Figure 1

Dose response prototypes for linear, transient, and two-phase models. Typical dose response curves for the linear model ERR = βD where ERR is Excess Relative Risk and D is a dose variable (arbitrary units), the transient model ERR = σDe^(-τD), and the two-phase model ERR = βD + σDe^(-τD). Here β, σ, τ are parameters with τ ≥ 0. The linear model is shown with β > 0. Two versions of the transient model are shown, with σ > 0 and with σ < 0. The transient model converges to 0 as dose → ∞. Two versions of the two-phase model are shown, with σ >> β > 0 and -σ >> β > 0; the first version occurs when β > 0 and σ/β > e² ~ 7.39. Other possibilities (not shown) lack local maxima and minima, but the two-phase model always converges to the linear model as dose → ∞.