Sensitivity, Specificity and Predictive Value
What They Are
Sensitivity and specificity are aspects of how well a test performs in determining whether a patient has a disease (or condition). When calculating sensitivity, you restrict your population (or denominator) to only the people who truly have the disease. For calculating specificity, you restrict your population (or denominator) to only the people who truly are disease-free.
Sensitivity is the proportion of those people who truly have the disease, who test positive. The table below provides the information to calculate sensitivity. The usual format has the actual disease status of the people in the columns, and the test result in the rows. If creating your own table, set it up so that patients who truly have disease are on the left and patients without disease are on the right. The row with positive test results goes above the row with negative test results.
Calculating Sensitivity
| Patient has disease | Disease is absent in the patient | Total | |
| Test: positive for disease | 2,250 | 375 | 2,625 |
| Test: negative for disease | 250 | 7,125 | 7,375 |
| Total | 2,500 | 7,500 | 10,000 |
When calculating sensitivity, use the column with orange numbers.
We restrict our population to patients who truly have disease, n=2,500 (the denominator).
- The number among these who test positive is 2,250 (the numerator).
Sensitivity = (# with disease who test positive) / (everyone who truly has the disease) = 2,250 / 2,500 = 0.9 (90%)
Specificity is the proportion of those people who are truly disease-free (the disease is absent), who test negative. The same table as above provides the information to calculate specificity, only now we use the column with purple numbers.
Calculating Specificity
| Patient has disease | Disease is absent in the patient | Total | |
| Test: positive for disease | 2,250 | 375 | 2,625 |
| Test: negative for disease | 250 | 7,125 | 7,375 |
| Total | 2,500 | 7,500 | 10,000 |
When calculating specificity, use the column with purple numbers.
We restrict our population to patients who are truly disease-free, n=7,500 (the denominator).
- The number among these who test negative is 7,125 (the numerator).
Specificity = (# of disease-free patients who test negative) / (everyone who is truly disease-free) = 7,125 / 7,500 = 0.95 (95%)
Positive and negative predictive value are two other aspects of how a test performs in determining whether a patient has a disease (or condition). It’s not enough to know sensitivity and specificity, because the clinical reality is that when a test is performed on a patient, it’s not known ahead of time whether they truly have disease or not. It’s possible (and not that uncommon) for a test to have a high sensitivity – it tests positive in almost everyone who truly has the disease – but which also tests positive in a lot of people who are disease-free. That wastes time and resources, may delay making the correct diagnosis, and causes unnecessary patient anxiety.
We use the same table as above to explain positive and negative predictive value. In other words, if a patient tests positive, how confident can we be that the patient really has the disease? If negative, that they don’t have it? For positive predictive value, we restrict our population to only those patients who have tested positive. In what percent of those patients do they truly have disease? We use the row with red numbers to answer that question.
Calculating Positive Predictive Value
| Patient has disease | Disease is absent in the patient | Total | |
| Test: positive for disease | 2,250 | 375 | 2,625 |
| Test: negative for disease | 250 | 7,125 | 7,375 |
| Total | 2,500 | 7,500 | 10,000 |
When calculating positive predictive value, use the row that has red numbers.
We restrict our population to patients who test positive, n=2,625 (the denominator).
- The number among these who truly have disease is 2,250 (the numerator).
Positive predictive value = (# testing positive who truly have disease) / (everyone who tests positive) = 2,250 / 2,625 = 0.86 (86%)
Finally, for negative predictive value, we use the row with blue numbers in the table below. We restrict our population to the patients who have tested negative.
Calculating Negative Predictive Value
| Patient has disease | Disease is absent in the patient | Total | |
| Test: positive for disease | 2,250 | 375 | 2,625 |
| Test: negative for disease | 250 | 7,125 | 7,375 |
| Total | 2,500 | 7,500 | 10,000 |
When calculating negative predictive value, use the row with blue numbers.
We restrict our population to patients who test negative, n=7,375 (the denominator).
- The number among these who are truly disease-free is 7,125 (the numerator).
Negative predictive value = (# testing negative who are truly disease-free) / (everyone who tests negative) = 7,125 / 7,375 = 0.97 (97%)
Disease Prevalence Affects Predictive Value
Be aware that for a given test, regardless of its sensitivity and specificity, the prevalence of the disease in the population who receive the test will affect the test’s predictive value, especially positive predictive value. The tables above involve a population where the disease prevalence is 25% (2,500/10,000). Suppose the disease prevalence was 2.5% (250/10,000)? See below.
| Patient has disease | Disease is absent in the patient | Total | |
| Test: positive for disease | 225 | 487.5 | 712.5 |
| Test: negative for disease | 25 | 9,262.5 | 9.287.5 |
| Total | 250 | 9,750 | 10,000 |
Positive predictive value is now 225 / 712.5 = 0.316 (31.6%), a large drop from 86% when disease prevalence was 25%, even though sensitivity and specificity are exactly the same (you can check this for yourself). [Ignore the “.5” number of individuals; obviously you don’t have “half a person” in a study. I had to allow for this in order to keep sensitivity and specificity the same.] What the heck happened? If you compare the two tables, you see that the number of patients who actually have disease and test positive has decreased dramatically, from 2,250 to 225. Meanwhile, the number of patients who are disease-free but test positive has increased somewhat, from 375 to 487.5. This is simply because there are so few patients who actually have the disease while there are lots and lots of patients who don’t have the disease.
Any time you read an article evaluating the diagnostic performance of a test, it’s important to note the prevalence of disease in the population involved in the study. This is also important when articles report that the negative predictive value of the test was very high (e.g., 99%). Sometimes a claim is made that “this test can rule out the disease.” Sure, if no one in your study has the disease, no one will test positive.
Also, pay attention to the number of patients in the study who actually had the disease. Sometimes the estimate obtained for sensitivity is unreliable because of the low number of patients who truly have the disease. Remember that all research studies give you an estimate of the truth, not the truth itself. For example, a study may involve 200 patients, with 40 who have the disease. The new diagnostic test is positive in 36 of them. The 95% confidence interval for this 90% (36/40) sensitivity is 76% – 97%. So be aware that in another group of patients the diagnostic test may not perform as well.
You might ask, “How do we know which patients actually had the disease?” Good question. In order to determine the sensitivity and specificity of a test, you need to compare it against a confirmatory method which is used in all patients in the study. Typically, this is a “gold standard” test that is known to be extremely accurate for diagnosing a disease.
Why They’re Important
In many clinical situations, the gold standard test isn’t practical to use on a regular basis. It may be too expensive or technically complex, put the patient at unacceptable risk, or some other reason. Or, perhaps the goal is to screen asymptomatic people. So more practical tests are developed which the investigators hope will be “good enough,” especially when considering other information about the patient’s clinical situation. Sensitivity, specificity and predictive value help to place that test’s performance on a scale from “useless” to “excellent.” In addition, these quantities can be used to compare a newer test to the current one.