Invalidity of, and alternative to, the linear quadratic model as a predictive model for postirradiation cell survival

The linear quadratic (LQ) model has been the dominant tool in preclinical radiobiological modeling of cell survival as a function of dose. However, as a second-order polynomial approximation, it suffers from two well-known pitfalls: nonmonotonic behavior and poor extrapolation. This study examined the raw data of 253 sets of photons and 943 sets of the ion beam from the Particle Irradiation Data Ensemble (PIDE) project to understand how often the LQ model could result in a negative β, which would give unrealistic predictions. Additionally, the predictive performance of the LQ model, the power model, and the linear model's predictive performance was studied using leave-one-out cross-validation (LOOCV) and twofold cross-validation. It was found that, when fitted to the LQ model, 7.5% of the photon and 29.8% of the ion beam dose-response data would result in negative β, compared to 0.77% and 2.0%, respectively, reported in published works. The LQ model performed poorly in LOOCV compared to the alternative power model, and performed the worst among the three models in twofold cross-validation. The LQ model leads to unrealistic parameters, which are vastly under-reported in published studies, and performs poorly in standard cross-validation tests. Therefore, the LQ model is not a valid predictive dose-response model for cell survival. Alternative models need to be investigated.