I suspect the test would be high sensitivity very low specificity in the general population, but that is an intuition not backed by any data.
Thanks for clarifying.
This kind of thing is almost always a weighted coin toss: with sensitivity or specificity alone, you only have two possible outcomes (present/relevant, absent/irrelevant), and the thing that changes is the probability distribution of those outcomes.
Combining the two gets you the full four: present and relevant; present and irrelevant; absent and relevant; and absent and irrelevant. Taking the uniform distribution, they're all 25% likely, but the idea is to find a probability distribution that makes the "present and relevant" and "absent and relevant" outcomes more likely.
Since I myself don't work in a clinical setting, I simply hadn't considered that the clinician would want to exercise discretion in pre-screening for specificity before ordering the test in order to get there. Oops.
* 100 true positives
* 100 false positives (100-90=10% of 1000)
That's still just a 10% false positive rate across the population, but if you get a positive test, it's only 50/50 correct.
Did I do this wrong? I'm assuming I did this wrong.
If we take your 10% base rate to be disease prevalence, that gives us 100 sick and 900 well.
Of the 100 sick, something with 90% sensitivity should get me 90 true positive tests and 10 false negative tests.
Of the 900 well, I should expect to see for a test with 90% specificity, what, 80 false positives and 810 true negatives? if I did my arithmetic right?