Extension of IMPRES-M, the smoothing impulse-response PK-PD framework, to population pharmacokinetic analysis
Jeroen Elassaiss-schaap1, Lorenzo Cifelli1, Paul H.C. Eilers1
1PD-value B.V., 2PD-value B.V., 3PD-value B.V.
Introduction Population pharmacokinetic (popPK) modeling is the cornerstone of quantitative pharmacology, but construction of proper PK models can be laborious. We previously presented a new framework in PK-PD modeling based on a combination of smoothing and impulse-response modeling, IMPRES-M® (patent pending). This framework can construct continuous, smooth, PK models without the need for model specification [1], and we have shown that it performs similar to -compartmental estimation in extrapolation to different dosing regimens [2]. IMPRES-M furthermore is capable of capturing PK-PD relationships, eliminating the need for the use of ODEs in, for example, TTE modeling [3]. Within the framework, PK or PK-PD curves are represented as a sum of -ample-B-spline functions, with a penalty applied to differences of their coefficients. PopPK modeling refers to the approach where non-linear estimation of pharmacokinetic profiles is combined with estimation of within-individual (residual) variability and between-individual (inter-individual) variability. Typical approaches such as linearized likelihood (FOCE) can be expected to have limited success when directly applied to smoothing because of strong correlation between neighboring B-splines. The extension of IMPRES-M to popPK modeling was therefore explored using various other methodologies as described below. Methods We simulated concentration profiles from multi-compartmental models with proportional errors. These simulations varied in terms of administration type (intravenous or oral), number of compartments and number of individuals. The IMPRES-M population analyses were assessed using standard goodness-of-fit plots but the focus was on the performance in the visual predictive checks (VPCs). Results The following approaches were explored for their performance in providing population estimation within the IMPRES-M framework. (1) Scaling of amplitude and time of a common population shape function across individuals, a method known as Self-Modeling Nonlinear Regression [4]. Such a scaling approach does not have the flexibility to describe non-correlated variation in absorption and elimination and thus this approach was dismissed. (2) Functional principal component analysis (fPCA) [5]. fPCA decomposes the curve into components that maximize variability captured per component. This method was able to capture the variability among individuals reasonably well. However, it does not provide a natural method to simulate new populations. This is because the resulting components can not be linked to specific PK characteristics and their variability does not adhere to a multivariate normal distribution complicating definition of a general probabilistic model; fPCA was therefore also deselected. (3) Hierarchical curve registration (hReg) [6] was furthermore implemented as a method of interest. Individual profiles are constructed by applying amplitude scaling and flexible non-parametric time warping. The time warping transformation accounts for differences in peak timing and variations in absorption and elimination rates. Due to its Bayesian nature, simulation of population of individuals is possible. Partially satisfactory results were obtained using hReg, with a decent VPC in the majority of time points but typically partial bias in variability near the peak and in the terminal part of the curves. hReg was therefore deselected. (4) Finally, a decomposition approach based on convolution theory was set up. The pharmacokinetic profile is decomposed into absorption and elimination components, and further components as needed. The individual curves are then represented by scaling the components along the concentration and time axes. These individual scaling parameters are treated within a Bayesian mixed effects framework. Estimation runs take typically in the order of minutes and are stable. Resulting VPCs show adequate simulation properties. On top of that, the components can be interpreted as usual in the context of compartmental modeling. The decomposition approach was therefore selected. Conclusion We have successfully expanded IMPRES-M® to a method for population analysis of PK profiles. Multiple approaches were evaluated but the best appeared to be decomposition of full profiles into separate components which are subsequently subjected to mixed effects estimation in an efficient framework.
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