The studies are mixed. Some show the radiation given off is a factor, some show it is not. The information on the radiation given off, I believe, is readily available so you can pick a phone with a low SAR rating. Some sites even rank phones by their SAR rating.
You can also you bluetooth if you are very concerned, or not use a cell phone.
You do realize too that sunshine is radiation too? And an airplane ride gives you radiation? It is all around you - so it is part of everyday life. So it is hard to just pinpoint *one* factor.