it reads in the normal range, telling her she does not have hypertension (high blood pressure). A true-negative test result means not only that the test says the disease is absent, but that the disease really is absent. The patient wears a 24-hour blood pressure monitor and it does not pick up a high blood pressure, nor does her doctor when he checks her blood pressure repeatedly over the years. The patient does not have hypertension, and the drugstore test result was a true negative.

False positives and false negatives

No medical test is perfect. Sometimes test results can be positive in people who don't have the disease, a phenomenon called a false positive. Other times, they can be negative in people who in fact do have the disease—a false negative. So it is important to know how helpful a test is when deciding how to interpret its results.

Ideally, one would like a test to be both very sensitive (it picks up almost all true positives) and very specific (it has almost no false negatives).

Sensitivity

The sensitivity of a test refers to how many cases of a disease a particular test can find. A very sensitive test is likely to give a fair number of false-positive results, but almost no true positives will be missed. A numerical value can be calculated for a test's sensitivity that represents the probability of it returning a "true" value for samples (i.e., patients) from the population of interest (i.e., samples from patients who do in fact have the disease in question); this is often described as a test's "positivity in disease."

Numerically, sensitivity is the number of true positive results (TP) divided by the sum of true positive and false negative (FN) results, i.e., sensitivity = TP/(TP + FN).

Specificity

The specificity of a test refers to how accurately it diagnoses a particular disease without giving false-positive results. For example, the Western blot test is very specific for HIV—if the test shows HIV, then HIV is very likely to be present in the person being tested (true positive), and the result is not likely to be due to some error in the test. A numerical value can be calculated for a test's specificity that represents the probability of it returning a "false" value for samples (i.e., patients) from the population of interest (i.e., samples from patients who are in fact healthy); this is often described as a test's "negativity in health."

Numerically, specificity is the number of true negative results (TN) divided by the sum of true negative and false positive (FP) results, i.e., specificity = TN/(TN + FP).

Why Highly Sensitive Tests Are Important

Tests with a high sensitivity are often used to screen for disease. Screening tests tend to cast a wide net in order to pick up all cases of a disease and not miss anyone, but they often include some accidental positive results in people who don't actually have the disease.

Why Highly Specific Tests Are Important

Tests with a high specificity are used to confirm the results of sensitive, but less specific screening tests. People who came up positive on a very sensitive screening test may come up negative on a specific confirmatory test, which means the doctor can reassure them they do not actually have the disease.

For example, if 100 people were to be tested for HIV, one would start by testing them with ELISA, a test that is very sensitive (picks up almost all cases) but not very specific (may show HIV even in some people who don't have the virus—a false-positive result). Then, all the people who had positive ELISA tests would be retested with a Western blot, which is so specific that it would almost never falsely show HIV. The people with false-positive results could then be reassured that they almost certainly do not have HIV, because the very specific Western blot can accurately tell the difference.

Tests can be very specific without being sensitive, which is why it is important to take both factors into consideration. For example, if one were to screen 100 at-risk people for HIV with a Western blot, everyone who tested positive would be a true positive, but some people who actually had HIV would test negative—their disease would be missed, a false-negative test result.

Tests Need to Be Both Sensitive and Specific

A test that is completely sensitive without being specific isn't helpful, and neither is a test that is specific but not sensitive.

For instance, suppose a doctor is considering using a new test to measure hematocrit, the percentage of blood volume that is taken up by red blood cells. The normal value of hematocrit is about 46% in men and about 38% in women. If the hematocrit is too low, that means the person has anemia.

Too sensitive

Suppose the XYZ Company has devised a test for anemia that they say is 100% sensitive. Every single person with anemia will be found with this test. The test is such that, if the person's hematocrit is under 40%, the test labels them as anemic.

It is true that this test will detect everyone who truly is anemia. People with an anemic - range hematocrit of 25% will be picked up, since they fall below 40%. But many, many people with normal hematocrits will be lumped in with the anemic people, because the cutoff value is so high that it includes many normal values (38%–40%). Obviously this test won't be of much help, because although it finds everyone who's anemic —it is 100% sensitive—it finds a lot of people who aren't, too. There are too many false positives. Not all those folks need treatment.

Too specific

Let's say that a competing company, the ABC Company, then devises a test for anemia that they advertise is 100% specific. In this test, there won't be any false positives. The test labels everyone with a hematocrit of 5% or below with anemia. If the person tests positive in ABC's test, unlike with XYZ's, a doctor can be absolutely certain they are anemia.

Unfortunately, that cutoff is so low that it will miss many people with milder degrees of anemia. In fact, it won't pick up many cases at all, since people with hematocrits of 5% are extremely rare—that level is so anemia that they would be near death. People with the dangerously low hematocrit of 10% will not be picked up with this test. It may be 100% specific, but it's also essentially useless.

An ideal combination

Tests, then, should be both sensitive and specific as much as possible. Neither one is less important than the other.

References

1. ↑ Simon D, Boring III JR. Sensitivity, Specificity, and Predictive Value. In: Clinical Methods: The History, Physical, and Laboratory Examinations, Walker HK, Hall WD, Hurst JW, eds. Butterworths, 3rd edition, 1990. Full Text