Understanding medical tests: sensitivity, specificity, predictive value (2018)
healthnewsreview.org
healthnewsreview.org
“Precision and recall” are positive predictive value and sensitivity, respectively.
i develop a test for disease X and give it to 1 billion walking around grocery stores in the whole world. it is 85% accurate. results are 200 million people are positive? how many of those people actually have disease X? do you have a guess?
disease X i was testing for was death. every single positive test was wrong. how close was your guess?
you must, at a minimum, know test accuracy _as well as_ disease prevalence to form a statistical guess. death is prevalent in 0% of alive people, so test accuracy is worthless.
Here's the flaw in your proof - If the test has 85% specificity, then the chance of 200 million positives is essentially 0% (you'd get ~150 million if no one really has the disease). Getting a result of 200 million positive means either you DO have a significant number of true positives (50 million), or your 85% number for specificity was wrong.
(Yes, adding the disease prevalence % is essentially bayesian, but testing everybody isn't)
Even better than knowing the disease prevalence is knowing possible proxies (again, Bayesian).
Your Covid-19 test might have a low sensitivity but if the person has a temperature and other symptoms you might want to redo the test later even if it comes out negative.