I'm trying to work out out that if, for example, you were doing a test, and the chances of the test returning a false positive or false negative were worked out to be a specific percentage, say 20%, can that number then just simply be applied to the overall number of you did 1000 tests, or is it more advanced with that when probability comes into play?
For example, consider when they do seroprevalence tests for a virus in the community, such as Sars-Cov-2.
If the prevalence in the community is 5% and the tests we are using have a:
- Positive predictive value (PPV) for sensitivity = 90%, specificity = 99%
- Negative predictive value (NPV) for sensitivity = 90%, specificity = 99%
With the above parameters this means that:
- The chance of a false positive is: 17.43%
- The chance of a false negative is: 0.53%
I am generating this data here.
Now does that mean we can take this probability and use it as a whole as well? As in, if we test 1000 people, assuming the prevalence remains at 5%, and not accounting for false outcomes, let's say we get 50 positives and 950 negatives.
So does that mean we can easily calculate the expected number of false positives and negatives by simply using the expected rates above?
50 * 0.1743= 8.715 false positives980 * 0.0053= 5.194 false negatives