The answer is the "gold standard" double blind, placebo controlled study.
Antioxidant supplementation for the prevention of kwashiorkor in Malawian children: Randomised, double blind, placebo controlled trial
The study was a double blind placebo controlled study adequately powered for OS as primary end-point.
So, in fact, this double blind placebo controlled study does not guarantee safety or efficacy because the test leaves far too many questions unanswered.
Many of these benefits have been proven repeatedly in double blind, placebo controlled studies, some only noted in a limited number of test subjects.