Simulation-based fully Bayesian experimental design for mixed effects models

Abstract

a b s t r a c tBayesian inference has commonly been performed on nonlinear mixed effects models. However, there is a lack of research into performing Bayesian optimal design for nonlinear mixed effects models, especially those that require searches to be performed over several design variables. This is likely due to the fact that it is much more computationally intensive to perform optimal experimental design for nonlinear mixed effects models than it is to perform inference in the Bayesian framework. Fully Bayesian experimental designs for nonlinear mixed effects models are presented, which involve the use of simulation-based optimal design methods to search over both continuous and discrete design spaces. The design problem is to determine the optimal number of subjects and samples per subject, as well as the (near) optimal urine sampling times for a population pharmacokinetic study in horses, so that the population pharmacokinetic parameters can be precisely estimated, subject to cost constraints. The optimal sampling strategies, in terms of the number of subjects and the number of samples per subject, were found to be substantially different between the examples considered in this work, which highlights the fact that the designs are rather problem-dependent and can be addressed using the methods presented.

A Review of Modern Computational Algorithms for Bayesian Optimal Design

“…no search over a continuous design space is performed). Ryan et al () extended this by searching over a continuous design space to determine (near) optimal sampling times for a horse population pharmacokinetic study. Kim et al () found optimal sequential designs for population studies.…”

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

“…An important step in Bayesian MBDoE is to select an appropriate utility function, u ( d | θ , Y ), that reflects the goal of the experimentation. For example, one may decide to maximize the Kullback–Leibler distance between the prior and posterior probability distribution for the parameters 13,57,74,76 : …”

“…The main benefit of the simplified Bayesian MBDoE framework is that it accounts explicitly for prior knowledge about plausible values of the model parameters 13 . However, many researchers raise concerns about the use of Bayesian approaches in practical engineering systems 13,56,57 . Disadvantages of the Bayesian approach include uncertainty about the reliability of assumptions made when specifying prior information 55,56,58 .…”

Optimal Bayesian experimental design for subsurface flow problems

“…Optimal experimental design is concerned with finding of the best experimental setup for a given physical system or mathematical model in order to achieve extremum value of a certain well-defined quantitative criterion. Common examples of the criterion concerned are based on the variance of model parameters [4,36,37]. It is important to note that the optimal solution reflects features not only of physical system itself but also it can be highly sensitive to the selection of the optimality criterion [5].…”

“…design) and f is a linear or nonlinear operator describing the system dynamics. For instance, numerical simulations are widely used for partial replacement of real experiments in geophysics [1], subsurface flow problems [2,3] and pharmacokinetics [4] studies. Representation of real-world systems as done in Eq.…”