Oh Dear Sonny
I could have warned you against this
the predictable flood of "whaaaaa?" 'answers' wind out like a motorway to oblivion in front of you.
actually from your post it is reasonable assume that the false neg rate is zero cos you didnt mention it and on your figures then
of a 1 000 tested, 100 have the disease, another one percent dont have the disease but test positive which is 90,
so of the 190 who have tested positive, 100 have it so the PPV is around one half ( if you have a positive test the chance of having the disease is around 1/2 )
so yup your point is that in a screening test
you need to know the PPV - positive predictive value
pt well made and not understood by the huddled masses who should be out at work or feeding the cats
why not get the cat fur flying by asking if breast screening works?
PPV of mammography is pretty crap in fact
or get into PSA tests - these return a value on a continuum, and there is a cut off value. Obviously set it too low and you will flood the surgeries with worried well, and set it too high and men with the disease will croak when you reassure them they are cancer free.
You need rocks to get over that one ( ROCs - receiver operating curves, and that is really taxing )
honestly if you asked, I would have told you not to do this !