Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses

TL;DR

This paper introduces a nonparametric goodness-of-fit test for covariate models in pharmacometrics, enabling rigorous evaluation of parametric assumptions using kernel-based methods, demonstrated through simulations and a case study.

Contribution

It develops a novel nonparametric testing approach for covariate models, bridging statistical learning and pharmacometric analysis, to improve model validation.

Findings

Test correctly identified misspecified models with high power.

Approach is effective across varying data sparsity and error scenarios.

Proof-of-concept demonstrated in a pharmacokinetic case study.

Abstract

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.