How do you know?: exactly as reported: GMO foods have been eaten over 16 years by billions of humans and livestock with no problems. No long term individual study can equal this experience. Long term animal studies have indeed been done (click here for a review and list of over 600 studies]. Such studies are very difficult to do with regard to controlling for all variability; e.g., rats can get sick from too many tomatoes. Long-term studies are also very expensive. As we know the genes involved, and there is no cause to think that either the DNA or protein is any different from those contained in other plants of the same species, there is no reason, given our experience and cost, to start such studies. Indeed some scientists have pointed out that so much testing has been done that it is time to stop testing and start reaping the benefits of GMO crops (additional information available here].
Human studies: by default these have been done (including by members of the biotech industry) as reported above.
The other possible approach, regarded by statisticians as very powerful, is a combined analysis of a large amount of published data. Here is a statement from Ricroch New Biotechnology _ Volume 30, Number 4 _ May 2013. “None of these ‘-omics’ profiling studies has raised new safety concerns about GE varieties; neither did the long-term and multigenerational studies on animals. Therefore, there is no need to perform such long-term studies in a case-by-case approach” Snell et al (2012) point out: “We examined 12 long-term studies (of more than 90 days, up to 2 years in duration) and 12 multigenerational studies (from 2 to 5 generations). We referenced the 90-day studies on GM feed for which long-term or multigenerational study data were available. Many parameters have been examined using biochemical analyses, histological examination of specific organs, hematology and the detection of transgenic DNA. The statistical findings and methods have been considered from each study. Results from all the 24 studies do not suggest any health hazards and, in general, there were no statistically significant differences within parameters observed.” “The studies reviewed present evidence to show that GM plants are nutritionally equivalent to their non-GM counterparts and can be safely used in food and feed.”
It is interesting to note a statement by Dr. Roger Beachy, a prominent leader of the field, "I got into biotech because I wanted to reduce the use of pesticides". As many pesticides (especially insecticides) are toxic GMO crops represent a considerable step forward in food safety.