Those assumptions include, but are not limited to:
1) the electromagnetic radiation from the cell phone causes this clinical phenomenon/effect
2) the cell phone radio antenna broadcasts in all directions (i.e. inverse square law applies)
3) whatever is causing this effect has some dose-to-effect relationship even if nonlinear
In theory, cell phones use frequencies which are "non-ionizing radiation" meaning that they cannot break the covalent chemical bonds in DNA because they lack the energy to do so. So, if we assume that the findings/implications of causality are true, we need to consider one of the following may be true:
1) there is a significant misunderstanding in the biomedical sciences about what energies of electromagnetic radiation are capable of breaking covalent bonds in DNA
2) that electromagnetic radiation emitted by cell phones (and many other things, btw) causes an effect which (indirectly in terms of DNA) increases cancer/tumor risk (increased tissue temp? altered enzyme/protein activity? altered cellular metabolism?)
Many years ago an electrical engineer who worked in the field of radio transmitters associated with cell phones said to me, regarding this topic, "Look, cell phone antennas put out one watt of power. You put the phone up to your head, your head absorbs half a watt of microwave radiation. Whether or not there's medical proof yet, that's probably not good." Maybe that's outdated or simplistic, but it doesn't seem completely out of line considering that most of us cannot know with either certainty or expertise the truth of this matter.