Modeling the protein binding non-linearity in population pharmacokinetic model of valproic acid in children with epilepsy: a systematic evaluation study

Background: Several studies have investigated the population pharmacokinetics (popPK) of valproic acid (VPA) in children with epilepsy. However, the predictive performance of these models in the extrapolation to other clinical environments has not been studied. Hence, this study evaluated the predictive abilities of pediatric popPK models of VPA and identified the potential effects of protein binding modeling strategies.

Methods: A dataset of 255 trough concentrations in 202 children with epilepsy was analyzed to assess the predictive performance of qualified models, following literature review. The evaluation of external predictive ability was conducted by prediction- and simulation-based diagnostics as well as Bayesian forecasting. Furthermore, five popPK models with different protein binding modeling strategies were developed to investigate the discrepancy among the one-binding site model, Langmuir equation, dose-dependent maximum effect model, linear non-saturable binding equation and the simple exponent model on model predictive ability.

Results: Ten popPK models were identified in the literature. Co-medication, body weight, daily dose, and age were the four most commonly involved covariates influencing VPA clearance. The model proposed by Serrano et al. showed the best performance with a median prediction error (MDPE) of 1.40%, median absolute prediction error (MAPE) of 17.38%, and percentages of PE within 20% (F ₂₀, 55.69%) and 30% (F ₃₀, 76.47%). However, all models performed inadequately in terms of the simulation-based normalized prediction distribution error, indicating unsatisfactory normality. Bayesian forecasting enhanced predictive performance, as prior observations were available. More prior observations are needed for model predictability to reach a stable state. The linear non-saturable binding equation had a higher predictive value than other protein binding models.

Conclusion: The predictive abilities of most popPK models of VPA in children with epilepsy were unsatisfactory. The linear non-saturable binding equation is more suitable for modeling non-linearity. Moreover, Bayesian forecasting with prior observations improved model fitness.