An Induced Natural Selection Heuristic for Finding Optimal Bayesian Experimental Designs

Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal designs for problems with large, or high-dimensional, design spaces. We propose an efficient search heuristic suitable for general optimisation problems, with a particular focus on optimal Bayesian experimental design problems. The heuristic evaluates the objective (utility) function at an initial, randomly generated set of input values. At each generation of the algorithm, input values are "accepted" if their corresponding objective (utility) function satisfies some acceptance criteria, and new inputs are sampled about these accepted points. We demonstrate the new algorithm by evaluating the optimal Bayesian experimental designs for the previously considered death, pharmacokinetic and logistic regression models. Comparisons to the current "gold-standard" method are given to demonstrate the proposed algorithm as a computationally-efficient alternative for moderately-large design problems (i.e., up to approximately 40-dimensions)

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Modelling the influence of MDR1 polymorphism on digoxin pharmacokinetic parameters.

OBJECTIVES: Digoxin is a well-known probe for the activity of P-glycoprotein. The objective of this work was to apply different methods for covariate selection in non-linear mixed-effect models to study the relationship between the pharmacokinetic parameters of digoxin and the genotype for two major exons located on the multi-drug-resistance 1 (MDR1) gene coding for P-glycoprotein. METHODS: Thirty-two healthy volunteers were recruited in three pharmacokinetic drug interaction studies. The data after a single oral administration of digoxin alone were pooled. All subjects were genotyped for the MDR1 C3435T and G2677T/A genotypes. The concentration-time profile of digoxin was established using 12-16 blood samples taken between 15 min and 72 h after administration. We modelled the pharmacokinetics of digoxin using non-linear mixed-effect models. Parameter estimation was performed using the stochastic approximation EM method (SAEM). We used three methods to select the covariate model: selection from a full model using Wald tests, forward inclusion using the log-likelihood ratio test and model selection using the Bayesian Information Criterion. RESULTS: The three covariate inclusion methods led to the same final model. Carriers of two T alleles for the C3435T polymorphism in exon 26 of MDR1 had a lower apparent volume of distribution than carriers of a C allele. The only other covariate effect was a shorter absorption time-lag in women. CONCLUSION: The apparent volume of distribution of digoxin is lower in TT subjects, probably reflecting differences in bioavailability. Non-linear mixed-effect models can be useful for detecting the influence of covariates on pharmacokinetic parameters

A genetic algorithm based global search strategy for population pharmacokinetic/pharmacodynamic model selection

The current algorithm for selecting a population pharmacokinetic/pharmacodynamic model is based on the well-established forward addition/backward elimination method. A central strength of this approach is the opportunity for a modeller to continuously examine the data and postulate new hypotheses to explain observed biases. This algorithm has served the modelling community well, but the model selection process has essentially remained unchanged for the last 30 years. During this time, more robust approaches to model selection have been made feasible by new technology and dramatic increases in computation speed. We review these methods, with emphasis on genetic algorithm approaches and discuss the role these methods may play in population pharmacokinetic/pharmacodynamic model selection