org-mode relative deadlines?

I have an org-mode tree that looks like:

* Schedule
** First Session <2016-01-15 Tue>
*** TODO send introduction email
*** TODO write survey

I would like to be able to add relative deadlines to the TODO items. Basically, something like:

*** TODO write survey
DEADLINE: -3w

and then have that TODO show up in my agenda as if the deadline were <2016-01-05 Tue> - 3 weeks. The goal is that when the date in the parent headline changes, the deadlines would move along with it.

Is this possible? I know that the date picker for deadline supports default dates, but it’s only used in the case of a date range.