I'm not good at this (yet), but my understanding is that your prior for just this test would be the likelihood of having Alzheimer's based on the statistical oc

I'm not good at this (yet), but my understanding is that your prior for just this test would be the likelihood of having Alzheimer's based on the statistical occurrence within the general population. After this test you now have updated priors which may not be good enough to make a certain diagnosis, but wouldn't it still be useful combined with another independent test that has similar rates, since you'd be using these updated priors?