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Fundamentally you're trying to combine two accuracy figures (one for getting it right with a positive outcome and one for getting it right with a negative outcome) into a single accuracy figure for the test. You can only do this if you know the prevalence population wide.
If you don't look at it population wide then you can't combine the two accuracy figures (sensitivity and specificity) into a single "accuracy" figure.
Which is why you have a test/sample group. That's the population for which you know the number of false positives, false negatives, true positives, and true negatives. That's the population from which the accuracy of a test can be calculated.
Extrapolation to the world becomes more complicated. The prevalence in the population will impact raw results. But the accuracy at an individual level will remain the same (within reason/whatever p value).
As far as I understand! Not a doctor! Etc!
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Which is why you have a test/sample group. That's the population for which you know the number of false positives, false negatives, true positives, and true negatives. That's the population from which the accuracy of a test can be calculated.
OK, so if you have 10,000 people and you know exactly 500 of them are positive. That's 5%. So 95% are negative.
Nopw imagine you have a test that where sensitivity and specificity are 95%.
When you test the 9500 people who are negative how many -ves and how many +ves do you expect to get?
When you test the 500 people who are positive how many +ves and how many -ves do you expect to get?
What is the accuracy for those who were negative?
What is the accuracy for those who were positive?What is the accuracy for those that received a negative result?
What is the accuracy for those that received a positive result?
What is the accuracy of the test?(Bonus question: Why are none of the last 3 answers 95%?)
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But the accuracy at an individual level will remain the same
The "accuracy" of the test remains the same but the accuracy of the result depends on your likelihood of having the thing in the first place.
This is because there are really 4 results: positive, false positive, negative, false negative. The proportion of positives that are false becomes relatively more or less important when compared with the proportion of results that are true positives.
If I, a biological male, take a pregnancy test with a 5% false positive rate, that doesn't mean that my chances of actually being pregnant are 5% - they are in effect 0% and all positives results are false positives. But the test is still correct 95% of the time.
Edit: I don't think my comment is going to help you, I'm just restating what you've already said.
Greenbank
frankenbike
If you have a test that has a specificity of one value (97%) and a sensitivity of another value (98%) then it will have a different accuracy if you give it all expected positive test inputs than if you give it all expected negative test inputs. Therefore the accuracy of a test depends on the prevalence of the disease in the population.
This page may help explain it: https://www.medcalc.org/calc/diagnostic_test.php
That page goes further and does 95% confidence intervals.
Fundamentally you're trying to combine two accuracy figures (one for getting it right with a positive outcome and one for getting it right with a negative outcome) into a single accuracy figure for the test. You can only do this if you know the prevalence population wide.
If you don't look at it population wide then you can't combine the two accuracy figures (sensitivity and specificity) into a single "accuracy" figure.