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Sensitivity vs specificity
Sensitivity is the proportion of people with a condition whom a test correctly identifies as positive. Specificity is the proportion of people without it whom the test correctly identifies as negative. A highly sensitive test misses few cases; a highly specific test raises few false alarms. Both describe the test itself.
Every screening and diagnostic poster leans on these two numbers, and they are easy to swap. A worked table fixes them, and shows why a test with impressive figures can still be wrong most of the times it says yes.
Nuwan Madhusanka · Co-founder
4 min read · Published
| Condition present | Condition absent | Total | |
|---|---|---|---|
| Test positive | 90 (true positives) | 45 (false positives) | 135 |
| Test negative | 10 (false negatives) | 855 (true negatives) | 865 |
| Total | 100 | 900 | 1,000 |
| Derived | Sensitivity 90 of 100 = 90% | Specificity 855 of 900 = 95% | PPV 90 of 135 = 66.7%; NPV 855 of 865 = 98.8% |
The two formulas
Sensitivity is true positives divided by everyone who has the condition: 90 divided by 100, or 90 percent, in the table. Specificity is true negatives divided by everyone who does not have it: 855 divided by 900, or 95 percent. Each is read down a column of the 2x2 table, which is why they do not depend on how common the condition is. A useful memory aid is that a highly sensitive test, when negative, helps rule a condition out, and a highly specific test, when positive, helps rule it in.
Why predictive values tell a different story
A patient wants to know whether a positive result means they have the condition. That is the positive predictive value, read across the row: 90 of the 135 positives, or 66.7 percent. One in three positives is false, even with a test that is 95 percent specific, because the 5 percent of 900 healthy people outnumber the misses among 100 sick ones. Predictive values depend on prevalence, so the same test performs very differently in a specialist clinic and in population screening, a point both review articles in the sources make at length.
The trade off
Most tests give a number, and a cut off decides positive or negative. Lowering the cut off catches more cases, raising sensitivity, but flags more healthy people, lowering specificity. A receiver operating characteristic curve plots that trade off across cut offs. Screening tests usually favour sensitivity, then confirm positives with a more specific test, so that few cases are missed and few people are treated on a false alarm.
Reporting it on a poster
Give the 2x2 table, the reference standard the test was compared against, both measures with 95 percent confidence intervals, the prevalence in the study sample and the predictive values at that prevalence. Readers also need to know who was tested, since a test studied only in very sick and clearly healthy people will look better than it is. Reporting checklists for diagnostic accuracy studies ask for exactly these items.
Showing it on a poster board
The 2x2 table needs a board with a table slot, and only three of the 40 poster boards carry one, so choose the board first. Stat blocks, on 26 boards, suit the headline sensitivity and specificity with their intervals in the line beneath, and the chart figures offer ten kinds, such as vertical bars, for comparing the test against an existing one. The generator fills numbers only from your brief, so give every count.
Questions people ask
Can a test be both highly sensitive and highly specific?
Yes, some tests reach high values on both, but for most tests that use a cut off on a continuous measurement, improving one costs some of the other. The best cut off depends on the cost of each error: missing a serious treatable disease usually matters more than an extra confirmatory test.
What is a false negative rate?
The proportion of people with the condition whom the test calls negative, which is one minus sensitivity. In the worked table it is 10 of 100, or 10 percent. The false positive rate is one minus specificity, 45 of 900, or 5 percent. Reporting the rates instead of the percentages correct sometimes makes the consequences clearer.
Why do sensitivity and specificity need confidence intervals?
Because they are estimates from a sample. A sensitivity of 90 percent from 100 cases is far less certain than the same figure from 1,000. The interval shows how precisely the study pinned it down, and wide intervals are common in small diagnostic studies, which is easy to miss if only the point estimate is reported.
Does prevalence change sensitivity?
In principle no, because sensitivity is calculated only among people who have the condition. In practice the spectrum of disease matters: a test may detect advanced cases better than early ones, so a population with milder disease can show lower sensitivity. Predictive values, by contrast, change directly with prevalence.
What is the likelihood ratio?
A way of combining sensitivity and specificity into one number for a test result. The positive likelihood ratio is sensitivity divided by one minus specificity, which is 0.90 divided by 0.05, or 18, in the worked table. It says how much a positive result raises the odds of having the condition, whatever the starting prevalence.
Make one with posters
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Create a poster with OneCraftRelated questions
- What is a p value?What is a p value: how incompatible data are with a null model, not the chance a finding is true. What 0.05 means and how to report one on a poster.
- How to show a confidence interval on a chartHow to show a confidence interval on a chart: error bars, what SD, SE and CI bars mean, the overlap rules of eye, and what to do when a chart has no error bars.
- What is number needed to treat (NNT)?What is number needed to treat (NNT): how many people need a treatment for one more to benefit. The formula from absolute risk reduction and a worked trial.
- What is a chi-square test?What is a chi-square test: a test of association between two categorical variables using observed and expected counts. A worked 2x2 example and assumptions.
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