Probability of a correct result based on specificity, sensitivity and background rate.
Try it here:-
https://op12no2.github.io/ss-testing
Testing Demonstration
Use the sliders to set up scenarios.
Background rate: An estimate of the fraction of true positives in the population being tested.
Sensitivity: The probability of a correct positive result,
as defined by the manufacturer of the test.
Specificity: The probability of a correct negative result,
as defined by the manufacturer of the test.
Top left: True positive.
Bottom left: False negatives.
Top right: True negatives.
Bottom right: False positives.
When the background rate is low, specificity must be high to avoid false positives.
When the background rate is high, sensitivity must be high to avoid false negatives.
So for example if you were screening (effectively a random sample) nation-wide for virus
antibodies and very few
of the population were true positives, you would need near perfect specificity for personally
meaningful results, not dominated by false positives. Screening with a lower
specificity can be useful to see trends however.
If you were testing those that presented with symptoms, then by implication the background
rate would be much higher and specificity could be lower without the results being
biased towards false positives.
If you were testing NHS staff with symptoms and it was thought that the background rate
was probably quite high, then false negatives would become a problem unless sensitivity was
very high.