When a suspicious death of a pony made front page news on the NY Times there was some discussion of this–the article was from 2012, and the fact George Morris was asked for a quote about the issue is pretty rich in retrospect.
If you’ve run out of free articles, here is a shorter summary.
However, I am not really sure what the apples to oranges comparison is worth, to be honest, since the thread was started about eventing safety, and how and if it is possible to make the sport safer and still recognizably the sport.
I guess I’ll just throw in that I admit I’ve always felt safer riding dressage, although certainly there have been many terrible injuries in all horse sports of both horses and riders. But I don’t know if that’s backed up by statistics, to be perfectly honest, or if just because of my own highly subjective personal comfort level and skill set as a rider. (My feel for a horse has always been better than my eye and bravery over fences, so I am personally safer doing dressage IMHO, but I don’t have the stats to confirm how much safer it is as a discipline.)