I think that the question of risks/negative effects is a very important one. We should all keep asking our doctors about them.
Because research is sparce and slow, we will not know the real long term effects of anticoagulants for many years to come (other than the risk of bleeding of course). This is especially true for people diagnosed and becoming life-long warfarin/coumadin /anticoagulant users at a young age.
I recently ask two hematologists about the long term effects of coumadin, but none of them could really answer my questions. The first doctor almost laughed at me, as if to say I was crazy to even ask if it could be linked to things like liver problems for example. The second doctor was more honest in saying that, for the moment, the benifits of coumadin still outweigh the risk of DVT.