3 ms·
We're in the realm of probability, which is mysterious sometimes even to people who have a math background. I didn't fully grok it until I studied intensely for
by nrr 2y ago
We're in the realm of probability, which is mysterious sometimes even to people who have a math background. I didn't fully grok it until I studied intensely for my first actuarial exams. (:
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.
- tptacek 2y agoI'm just saying, 90% true positive rate, 10% base rate, 1000 pts: * 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.
- nrr 2y agoI think you may be close but likely for the wrong reasons. I had to sit down with this for a moment to feel comfortable with it. 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?