The closest thing to a definitive answer was the 2011 report of the International Agency for Research on Cancer (IARC), which concluded that cellphones and cordless landlines were "possibly" a cause of cancer.
"I don't think [our study] changes the position as described by IARC; it just adds another little piece of the jigsaw," said Professor Mark Elwood, one of the authors of the new study, published today in the Australian and New Zealand Journal of Public Health.
Figures on how many people talk on cellphones and for how long is hard to come by. Instead, Professor Elwood and his colleagues cite telco data to show that cellphone subscriptions increased from 0.2 per cent of the population in 1986, to there being more subscriptions than people by 2007.
There were 4212 cases of cancer of the brain or a related area in the 15-year study period.
The researchers say that if there was a substantial, causal relationship between cellphones and brain cancer, there should be a rise in the incidence of the tumour called glioma in both sexes. And the increase should be greater in the areas of the brain called the temporal and parietal lobes as they are exposed to more radio-frequency radiation than other areas when a person makes voice calls from a phone held to the ear.
They didn't find evidence of either.
The only clear glioma increases were in women aged 30-49, where it was not matched in men of the same age; and in men over 70, where the rise was smaller in the most-exposed areas of the brain.
Professor Elwood said, "Our study adds to the evidence against there being a substantial increase in risk within a short or moderate time-frame.
"That does not exclude the possibility that mobile phones could have a small increased risk or an increased risk with a very long time delay."
Brain cancer study
• 4212 cases of cancer of brain or related areas from 1995 to 2010.
• Rate of brain cancers per capita in people aged 10-69 reduced by 0.86% a year.
• If cellphones caused brain cancer, the rate of glioma cancers in the parts of the brain most exposed to cellphone radiation should have risen (It may have dropped by 0.39% a year).
• Conclusion: Cellphones don't increase brain cancer risk substantially in the short/medium term.
Frequent caller has no worries - for now
Real estate agent Geoff Thorne talks frequently on his cellphone, undeterred by the international scientific consensus that they may "possibly" cause brain cancer.
Mr Thorne, 62, sells commercial properties and is based in Takapuna on Auckland's North Shore. Like many real estate agents he does a great deal of work on a cellphone. He has had one since 1990.
He estimates he talks on his cellphone for 600 to 1000 minutes a month. That's about 20 to 30 minutes a day. Ninety-five per cent of his calls are for work.
Mr Thorne said he did not worry about the stories reporting a possible link between cellphone use and brain cancers.
"I have seen lots of speculation about it. We get radio waves from so many sources."
He said that because cellphones had been in use for more than two decades, he believed if they did cause brain cancers then by now there would be clear and certain evidence of this.
"I'm comfortable at this stage."
A father and grandfather of cellphone users, he said, "We've spoken about it. I think you tend to tell your children to do as I say, not as I do.
"I don't have any concerns at this stage. I do need to say 'at this stage' because - who knows?"
