Understanding sensitivity and specificity with the right side of the brain
Tze-Wey Loong Can you explain why a test with 95% sensitivity might identify only 1% of affected people in the general population? The visual approach in this article should make the reason clearer
Department of Community, Occupational, and Family Medicine, National University of Singapore, SingaporeTze-Wey Loong clinical teacher (part time) Correspondence to: T-W Loong, King George’s Medical Centre, Block 803 King George’s Avenue, [01-144, Singapore 200803, Singapore tzewey@ singnet.com.sg
I first encountered sensitivity and specificity in medical school. That is, I remember my eyes glazing over on being told that “sensitivity = TP/TP+FN, where TP is the number oftrue positives and FN is the number of false negatives.” As a doctor I continued to encounter sensitivity and specificity, and my bewilderment turned to frustration—these seemed such basic concepts; why were they so hard to grasp? Perhaps the left (logical) side of my brain was not up to the task of comprehending these ideas and needed some help from the right (visual) side. What follows are diagramsthat were useful to me in attempting to better visualise sensitivity, specificity, and their cousins positive predictive value and negative predictive value.
Fig 2 Hypothetical population
Sensitivity and specificity
I will be using four symbols in these diagrams (fig 1).
....is a well person ....is a person with a disease ....is a negative test result ....is a positive test resultand therefore.... ....is a well person who tests negative (a true negative) ....is a person with a disease who tests positive (a true positive) ....is a well person who tests positive (a false positive) ....is a person with a disease who tests negative (a false negative)
Fig 3 Results of diagnostic test on hypothetical population
Fig 1 Key to symbols
Sensitivity refers to how good a test isat correctly identifying people who have the disease. When calculating sensitivity we are therefore interested in only this group of people (fig 4). The test has correctly identified 24 out of the 30 people who have the
Let us start by looking at a hypothetical population (fig 2). The size of the population is 100 and the number of people with the disease is 30. The prevalence of the diseaseis therefore 30/100 = 30%. Now let us imagine applying a diagnostic test for the disease to this population and obtaining the results shown in figure 3. The test has correctly identified most, but not all of the people with the disease. It has also correctly labelled as disease free most, but not all, of the well people. Calculating sensitivity and specificity will allow us to quantify thesestatements.
Fig 4 Sensitivity of test
BMJ VOLUME 327
27 SEPTEMBER 2003
disease. Therefore the sensitivity of this test is 24/30 = 80%. Specificity, on the other hand, is concerned with how good the test is at correctly identifying people who are well (fig 5). The test has correctly identified 56 out of 70 well people. The specificity of this test istherefore 56/70 = 80%.
Fig 8 Positive predictive value
On the other hand, negative predictive value is concerned only with negative test results (fig 9). In our example, 56 out of 62 negative test results are correct, giving a negative predictive value of 56/62 = 90%.
Fig 5 Specificity of test
Having a high sensitivity is not necessarily a good thing, as we can see from figure 6. This test hasachieved a sensitivity of 100% by using the simple strategy of always producing a positive result. Its specificity, however, clearly could not be worse, and the test is useless. By contrast, Figure 7 shows the result a perfect test would give us.
Fig 9 Negative predictive value
The interesting thing about positive and negative predictive values is that they change if the prevalence of the...