Adaptive modelling of dose–response relationships using smoothing splines

We consider the use of smoothing splines for the adaptive modelling of dose-response relationships. A smoothing spline is a nonparametric estimator of a function that is a compromise between the fit to the data and the degree of smoothness and thus provides a flexible way of modelling dose-response data. In conjunction with decision rules for which doses to continue with after an interim analysis, it can be used to give an adaptive way of modelling the relationship between dose and response. We fit smoothing splines using the generalized cross-validation criterion for deciding on the degree of smoothness and we use estimated bootstrap percentiles of the predicted values for each dose to decide upon which doses to continue with after an interim analysis. We compare this approach with a corresponding adaptive analysis of variance approach based upon new simulations of the scenarios previously used by the PhRMA Working Group on Adaptive Dose-Ranging Studies. The results obtained for the adaptive modelling of dose-response data using smoothing splines are mostly comparable with those previously obtained by the PhRMA Working Group for the Bayesian Normal Dynamic Linear model (GADA) procedure. These methods may be useful for carrying out adaptations, detecting dose-response relationships and identifying clinically relevant doses.