Adaptive Bayesian P-splines to estimate varying regression coefficients: application to receptor occupancy estimation

In many applications of linear regression models, the regression coecien ts are not regarded as xed but as varying with another covariate named the eect modier. A useful extension of the linear regression models are then varying coecien t models. To link the regression coecien t with the eect modier, several methods may be considered. Here, we propose to use Bayesian P-splines to relate in a smoothed way the regression coecien t with the eect modier. We show that this method enables a large level of exibilit y: if necessary, adaptive penalties can be introduced in the model (Jullion and Lambert 2007) and linear constraints on the relation between the regression coecien t and the eect modier may easily be added. We provide an illustration of the proposed method in a PET study where we want to estimate the relation between the Receptor Occupancy and the drug concentration in the plasma. As we work in a Bayesian setting, credibility sets are easily obtained for receptor occupancy, which take into account the uncertainty appearing at all the dieren t estimation steps.