How does a neck brace work?
A neck brace limits range of motion to protect the neck and spine  

BikeProducts


  A neck brace restricts any extreme movement of your neck during a
  crash. In other words, it prevents your head from tilting too far
  forward, backward, or to the side, all of which can damage the spinal
  cord. A spinal cord injury can, at best, keep you off the bike for six
  to eight weeks or, at worst, put you in a wheelchair. Why take the
  risk of serious injury?


As for statistics Nascar instituted HANS like 13 years ago and they feel they have statistics that demonstrate that it is effective.
HANS
I get Nascar is not the same as a bicycle but once you protect the head the next thing you need to protect is the neck.