The German Shepherd that runs after Adam on his bike is, it turns out, a dog that lives at the hospital with the patients. In the earlier chapters of the book, he's described as a guard dog. Adam thinks "he's been waiting for me all my life" (7.1), which gives us the sense that the dog recognizes him somehow. It chases after Adam on his bike, biting at his front tire, trying to get the bike to fall over.
Maybe the most important thing to remember about the dog, though, is what happens after the incident: he gets distracted by a passing car and Adam finally sees the dog "streaking away, down the road in pursuit of the VW, barking wildly" (7.9). Sounds normal for a dog, right? Exactly. We realize that this is just a normal dog, that does normal dog things, but Adam's fears get the best of him and everything becomes exaggerated in his mind.