Ars covered this particular story and were deeply skeptical, attributing the findings to selective use of p values:
https://arstechnica.com/science/2018/03/a-critical-analysis-...
https://arstechnica.com/science/2018/03/a-critical-analysis-...
But there's still one significant increase in cancer in their data, so let's look more closely at that: "A statistically significant increase in the incidence of heart Schwannomas was observed in treated male rats at the highest dose." When it comes to this type of cancer, the control group of 817 rats developed four tumors. But critically, all of those tumors occurred in females; none in males. This apparent sex bias will necessarily exaggerate the impact of any tumors in any of the male experimental populations.
And that's exactly what you see happening. In one female population, 2.2 percent of an experimental group developed this type of tumor, but that was not a statistically significant result. By contrast, in this male population with the significant difference, only 1.5 percent of the animals developed these tumors. A low-dose group of males had the same number of tumors, but the group was larger and so the result slipped below significance.
These numbers suggest that the one statistical effect seen in this study is caused by the unusually low tumor incidence in the control group, rather than a specific effect of cellphone radiation.