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

In many applications of linear regression models, the regression coefficients 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, credibility sets are easily obtained for receptor
occupancy, which take into account the uncertainty appearing at all the different estimation
steps.