Estimation of receptor occupancy using varying coefficients models

In many applications of linear regression models, the regression coeffi- cients are not regarded as fixed but as varying with another covariate named the effect modifier. A useful extension of the linear regression models are then varying coefficient models. To link the regression coefficient with the effect modifier, several methods may be considered. Here, we propose to use Bayesian P-splines to relate in a smoothed way the regression coefficient with the effect modifier. We show that this method enables a large level of flexibility: if necessary, adaptive penalties can be introduced in the model (Jullion and Lambert 2007) and linear constraints on the relation between the regression coefficient and the effect modifier 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, credibil- ity sets are easily obtained for receptor occupancy, which take into account the uncertainty appearing at all the different estimation steps.