The Royal Australasian College of Surgeons wants the New Zealand and Australian Governments to ban the use of quad bikes by children - thanks to Chris Keall for picking up on this one. There appears to be a combination of factors which makes quad biking fabulously dangerous: no roll bar, uneven ground (as they are typically used off-road), an atmosphere of fun, and inexperienced drivers.
Although the number of injuries and deaths is not high compared to other vehicle accidents, the hours / distance driven must be tiny. More data would be useful, but I bet the injury and death rate is high. I know of a young man who survived a crash but with horrific injuries. Months of rehab and he is still going back to hospital for more surgeries. The cost - physical, emotional, and financial - is very, very, high.