A multistage, probabilistic, biologically based model of carcinogenesis has been developed involving qualitative and quantitative aspects of the process. A chemical can affect the risk of cancer by directly damaging DNA and/or increasing the number of cell divisions during which errors in DNA replication can occur. Based on this model, carcinogens are classified as genotoxic versus nongenotoxic; nongenotoxic chemicals are further divided on the basis of whether or not they act through a specific cell receptor. Nongenotoxic compounds, particularly those acting through a nonreceptor mechanism, are likely to have dose and/or species-specific thresholds. This classification also implies the existence of chemicals that will be carcinogenic at high doses in animal models, but because of dose and/or mechanistic considerations, will not be carcinogenic to humans at levels of exposure. N-[4-(5-nitro-2-furyl)-2-thiazolyl] formamide (FANFT) and 2-acetylaminofluorene (AAF) are classical genotoxic bladder carcinogens that also cause proliferative effects at higher doses. Although there is an apparent no-effect level for the urinary bladder carcinogenicity of these two compounds at low doses, in reality, DNA adducts form at these low levels, and it is likely that there is a cancer effect (no threshold), but it is below the level of detection of the bioassay. These conclusions are based on studies involving multiple doses and time points in rodents, including results from the ED01. Pellets implanted directly into the rodent bladder lumen or calculi formed in the urine as a result of an administered chemical cause abrasion of the urothelium, and a marked increase in cell proliferation and cell number, and ultimately tumors.(ABSTRACT TRUNCATED AT 250 WORDS)