Chin implant: is it common not to use a screw fixture?

This is very common. You will find supporters of screw fixation of chin implants. IMO, this is unnecessary and every extra piece of hardware that we use during surgery can create potential issues/ complications down the road. Modern, anatomic type implants are long and fit into a very precise pocket along the jaw. As a result the risk of rotation and malposition of these implants is much lower than the older "cap" type implants. I hope this information is helpful for you.Stephen Weber MD, FACSDenver Facial Plastic Surgeon

The pocket is usually made under a thin but strong membrane called the periosteum with the pocket made to the exact size. The pocket then shrinks down around the implant to hold if firmly in place. A  a screw is not usually used for silicone implants (the most common type) but is used for others such as PTFE, Gortex, etc. 

This is a common practice.  I use three absorbable sutures to hold a silastic chin implant in position.  I am not sure there is ever a reason to use screw fixation, but it would not be unreasonable. If the pocket is dissected correctly and the implant 'fits' the pocket, then it will all work out well

Surgeons use many different methods of trying ensure chin implant position from a tight pocket to sutures to screws. While most surgeons do not use screws, it is hard to argue with the absolutely secure implant positioning that such a technique provides. 

In our practice, we use Silastic chin implants without screw fixation or application of any tapes. The chin implant procedure involves making a very precise pocket underneath the periosteum, and placing the implant directly between the bone and the periosteum itself. No screws or tape are  required. For more information, and many examples of chin implants, please see the link and video below

I have been performing chin implant surgery for over 20 years and have not needed to use a screw.  In my opinion, this is unnecessary.  

A chin implant can be placed through a small incision under your chin in the submental area or inside the mouth. I prefer under the chin. A pocket is then carefully dissected over the chin directly on the bone. This requires that the periosteum which is the covering of the bone. If placed in this position the implant will be come strongly adherent to the bone and will not move. I usually place one small stitch into the implant and attach it to some soft tissue in the central position to keep it centered. A chin implant in the properly chosen patient gives the most spectacular change in the patient's profile. It balances the proportions of the face in the most remarkable way.