Finally, the measurement of cell phone use in most studies has been crude. Most have been case-control studies, which have relied on people’s memories about their past cell phone use. In these types of studies, it can be hard to interpret any possible link between cancer and an exposure. People with cancer are often looking for a possible reason for it, so they may sometimes (even subconsciously) recall their phone usage differently than people without cancer.
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When we think of harmful radiation, things like X-rays or gamma rays usually come to mind, but these types of radiation are different from mobile phone radiation in important ways. Radiation on the ultraviolet side of visible light, like those types just mentioned, has a wavelength that is short enough to alter some of the chemical properties of the objects it interacts with. It is referred to as ionizing radiation, for this reason. Non-ionizing radiation, which includes visible light, microwaves and radio waves, is typically regarded as harmless. Large amounts of it can produce a heating effect, like in a microwave oven, but no short-term damage has been linked to exposure to non-ionizing radiation.
A large prospective (forward-looking) study of nearly 800,000 women in the UK examined the risk of developing brain tumors over a 7-year period in relation to self-reported cell phone use at the start of the study. This study found no link between cell phone use and brain tumors overall or several common brain tumor subtypes, but it did find a possible link between long-term cell phone use and acoustic neuromas.

W. Kim Johnson, a retired physicist and past president of the New Mexico Academy of Science, reviewed the Aires web site for Discovery News and described the material as gibberish, saying that the authors "of the technical description of the ‘Aires' device reads like a random selection of technical terminology. The working description for this device is made up of jargon that, in the end, really says nothing."

The program began, but Dr. Carlo soon discovered that everyone involved had underlying motives.“The industry wanted an insurance policy and to have the government come out and say everything was fine. The FDA, which looked bad because it didn’t require pre-market testing, could be seen as taking steps to remedy that. By ordering the study, law makers appeared to be doing something. Everyone had a chance to wear a white hat.”
I love this case. However, I don't understand what happens to the radiation that must collect under the case; isn't there a burst of radiation when the case is opened? I posted this question but the answers were from people who hadn't thought of that issue; they didn't have the answer, except for one who theorized that the radiation is slowly leaking out the top, bottom, and sides. I assume the case keeps radiation off the hand that holds the case with the phone in it, which is great, but I do wonder about the stored radiation when, for example, I'm listening to a podcast with the case closed, then open it later.
The studies are notable for their sizes. Researchers at the National Toxicology Program, a federal interagency group under the National Institutes of Health, tested 3,000 rats and mice of both sexes for two years—the largest investigation of RF radiation and cancer in rodents ever undertaken in the U.S. European investigators at the Ramazzini Institute in Italy were similarly ambitious; in their recent study they investigated RF effects in nearly 2,500 rats from the fetal stage until death.
Jump up ^ Gandhi, Om P.; Morgan, L. Lloyd; de Salles, Alvaro Augusto; Han, Yueh-Ying; Herberman, Ronald B.; Davis, Devra Lee (14 October 2011). "Exposure Limits: The underestimation of absorbed cell phone radiation, especially in children". Electromagnetic Biology and Medicine. 31 (1): 34–51. doi:10.3109/15368378.2011.622827. ISSN 1536-8378. Retrieved 2015-04-25.
Morbidity and mortality among study participants who have brain cancer. Gliomas are particularly difficult to study, for example, because of their high death rate and the short survival of people who develop these tumors. Patients who survive initial treatment are often impaired, which may affect their responses to questions. Furthermore, for people who have died, next-of-kin are often less familiar with the cell phone use patterns of their deceased family member and may not accurately describe their patterns of use to an interviewer.
Instead of more animal and even epidemiological studies, he thinks researchers should focus on finding the mechanisms by which cellphone radiation may affect human health. Since we’ll never have an RCT on cellphones and cancer, he added, studies should measure actual cellphone use and exposure to radio-frequency radiation, instead of estimations of how much people are exposed (which most studies currently do).
In one type of study, called a case–control study, cell phone use is compared between people with these types of tumors and people without them. In another type of study, called a cohort study, a large group of people who do not have cancer at study entry is followed over time and the rate of these tumors in people who did and didn’t use cell phones is compared. Cancer incidence data can also be analyzed over time to see if the rates of brain tumors changed in large populations during the time that cell phone use increased dramatically. These studies have not shown clear evidence of a relationship between cell phone use and cancer. However, researchers have reported some statistically significant associations for certain subgroups of people.