There's all sorts of anecdotes of pets reacting to people being ill well before the people put 2 and 2 together.

The primary problem, I think, is that you'd have difficulty convincing someone to fund this research without a priori knowledge - e.g. if you don't already know that there are (relatively) readily externally visible biochemistry changes from a degenerative brain problem, why would you see if you can train an animal to smell it?

It's similar to the question people posed after the PS3 signing key leak came out - while it is the case that Sony was signing all PS3 (and PSP, if memory serves) binaries with the same (all-zeroes?) random input, so they leaked information sufficient to eventually retrieve the private key from enough samples, why would you think to check if they did that without already knowing?

(Or, more generally, the large domain of problems that is relatively-trivial to verify a correct solution but infeasible to test all possible solutions in order to find one.)

Probably Parkinsons. In reality if you deploy at scale the dogs will just pretend to smell whatever it's handler rewards it for.

I don't have references, but my understanding is that the human nose is in general just as sensitive has a dog's. However humans tend to ignore what their nose tells them and so they don't know how to use it as well as the dog's. When a human is trained their become just as good as a dog.

Well, there are those perennial stories about cats detecting cancer...

Good point. It would be relatively cheap to do a larger study on this and perhaps we can prove some easy facts about Parkinson's, namely that it is correlated with a smell. It would be a cheap easy win towards answering the hard question, "What causes Parkinson's disease?".

I was recently reading "Surely You're Joking, Mr. Feynman", the last chapter contains a story about a researcher who was studying rats in mazes. The researcher wanted to put the rats into a long corridor of identical doors, and teach them to go exactly 3 doors down from where they were put in and get some food. The rats always went to the exact door where they last got food from though, no matter where they where put in. The researcher didn't know how they could tell the doors apart; was it smell, sight, sound, etc? He was determined to eliminate all these possibilities so that the rats would only have their entry point to go off of, and then they would learn to go 3 doors and get food. The final change he made before succeeding was to put the rat maze on sand, and then the rats finally stopped going to the door which last had food. Apparently the rats were able to use the subtle sounds the floor made to determine their exact location in the long corridor.

Then Richard Feynman mentioned that this researcher was largely ignored and unrecognized. He hadn't discovered anything about rats, so much as he had discovered something about experiments on rats. Other researchers continued to do rat maze experiments without putting their mazes on sand, and would publish papers without considering the possibility that the rats were navigating by the sound of the floor.

Coming back to my original point, I wonder if it was proven that Parkinson's is correlated with a smell, would such an odd experiment even be considered by anyone in the research community?