We've got a pretty good idea of what cancer rates are for various levels and types of radiation.
Toxic chemicals can cause cancer themselves - poisoning isn't the only option there. Coal tar, for example, has no (or minimal) radioactivity, but is still carcinogenic.
We actually have a rather poor understanding of long term effects of radiation. We have decent models for amounts of radiation that kill you over weeks, but long term low dose exposure is poorly understood.
Toxic chemicals can cause cancer themselves - poisoning isn't the only option there. Coal tar, for example, has no (or minimal) radioactivity, but is still carcinogenic.