Re:Half of women will get a false positive 3D mammogram, stu...
by dragonwriter on Friday March 25, 2022 @05:15PM
(#30807122)
> Let's say there is a terrible disease that 0.01% (1 in 10,000) of the population is infected with, and we develop a test that is 99% accurate. You go to the doctor and get a test. Oh no, it's positive. What are the chances that it's a false positive?
The correct answer is that the question doesn't give enough information to know.
I mean, a test that always said no would be 99.99% accurate. A mere 99% accuracy could be no false negatives and 0.99% of all tests false positives, in which case the answer is that a positive result is 1% likely to be correct, and 99% likely to be a false positive. Or it could be, on the other extreme, 0.01% false negative and 0.98% of all tests false positives, in which case the chance that a positive result represents an actual case would be 0%.
Presumably, though, approval processes for medical tests will constrain the actual distribution of results to be such that, a patient with positive result is not more likely to be clear of the condition than one with a negative result, so it won't be as bad as the latter extreme, but it's worth noting that your assumption (essentially that the false/true ratio is equal for negative and positive results) is not certain at all.
The correct answer is that the question doesn't give enough information to know.
I mean, a test that always said no would be 99.99% accurate. A mere 99% accuracy could be no false negatives and 0.99% of all tests false positives, in which case the answer is that a positive result is 1% likely to be correct, and 99% likely to be a false positive. Or it could be, on the other extreme, 0.01% false negative and 0.98% of all tests false positives, in which case the chance that a positive result represents an actual case would be 0%.
Presumably, though, approval processes for medical tests will constrain the actual distribution of results to be such that, a patient with positive result is not more likely to be clear of the condition than one with a negative result, so it won't be as bad as the latter extreme, but it's worth noting that your assumption (essentially that the false/true ratio is equal for negative and positive results) is not certain at all.