Modeling carcinogenesis under a time-changing exposure

A model of carcinogenesis for fractionated and continuous exposure is developed. The model is discussed from two points of view. First a “surface” statistical model is introduced by making assumptions about the hazard function for the time of tumor latency. Later it is shown that the model can be interpreted in a mechanistic sense as a discrete and a mixed discrete/continuous counterpart of a model of carcinogenesis recently proposed by Yakovlev and Polig [A. Yakovlev, E. Polig, Math. Biosci. 132 (1996) 1]. Two counteracting effects are combined: a protective multiplicative effect of the exposure on the hazard function along with an additive effect of cancer induction responsible for an additional hazard. The model is used to revisit the analysis by Yakovlev et al. [A. Yakovlev, W. Müller, L. Pavlova, E. Polig, Math. Biosci. 142 (1997) 107] of lymphoma-free survival in irradiated mice under acute and fractionated exposure.