Exposure–response modelling approaches for determining optimal dosing rules in children

Within paediatric populations, there may be distinct age groups characterised by different exposure–response relationships. Several regulatory guidance documents have suggested general age groupings. However, it is not clear whether these categorisations will be suitable for all new medicines and in all disease areas. We consider two model-based approaches to quantify how exposure–response model parameters vary over a continuum of ages: Bayesian penalised B-splines and model-based recursive partitioning. We propose an approach for deriving an optimal dosing rule given an estimate of how exposure–response model parameters vary with age. Methods are initially developed for a linear exposure–response model. We perform a simulation study to systematically evaluate how well the various approaches estimate linear exposure–response model parameters and the accuracy of recommended dosing rules. Simulation scenarios are motivated by an application to epilepsy drug development. Results suggest that both bootstrapped model-based recursive partitioning and Bayesian penalised B-splines can estimate underlying changes in linear exposure–response model parameters as well as (and in many scenarios, better than) a comparator linear model adjusting for a categorical age covariate with levels following International Conference on Harmonisation E11 groupings. Furthermore, the Bayesian penalised B-splines approach consistently estimates the intercept and slope more accurately than the bootstrapped model-based recursive partitioning. Finally, approaches are extended to estimate Emax exposure–response models and are illustrated with an example motivated by an in vitro study of cyclosporine.