@James
As I stated, I don't have solid confirmation. I haven't ran a concerted bit of research, nor has anyone else that I've ever seen. I can however state what I believe from viewing games/box scores/player history. If you think I'm wrong, I'd love to see the research to the contrary.
One thing I do think is interesting and could have an impact is the seeming "New Doctor causes injuries" although personally I think that this is just negative reinforcement. Someone buys a new doctor, happens to get an injury next game and therefore the new Doctor caused the injury. If it *is* a greater chance, that's another unknown to factor into any research on injuries in general.