Actually, there is research that proves that phones are NOT related to cancer. Holding your phone next to your ear for hours is certainly not good for your arm, but it won't have any ill effects on your head.
As IdrisSeabright said, which you ignored, is there has been no increase in brain cancer since the introduction of cell phones. That's over 30 years. That is probably the most telling single fact. In fact, if you look at the statistics, brain cancer rates have declined slightly over that time period. If there was a connection it would have showed up long ago. And IdrisSeabright works in medical research, and has access to all of the most up-to-date research on this.