Unfortunately it may take decades of exposure to low levels and very large high quality studies to answer that question.
Those studies don't exist. Is there strong evidence of carcinogenicity from non-ionizing radiation? No. Have some studies suggested possible harm? Yes. Has it been proven that there is no harm? No.
Science is never "proven", that's not part of what we do. You can never prove that something is completely impossible through experiments, because you can always argue that the next measurement would have been the one to produce the result that appears to be impossible. Instead, we gather data and analyze it, producing the best explanation for the process under study, and then we develop new, better instruments and do it again, improving or replacing the best explanation with something even better.
In this particular case, the physics of how radiation interacts with matter makes it pretty clear how this works. Note that "radiation" isn't the kind from nuclear reactors, those are actual particles of matter that can directly impact your cells and damage the DNA. This radiation is electromagnetic...visible light is radiation in this case. The energy required for electromagnetic radiation to damage a cell directly is really large, up in the UV...you can get skin cancer from sunlight because some of it is UV, and if you go higher it's more possible (which is why there are annual limits on X-ray exposure, for example). The iPhone outputs radio, which is very low energy, much lower than even visible light...it's so low level that the possibility of a radio photon directly causing damage to your DNA is, well, impossible. The heat can cause damage, but the radio just doesn't have the power to do anything to you. Quantum mechanics makes it clear that a particular radio photon might, possibly, damage a cell somewhere in the world, but it's so low probability that you're going to be long dead of something else first.
People fear radiation because of nuclear energy (and for good reason, when that gets out of control it does kill quickly), they just don't understand that it's a totally different thing than what is in the world around you. Heck, people themselves are radioactive (yes, you really are), but it's not dangerous at all to get close to another human (well, not for that reason anyways

). The radiation from an iPhone is safe, it's not going to give you cancer of any kind, so don't fall prey to people who want to use ignorance about it.