A simple technique for suggesting whether a chemical is mutagenic (and potentially carcinogenic) to humans is to test for its mutagenicity of bacteria.
This formed the basis of the Ames test and modifications thereof.
Essentially, a bacterial culture will contain a small number of cells with a (genetic) mutation that manifests itself in some property of the bacterium; say for example its resistance to a specific antibiotic.
The hypothesis is that adding a chemical to the culture will encourage mutations at a greater rate and thereby manifesting antibiotic resistance sooner and to a greater degree than otherwise.
Such a chemical would be a mutagen and, by extrapolation, a potential human carcinogen.