Vo Hong Thanh (1), Janak Wedagedera (1), Hiroshi Momiji (1), Richard Matthews (1), Masoud Jamei (1) and Frederic Y. Bois (1)
(1) Certara, Simcyp Division, Sheffield, UK
Objectives: We describe a general framework for integrating data on individual-specific covariates (measurable physiological characteristics and other parameters dependent on those) in physiologically based pharmacokinetic (PBPK) models. Our approach allows the efficient generation of individual parameters from a Bayesian covariate model. Using this framework, we can perform rigorous Bayesian inference on parameters when measured individual covariates are available. We demonstrate an application of this approach using a PBPK model implemented within the Simcyp Simulator with its built-in covariate model.
Methods: We model covariates as a probabilistic network [1], represented as a directed acyclic graph (DAG) in which nodes denote variables and edges represent their relationships. Each node defines a variable and is associated with a distribution, which may depend on time and/or other nodes. A directed edge from one node to another represents a directed dependency between these nodes. The relationships between nodes can either be probabilistic or deterministic. The fully specified probabilistic network therefore encodes a joint multivariate distribution of its nodes. This network view allows us to efficiently simulate and coherently update the values of all nodes. For simulation, we generate individual parameter values in topological order using Monte-Carlo simulations. To update the nodes’ distributions, given measured covariate values, we factorise the prior nodes’ distributions and the data likelihood. Bayesian numerical methods [2,3], (e.g., Markov Chain Monte Carlo, MCMC, simulations), are used to sample values from the nodes’ joint posterior distributions.
We illustrate our approach using a minimal PBPK model with first-order absorption, enzyme-mediated liver clearance and renal clearance, as implemented in the Simcyp Simulator [4]. In the Simcyp Simulator, the user can specify distributions or set values for some individual covariates. Covariates (e.g., height, body mass, body surface area) have normal or lognormal distributions, but the Simulator also allows non-normal distributions (e.g., Weibull or uniform distributions of age, or Bernoulli distribution of sex).
Results: We implemented part of the Simcyp Simulator covariate model in NIMBLE [5]. Our covariate model has 33 nodes of which 24 are random variables. The DAG representation eases various operations on our relatively complex covariate model. We can visualize and modify the network (e.g., add/remove/edit nodes) dynamically. To verify the distribution of nodes, we generated virtual individual parameter values according to the covariate model using Monte Carlo simulations. Histograms of 10,000 values sampled for the random nodes of the network were calculated and visually checked. The generation of 10,000 individual values took seconds on a laptop without parallelisation. We also carried out a fully Bayesian MCMC updating of the covariate model incorporating measurement (with and without uncertainty) of a subject’s body mass. We ran two chains of 15,000 MCMC iterations, which required only a fraction of a second to execute, and kept the last 10,000 samples to form posterior estimates. We finally calibrated the model to plasma PK data on theophylline for 18 subjects, in a population framework. Posterior kernel estimates of the probability density function for random nodes of the covariate model were validated against MCSim and Stan [6].
Conclusions: We developed a general framework that provides a network view of individual-specific covariates and their relationship in population pharmacokinetics. While the network view is a powerful conceptual representation, the most precise specification of such networks remains a set of ODE equations or, equivalently, a computer code. Our probabilistic network representation offers a range of efficient methods to simulate individuals through population-level distributions, but also to update the values of all the nodes in such a network on the basis of data directly on parameters or on the ODE model predictions. Bayesian updating of the network provides a reliable inference framework for incorporating subject-level covariate data in population pharmacokinetic analyses.
References:
[1] Dawid, A.P., 2002. Influence diagrams for causal modelling and inference. International Statistical Review 70, 161–189.
[2] Kjærulff, U.B., and Madsen, A.L., 2008. Bayesian Networks and Influence Diagrams. Springer New York. doi:10.1007/978-0-387-74101-7.
[3] Green, P.J., Łatuszyński, K., Pereyra, M., and Robert, C.P., 2015. Bayesian computation: a summary of the current state, and samples backwards and forwards. Statistics and Computing 25, 835–862. doi:10.1007/s11222-015-9574-5.
[4] Jamei, M., Marciniak, S., Feng, K., Barnett, A., Tucker, G., and Rostami-Hodjegan, A., 2009. The Simcyp Population-based ADME Simulator. Expert opinion on drug metabolism & toxicology 5 (2):211–223.
[5] https://r-nimble.org.
[6] Wedagedera et al., 2022. Population PBPK modeling using parametric and nonparametric methods of the Simcyp Simulator, and Bayesian samplers. CPT Pharmacometrics Syst Pharmacol. doi: 10.1002/psp4.12787.
Reference: PAGE 30 (2022) Abstr 10104 [www.page-meeting.org/?abstract=10104]
Poster: Methodology - Covariate/Variability Models