Automatic Development of Pharmacokinetic Structural Models – Pharmpy Model Search Tool
Alzahra Hamdan (1), Xiaomei Chen (1), Stella Belin (1), Rikard Nordgren (1), Simon J. Carter (1), Simon Buatois (2), João A. Abrantes (2), Andrew C. Hooker (1), Mats O. Karlsson (1)
(1) Department of Pharmacy, Uppsala University, Sweden (2) Roche Pharma Research and Early Development, Roche Innovation Center Basel, Basel, Switzerland
Introduction: The current development strategy of population pharmacokinetic models is a complex and iterative process that is manually performed. Such a strategy is time-demanding, subjective, and dependent on the modelers’ experience. In this work, we present a novel model search tool[1], as part of the Pharmpy/Pharmr [2,3] software package, that automates the development process of pharmacokinetic structural models.
Methods: Model Search is a Pharmpy tool that searches for the best structural model using an exhaustive stepwise search algorithm. Given a dataset, a starting model and a pre-specified search space, the tool creates and fits a series of candidate models that are then ranked based on a selection criterion, leading to the selection of the best model. The search space is a list of structural model features to be considered during the search and can include different models that describe the absorption delay, absorption, distribution, and elimination of the administered drug. The stepwise exhaustive algorithm tests all possible combinations of model features in a stepwise manner by adding model features one by one in each step. As a result, some models are repeatedly estimated from different orders of added features. The initial values of the models’ parameters are dynamically updated based on the final estimates of their parent models. For newly added parameters, initial values are algorithmically imputed.
The Model Search tool was used to develop structural models for 10 clinical PK datasets (5 orally and 5 i.v. administered drugs). A starting model for each dataset was generated using the assemblerr [3,4] package in R, which included a first-order (FO) absorption without any absorption delay for oral drugs, one-compartment disposition, FO elimination and a proportional residual error model. In order to understand the influence of different inter-individual variability (IIV) structures for the model parameters on the final selected models, 5 approaches were investigated: 1- naïve pooling, 2- IIV on the starting model parameters with a correlation between CL and V, but no IIV on new parameters 3- IIV on the parameter of mean delay time (MDT) in addition to the IIV structure in the 2nd approach, 4- diagonal IIV on all newly added parameters in addition to the IIV structure in the 2nd approach, and 5- full block IIV on all model parameters. The search space for the oral drugs included aspects of absorption rate (FO, zero-order (ZO), sequential ZO-FO) and absorption delay (Lagtime, and 1, 3, and 10 transit compartments), and distribution (1- and 2- compartments). For the i.v. drugs, 1-, 2- and 3- compartment models were included in the search space. The selection of the final structural model was made based on the Bayesian Information Criterion (BIC) for mixed effects models.[5]
Results: Comparing the selected structural models for each drug across the different approaches, it is shown that the same absorption rate (for oral drugs) and distribution components were selected through Approaches 1 and 2 for 9/10 drugs. Approach 2 also identified an absorption delay component in 4/5 oral drugs, whilst the naïve pooling approach only identified an absorption delay in 1 drug. Compared to Approaches 1 and 2, Approaches 3, 4 and 5 tended to select more complex models and more often resulted in minimization errors during the search.
Additionally, consistency between the same models resulting from different routes (hence different initial estimates) was observed in terms of the goodness-of-fit and parameter values.
Conclusions: The Model Search tool was able to automatically select a structural model with different strategies of setting the IIV model structure. This automatic procedure enables the evaluation of numerous combinations of model components, which would not be possible using a traditional manual model building strategy. Furthermore, the Model Search tool is flexible and can support multiple research investigations for how to best implement structural model selection in a fully automatic model development workflow.
Based on these results, strategies of further enhancement of the search algorithm will be developed and evaluated to increase the search efficiency such as avoiding analyzing redundant models and optimizing the development order of model components (i.e., absorption, distribution, and elimination).
Acknowledgment: This work was supported by F. Hoffmann-La Roche Ltd., Basel, Switzerland.
References:
[1] Model Search — Pharmpy 0.56.1 documentation [Internet]. [cited 2022 Mar 21]. Available from: https://pharmpy.github.io/latest/modelsearch.html
[2] Welcome to Pharmpy — Pharmpy 0.56.1 documentation [Internet]. [cited 2022 Mar 21]. Available from: https://pharmpy.github.io/latest/index.html
[3] Nordgren R, Ueckert S, Belin S, Yngman G, Carter S, Buatois S, et al. Pharmpy and assemblerr - Two novel tools to simplify the model building process in NONMEM. PAGE 29. 2021
[4] assemblerr [Internet]. Uppsala University, Pharmacometrics Research Group; 2022 [cited 2022 Mar 21]. Available from: https://github.com/UUPharmacometrics/assemblerr
[5] A note on BIC in mixed-effects models [Internet]. [cited 2022 Mar 30]. Available from: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-8/issue-1/A-note-on-BIC-in-mixed-effects-models/10.1214/14-EJS890.full
