When I ride in rural southern Indiana or Kentucky I see many loose dogs. Chases are common. Attacks are not. I know of one local cyclists who was bitten badly in the last few years. I know of a couple of others who went down after running into dogs.
A couple of years ago I was on a ride when two pit-puppies came running after me. I could tell they were friendly, and I didn't want to crash, so I stopped and pet them for a few minutes. They were quite happy and made it difficult for me to get going again. Once I did get away, noticed one of them had bit a hole in my water bottle. Oops.