Is there a link between athletic shoe drop and injury? Yes? No? Maybe?

I have been musing lately on the relationship between drop and injury. It is a discussion I have often had, trying to figure out if drop really is a performance and injury issue... or just a way to strip weight out of the shoe.

The discussion folds nicely into that of heel lifts for conditions like Achilles tendinopathy or even Sever's disease, which is common practice, and achieves results anecdotally. But, I am interested in what the science tells us.. is there a real reason to go up, or down with drop, as we look at injury?