Investigation of Bayesian inference in predicting tissue concentrations using RStan
Shan Pan, Stefano Zamuner, Shuying Yang
CPMS, GlaxoSmithKline, Stevenage, UK
Background & Objectives: A full PBPK model representing physiological profiles may not be available due to limited data. Minimal PBPK models can be an alternative to evaluate the target tissue concentrations. In this work we aimed to investigate the prediction of tissue concentrations using Bayesian approach, for compound X that is intended for the treatment of inflammatory liver disease.
Methods: A full PBPK model for compound X is available from a pre-clinical study, with the liver as the site of elimination. Using the full PBPK model scaled from pre-clinical species to humans, 1,000 subjects aged between 20 and 80 were simulated in R. Volume and blood flow in the liver were correlated and decreased by 20-40% with increase in age, and approximately one-fold decline in liver function with increase in age was considered [1]. Distributions of steady-state drug concentrations, volume, blood flow and clearance in the liver were obtained and referred to as true distributions.
Random sampling from the 1,000 subjects was conducted for the following two testing scenarios: (1) plasma data only, and (2) plasma and liver data. In each scenario, both sparse and rich samples were considered for 10 and 100 subjects, respectively. In total three runs of random sampling were considered.
Bayesian modelling with a minimal PBPK [2] was performed in RStan, with prior distributions defined on tissue volume, blood flow and clearance. Due to the structural identifiability with plasma data only, the minimal PBPK model was simplified into the classical two-compartment model via re-parameterisation. Posterior distributions of liver volume and clearance were compared with true parametric distributions. Posterior predictive distributions of steady-state concentrations in the liver were compared with true concentrations distribution.
Results: When plasma data was available only, rich or sparse plasma data had little impact on the prediction of drug concentrations in the liver. Strong prior distributions of liver clearance and volume, however, predicted close to true drug concentrations in the liver. When both plasma and liver data were available, even sparse samples in the liver gave good predictions of drug concentrations in the liver using the minimal PBPK.
Conclusions: The current study explored scenarios where Bayesian interference may be useful in predicting drug concentrations in tissue, and this in return may increase the predictive power of target engagement in tissue.
References:
[1] Schmucker DL. Age-related changes in liver structure and function: Implications for disease? Exp Gerontol. 2005;40(8–9):650-9.
[2] Cao and Jusko. Applications of minimal physiologically-based pharmacokinetic models. J Pharmacokinet Pharmacodyn. 2012;39(6):711-23.
