Are there any studies that have looked at whether the bone-thinning side-effect of most aeds is dose dependent?

Yes : A few studies have shown a dose relationship, especially for Phenytoin and carbamazepine. We also know that aed's can cause bone disease at therapeutic doses. Adequate calcium and vitamin d supplementation, regular weight-bearing exercise, smoking cessation, and limiting alcohol intake are somethings you can do to help sop or slow the progression of bone disease.