What is the meaning of 'A compound is carcinogenic'?

In case the compound is clearly directly genotoxic, an ineffective threshold dose cannot be assumed. However, also in this case it is evident that high doses of the compound are generally associated with a high cancer risk, low doses with a lower one. Based on dose-response data from animal experiments, quantification of the cancer risk is carried out by mathematical modeling. If the safety margin between the lowest carcinogenic dose in animals and the relevant level of exposure in humans exceeds 10,000, the degree of concern is classified as low. Cases, where the compound turns out to be genotoxic in one study or one test only but not in others or only in vitro but not in vivo, are particularly difficult to explain and cause controversial discussions. Also for indirectly genotoxic agents, an ineffective (threshold) dose must be assumed. The situation is aggravated by the use of doubtful epidemiological studies in humans such as in the case of glyphosate, where data from mixed exposure to various chemicals were used. If such considerations are mixed with pure hazard classifications such as 'probably carcinogenic in humans' ignoring dose-response behavior and mode-of-action, the misinformation and public confusion are complete. It appears more urgent but also more difficult than ever to return to a scientifically based perception of these issues.