Sensitivity and specificity are two statistical measures of test performance. The origins of these measures comes (unsurprisingly) from screening tests for diseases whereby the purpose of the test is to differentiate between those who do and do not have the disease (so that appropriate diagnosis and treatment can occur).
The key thing here is to acknowledge that tests are rarely 100% accurate… but the purpose of Sensitivity and Specificity is to identify how accurate tests are in their discrimination between diseased and non-diseased individuals.
Definition – Sensitivity
- Sensitivity identifies the proportion of individuals who truly DO have the disease AND are given a positive test result
- I find it helpful to remember: sensiTivity = sensitive to the Truth (i.e. do have disease + do have positive result)
Formulae – Sensitivity
We want to know what proportion of individuals who have the disease (a+c) were given a positive test result (a), therefore…
- Sensitivity = a / (a+c)
Definition – Specificity
- Specificity identifies the proportion of individuals who truly DO NOT have the disease AND were given the correct negative test result
- I find it helpful to remember: specificity = speciFies the False (i.e. do not have disease and do not have positive test result
Formulae – Specificity
This time we want to know what proportion of people who do not have the disease (b+d) were given the correct negative test result (d), therefore…
- Specificity = d / (b+d)
Interpretation – So what does it mean…?
Calculating sensitivity and specificity help to understand how accurate the tests are at providing the correct result. This is really important information for understanding how much harm individuals could be subjected to through taking the test.
For example, in screening harm can be receiving a false positive (b – you get a positive test result, but you don’t have the disease) or a false negative (c – you have a negative test result, but unknowingly you do have the disease)… these psychological implications for the individual should never be taken lightly, and therefore it is important to minimise such harms by a) explaining the potential risks to all participating individuals and b) using tests which are as accurate as possible
Ideally a test would be 100% sensitive and specific. Yet in reality, there is usually a trade-ff between the two properties. The cut-off point (or ‘criterion for positivity’) depends on the consequences of missing positives and falsely classifying negatives. For example
Sensitivity is often prioritised when…
- Disease is serious (we want to identify as many true cases as possible)
- Treatment is effective + available (we want to identify + treat as many cases as possible)
- High risk of infectivity if individuals are not treated (we want to minimise harm to others)
- Subsequent test is cheap and low-risk
Specificity is often prioritised when…
- Treatment is unpalatable (we only want to treat those we are confident have the disease and would benefit from the treatment)
- Subsequent test is expensive and risky
So sensitivity and specificity is all about how accurate is the test at discriminating those who are healthy from those with the disease.