Mathematical aspects of dose-response studies in carcinogenesis--the concept of thresholds.

Many of the previously proposed theories of carcinogenesis which relate the exposure level of a carcinogen to expected tumor response, are summarized and it is pointed out that these theories assume the existence of no threshold level. A modification of the one-hit carcinogenic model which would incorporate a threshold, is proposed along with a generalization to variable thresholds over the population at risk. The statistical problems of discriminating between threshold and non-threshold models from experimental bioassay data are discussed and an example is given.