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Abstract:
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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 model is then varying coefficient model. 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 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 Positron Emission Tomography study where we want to estimate the relation between the drug concentration in plasma and the Receptor Occupancy, i.e. the number of specific receptors to which the drug is bound.
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