To perform a diagnostic test we take body samples and measure the presence and quantity of a specific substance. We then compare that value to standardized ranges to help rule in or rule out the presence of pathology. One way we do this is by calculating sensitivity.
A diagnostic test is accurate when:
- it has identified the presence of a diagnostic marker in sufficient quantities in a patient who truly has the pathology associated with that marker.
- it fails to detect the presence of diagnostic marker in a patient where the pathology is truly absent.
This does not happen every time. Most diagnostic tests are not 100 percent accurate.
Sometimes, the test will detect the presence of diagnostic markers in patients that do not the associated pathology. Sometimes it can fail to detect in patients who truly have the pathology.
Detecting Presence
Sensitivity detects presence. It focuses on the part of the population that truly has the diagnostic marker.
The expected proportion of times a diagnostic test will positively detect a diagnostic marker, in sufficient quantities, in a patient who truly has a disease is known as its sensitivity.
The higher the sensitivity, the more likely a test will identify true patients with diagnostic markers for disease.
Because sensitivity indicates a high ability to detect presence of a diagnostic marker, this also means that if it detects nothing, it is very likely that the diagnostic marker is truly not present. Test with high sensitivity are therefore useful for ruling OUT disease.
.
Detection Dogs
Tests with high sensitivity are like police detection dogs. They are trained to be very sensitive to scents. They help to sniff out explosives, illegal drugs, criminals etc. and will alert their handler when they detect a specific scent (true positive).
If the target scent is not there, they will not alert the handler (true negative).
Detection dogs, like diagnostic tests, don’t always get it right. They have a hard time distinguishing contamination or residual scent from the desired target. They maybe be influenced or distracted by what is going on around them. So there is the potential for false-positives (they alert when there is nothing there) and also false-negatives (they fail to alert when the target is there).
Sensitivity is the medical detection dog.
These tests are very good at sniffing out the presence diagnostic markers. No alert (negative test result) can reliably rule out the presence of a diagnostic marker.
If they detect nothing, there is a high probability there is nothing there.
Subscribe for Access to Exclusive Content
4 Sensitivity Outcomes
True Positive: alert + disease present
This is one of our two diagnostic ideals.
This is the proportion we are trying to figure out when we calculate sensitivity.
However much like our detection dogs there are things that can influence the ability to detect.
False Negative: no alert + disease present
This would be a missed diagnosis.
This is where those distractions and residuals that can affect our medical detection dog come into play.
The marker is there but the dog missed it.
False Positive: alert + no disease
Our medical detection dog (sensitivity) is very unlikely to smell something that is not there but it is possible.
True Negative: no alert + no disease
No scent, no alert.
This is our second diagnositic ideal.
Sensitivity Calculation
Sensitivity calculations are descriptive of the test, not the diagnosis. When we calculate sensitivity we only include the values where the marker is actually present. Sensitivity focuses on those patient we truly have the disease regardless of detection by the test, This would include both true-positives and false-negatives.
The sum of true positives and false negatives is the number of patients who truly have the disease regardless of detection by the test. This is the population we are concerned about when we calculate sensitivity of a test.
We calculate sensitivity by dividing the number of diagnostic markers detected by the total number of markers present.
Using our detection dog analogy, we divide the number of times our dog accurately alerts to the total number of times he should have alerted.
Sensitivity Grid
We can lay out our values on a grid to calculate sensitivity.
Calculating sensitivity centers on true positive and true negative values i.e. those patients who truly have the disease (see equation above).
Sensitivity in 3 Steps
- Determine the total number of patients tested with presence of diagnostic marker/disease (true positives + false negatives)
- Determine how many of those patients had a positive test result
- Divide the number of positive results (2) by the total presence population (1)
Calculations
Sensitivity is a fundamental calculation that can be further applied to more complicated calculations like positive predictive value and positive likelihood ratio.
Calculating sensitivity is also commonly grouped together with specificity. I have opted to separate the two so that we can understand each value individually.
Books on statistics that I’ve found helpful:
If you’ve found this unit helpful I would love to hear from you! Leave a question or comment below.
Subscribe
Subscribe to get the latest study unit in your inbox.
The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.
2 thoughts on “Statistics: How to Calculate Sensitivity”