Applying Hierarchical Generalized Additive Models to Non-Compartmental Analysis of Pharmacokinetic Data

Non-compartmental analysis (NCA) is a popular strategy for obtaining estimates of pharmacokinetic parameters, while requiring both minimal structural assumptions, and limited input by the analyst. As typically applied, its scope and depth are constrained by its statistical simplicity. Embedding the NCA within a hierarchical generalized additive model (HGAM) may facilitate the simultaneous analysis of data from multiple subjects, estimation of covariate effects in one stage, and implementation of censored responses, similarly to the capabilities of nonlinear multilevel models as widely applied in pharmacometrics. HGAM is an interesting extension to multilevel linear models that allows the effects of predictors to be implemented as smooth functions, which has been widely implemented in various disciplines to nonlinear trends, including for longitudinal data. This approach extends the capability of previous implementations of spline-based methods applied to NCA, within an accessible workflow in open software. Application of HGAM to two example datasets, one describing oral drug administration, and one describing IV and oral drug administration with categorical covariates and censoring, illustrates the overall approach, including parameter estimation, visualization and model checking, and uncertainty quantification. A Bayesian approach to estimation facilitates interpretable expressions of the uncertainty in individual parameters, population parameters, and functions of parameters such as contrasts.