-
Absolutely. Agree with all of that.
But the part I'm trying to decipher follows from this: The accuracy of a pregnancy test does not change depending on how many women are currently pregnant.
What does change is the raw number of positive and negative results due to there being more people who can get false negatives. But any given man or woman will still have the same likelihood of getting a particular result.
-
The accuracy of a pregnancy test does not change depending on how many women are currently pregnant.
It does if you compare the results of the test applied over a population with the actual number of results in that population, which is how you would define the accuracy of the results generally. The accuracy being referred to is, by definition, the accuracy of the results from a set group of people, not merely an individual. Because without referring to a group, you can't work out the actual probability of you being positive to whatever's being tested.
-
I can save you the hassle of doing the maths:-
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?
With a 95% specificity (true negatives). You'd expect 9500 * 0.95 = 9025 to truly test negative. You'd also expect 500 * 0.95 = 475 to falsely test positive.
When you test the 500 people who are positive how many +ves and how many -ves do you expect to get?
-ve is 500 people * 0.05 (false negatives) = 25 people who are positive to incorrectly test negative
+ve is 500 people * 0.95 (true positives) = 475 people who are positive to correctly test positiveWhat is the accuracy for those who
wereare negative? (Fixed the wording slightly.)Simple one this. 95% of the people who are negative tested negative. So the accuracy for the people who are known to be negative is 95%.
What is the accuracy for those who
wereare positive?Likewise 95% of the people who are positive tested positive. So the accuracy for the people who are known to be positive is 95%.
What is the accuracy for those that received a negative result?
9025 people who are negative correctly tested negative.
25 people who are positive tested negative (false negatives)So 9025/9050 who got a negative result got the correct result = 99.72% (2dp) for them
What is the accuracy for those that received a positive result?
475 people who are positive correctly tested positive
475 people who are negative tested positive (false positives)So 475/950 who got a positive result got the correct result = 50% accuracy for them
What is the accuracy of the test?
If you measure it as how many people got the right result, it's 95%.
But, as I've shown, that doesn't mean that 95% of positive results are correct, so saying a positive result is 95% accurate is false. Only 50% of positive results are likely to be correct, but because there are many (19 in this case) times as many negative results that individual low accuracy gets drowned out in a single overall 'accuracy' stat.
(Nowhere did I give a single figure for the accuracy of a test, only the accuracy of a test result of a specific outcome.)
-
If I am understanding you correctly, I think the reason it works out is that we're talking about probabilities/proportions, which will always sum to 1. By adjusting the true incidence rate you simply just move the proportioning of false positives/negatives around leaving the same overall 95% accuracy figure.
Brommers
Greenbank
frankenbike
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.