This Slate Magazine (online only) goes over the dangers and lack of evidence for supplements high in antioxidants. While it does link to some research, these links do not deal with effect sizes. The article does, however, present the possible active mechanisms pro and con such supplementation.
However, the main point of the article is to stress how reluctant Doctors are to point out the inadvisability of using such supplements – their patients have a religious belief based on what they see on television or over the Internet. Maybe if patients have taken responsibility for gathering their own health information, they should also take responsibility for being stupid.