A couple of things to think about here.
First, this study is for the United Kingdom and no such study is being/has been done here, or at least not one we can find. Why not? Because we don't have a theater culture in the United States. Do we stand a rat's chance in hell of changing this situation?
Second, how? How do we change this (assuming we do stand a rat's chance)? Are we just not presenting theater interesting to young adults? Have we, as theater artists, let them fall through the cracks between children's theater and non-children's theater? In the last couple of decades, the publishing industry figured out there is a big market for YA liturature, provided you provided books that were actually concerned with young adult issues and not those issues adults (insert "parents" here) wished were young adult issues.
1) Drag young adults to adult theater. Who knows, they might love it.
2) Find a way to create young adult theater (and then sell it).
3) Give up and hope non-theater going young adults magically turn into theater-going adults.
Here's an article from The Guardian on the report.