Pharmacokinetic parameters estimation using adaptive Bayesian P‐splines models

Abstract

In preclinical and clinical experiments, pharmacokinetic (PK) studies are designed to analyse the evolution of drug concentration in plasma over time i.e. the PK profile. Some PK parameters are estimated in order to summarize the complete drug's kinetic profile: area under the curve (AUC), maximal concentration (C(max)), time at which the maximal concentration occurs (t(max)) and half-life time (t(1/2)).Several methods have been proposed to estimate these PK parameters. A first method relies on interpolating between observed concentrations. The interpolation method is often chosen linear. This method is simple and fast. Another method relies on compartmental modelling. In this case, nonlinear methods are used to estimate parameters of a chosen compartmental model. This method provides generally good results. However, if the data are sparse and noisy, two difficulties can arise with this method. The first one is related to the choice of the suitable compartmental model given the small number of data available in preclinical experiment for instance. Second, nonlinear methods can fail to converge. Much work has been done recently to circumvent these problems (J. Pharmacokinet. Pharmacodyn. 2007; 34:229-249, Stat. Comput., to appear, Biometrical J., to appear, ESAIM P&S 2004; 8:115-131).In this paper, we propose a Bayesian nonparametric model based on P-splines. This method provides good PK parameters estimation, whatever be the number of available observations and the level of noise in the data. Simulations show that the proposed method provides better PK parameters estimations than the interpolation method, both in terms of bias and precision. The Bayesian nonparametric method provides also better AUC and t(1/2) estimations than a correctly specified compartmental model, whereas this last method performs better in t(max) and C(max) estimations.We extend the basic model to a hierarchical one that treats the case where we have concentrations from different subjects. We are then able to get individual PK parameter estimations. Finally, with Bayesian methods, we can get easily some uncertainty measures by obtaining credibility sets for each PK parameter.

Physiologically Based Modeling of Food Digestion and Intestinal Microbiota: State of the Art and Future Challenges. An INFOGEST Review

“…As such, they commonly fail when used for predictions outside the range of data used to establish them. Examples of these kinds of pharmacokinetic models include those with sum-of-inverse-Gaussian functions to describe drug absorption profiles (Csajka et al 2005) or Bayesian p-splines to estimate pharmacokinetic parameters ( Jullion et al 2009). By contrast, a purely mechanistic model incorporates physiologically based assumptions about the mechanisms controlling the system.…”

Spatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors

“…We develop the corresponding Bayesian inferential methodology using a simple, previously unknown, solution. Spatially adaptive penalty parameters have also been used before (Ruppert and Carroll 2000;Eilers and Marx 2002;Baladandayuthapani, Mallick, and Carroll 2005;Lang and Brezger 2004;Jullion and Lambert 2006;Pintore, Speckman, and Holmes 2006). However, this is the first article to combine these features.…”

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

“…The population smooth function in this case, where the basis is not specified, is a thin-plate regression spline (Wood, 2003). Note that the pseudo-logarithmic transformation of 𝑡𝑖𝑚𝑒 allows 𝑡𝑖𝑚𝑒 = 0 to be included (Jullion et al, 2009), but is somewhat non-linear especially for small values of 𝑡𝑖𝑚𝑒, which requires some caution to select an appropriate unit. This corresponds to a group-level model with shared wiggliness, as expressed in Pedersen et al, (2019).…”

“…Notably, Park et al, (1997) reported semiparametric modelling using splines, as a convenient and flexible alternative to nonlinear multilevel models, including random effects for between-subject variation. Jullion et al, (2009) described application of Bayesian P-splines, including extensive mathematical details and consideration of priors, with a focus on sparse problems. Most recently, Willemsen et al, (2017) described the application of a specific variant of multilevel spline model to bioequivalence determination with NCA, and nominated several potential advantages, including handling of sparsity and implementation of censoring, which are directly relevant to the HGAM approach evaluated here.…”

“…Use of readily available and accessible implementations is thus a key priority. The objective of this manuscript is to explore the application of the hierarchical generalized additive model (HGAM) to NCA, building upon previous applications of semiparametric models for NCA (Park et al, 1997;Jullion et al, 2009;Willemsen et al, 2017). A Bayesian workflow in the open software environment R (R Core Team, 2022) via 'brms' (Bürkner, 2017)…”