Also single engine vs multi engine.
In the jet world, multiengine ops become easier again, as the airplane is less trying to kill you in the event of a failure (much lower drag from a failed engine, no runaway prop concerns, less yaw from asymmetric thrust) and you have massive amounts of surplus power at low altitude. There are situations in a jet where you can lose an engine on the takeoff roll, even prior to lifting the nosewheel, and for the safest course of action to be to continue the takeoff, take the problem airborne, and consider a return or divert in the air. (Failures after V1 ["takeoff decision speed"] and before Vr ["rotate"].) There are no such times in the piston or (edit to add: light) turboprop world.
The safety rates and reasons are frequently debated. As a pilot who frequently flies my family around and is strongly disinterested in making the numerator part of the statistics, I read every NTSB fatal, every crash of the types I fly, and most of the serious crashes of other types.
My thoughts are that the pilots are, by a wide margin, the weakest link in general aviation (non-military, non-commercial) piston singles, making poor decisions on fuel, weather, and other dispatch-related topics. I'd bet that 3/4ths of the piston single fatals have pilot or dispatch (also pilot) as the root cause, not engine or mechanical.
Accelerate-go calculations do not necessarily mean that engine failures before rotation are to be taken aloft. My 58P has accelerate-go charts published (they're not pretty at heavy weights on high/hot days). Nevertheless, any engine failure with the nosewheel on the ground is an abort/RTO.
The DA-42 I can't find any reference for V1 below Vr and to take an engine failure prior to Vr aloft. That was looking in the QRH and checklists for the aircraft. I see both specified at 75 knots and the checklist response for engine failure on the roll is only the rejected takeoff instructions.
It seems so easy: when one engine fails you still have the other left to power the aircraft, right? People often forget that the prop on the stalled engine creates a huge amount of drag, like a stuck paddle on a canoe. You have to compensate for the drag, feather the prop (adjust the angle of the blades to minimize drag) and adjust for that again. When you have sufficient altitude that can be done, but on takeoff or landing you'd have to be a really cool cat to pull it off...
As for pilot error: I think that number is actually a lot closer to 100%. This also rings true for car accidents, and I bet most planes are maintained a lot better than cars...