Bayesian Nonlinear Hierarchical Models: Applications in Preclinical Pharmacometrics

Abstract

Although Bayesian methods are expanding considerably in various scientific areas, their applications in the field of pharmacokinetic/pharmacodynamic (PK/PD) modelling and simulation is still relatively limited. In this work, Bayesian techniques are used to facilitate the estimation of a novel PK/PD model which is developed to quantify the extent of PD synergy between two compounds using historical in vivo data. The model is fitted using package rstan, the R interface to Stan. Stan is a recently developed software package which allows an efficient estimation using the No-U-Turn Sampler (NUTS).

Since the data consist of a series of 11 trials performed sequentially, a Bayesian sequential integration is considered: the posteriors resulting from the analysis of one trial are used to specify the hyperparameters of the priors of the next trial. The recursive update of posterior distributions whenever new information is available is less computationally intensive compared to the analysis of all data up to the current trial. However, this method implies the analysis of a limited amount of information during the first integration steps, which may hinder the estimation process. The aim of the present work is to discuss challenges as well as opportunities which are related to the impact of (i) prior specification, (ii) random effect choice and (iii) experimental design. In addition, the results from an extensive simulation study assessing the performance of the Bayesian sequential integration for an increasing model complexity are evaluated.

The results suggest that the use of informative prior distributions reduces the correlation among parameters and improves the accuracy of estimates. Moreover, choosing the random effect on a parameter that is not highly correlated with others avoids overcompensations, thus ensuring better predictions. On top of that, trials should be designed so that each of them explores an exhaustive number of doses and sampling times.