According to the Linear-no-threshold model [1], any level of radiation, no matter how small, causes cancer. According to this model, the 1,000 μsv/year of normal background radiation already cause cancer for 1% of people. And any additional dose increase the risk further.
However this model is contested. And the analysis on the cancers incidence in Hiroshima and Nagasaki and Chernobyl seems to indicate that this model is flawed. The exact model is difficult to estimate because of the low number of extra cancer is lost in the noise.
[1] https://en.m.wikipedia.org/wiki/Linear_no-threshold_model
However this model is contested. And the analysis on the cancers incidence in Hiroshima and Nagasaki and Chernobyl seems to indicate that this model is flawed. The exact model is difficult to estimate because of the low number of extra cancer is lost in the noise.