Some hybrid models applicable to dose-response relationships

A new type of models of dose-response relationships has been studied as an initial stage to explore a reliable extrapolation of the relationships decided by high dose data to the range of low dose covered by radiation protection. The approach is to use a 'hybrid scale' of linear and logarithmic scales; the first model is that the normalized surviving fraction (ρ S > 0) in a hybrid scale decreases linearly with dose in a linear scale, and the second is that the induction in a log scale increases linearly with the normalized dose (τ D > 0) in a hybrid scale. The hybrid scale may reflect an overall effectiveness of a complex system against adverse events caused by various agents. Some data of leukemia in the atomic bomb survivors and of rodent experiments were used to show the applicability of hybrid scale models. The results proved that proposed models fit these data not less than the popular linear-quadratic models, providing the possible interpretation of shapes of dose-response curves, e.g. shouldered survival curves varied by recovery time. (author)