Comments on a time-dependent version of the linear-quadratic model

The accuracy and interpretation of the "LQ + time" model (E = D(α + βd) - γT) are discussed. Evidence is presented, based on data in the literature, that this model does not accurately describe the changes in isoeffect dose occurring with protraction of the overall treatment time during fractionated irradiation of the lung. This lack of fit of the model explains, in part, the surprisingly large values of γ/α that have been derived from experimental lung data. The large apparent time factors for lung suggested by the model are also partly explained by the fact that γT/α, despite having units of dose, actually measures the influence of treatment time on the effect scale, not the dose scale, and is shown to consistently overestimate the change in total dose. The unusually high values of α/β that have been derived for lung using the model ( ≈5 Gy) are shown to be influenced by the method by which the model was fitted to data. Reanalyses of the data using a more statistically valid regression procedure produce estimates of α/β more typical of those usually cited for lung ( ≈ 3 Gy). Most importantly, published isoeffect data from lung indicate that the true deviation from the linear-quadratic (LQ) model is nonlinear in time, instead of linear, and also depends on other factors such as the effect level and the size of dose per fraction. Thus, we do not advocate the use of the "LQ + time" expression as a general isoeffect model.