  The characterization of covariate effects on model parameters is a crucial
step during pharmacokinetic/pharmacodynamic analyses. While covariate selection
criteria have been studied extensively, the choice of the functional
relationship between covariates and parameters, however, has received much less
attention. Often, a simple particular class of covariate-to-parameter
relationships (linear, exponential, etc.) is chosen ad hoc or based on domain
knowledge, and a statistical evaluation is limited to the comparison of a small
number of such classes. Goodness-of-fit testing against a nonparametric
alternative provides a more rigorous approach to covariate model evaluation,
but no such test has been proposed so far. In this manuscript, we derive and
evaluate nonparametric goodness-of-fit tests for parametric covariate models,
the null hypothesis, against a kernelized Tikhonov regularized alternative,
transferring concepts from statistical learning to the pharmacological setting.
The approach is evaluated in a simulation study on the estimation of the
age-dependent maturation effect on the clearance of a monoclonal antibody.
Scenarios of varying data sparsity and residual error are considered. The
goodness-of-fit test correctly identified misspecified parametric models with
high power for relevant scenarios. The case study provides proof-of-concept of
the feasibility of the proposed approach, which is envisioned to be beneficial
for applications that lack well-founded covariate models.
