A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments

Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues

The electrical behaviour of a system, such as an electrode–tissue interface (ETI) or a biological tissue, can be used for its characterization. One way of accomplishing this goal consists of measuring the electrical impedance, that is, the opposition that a system exhibits to an alternating current flow as a function of frequency. Subsequently, experimental impedance data are fitted to an electrical equivalent circuit (EEC model) whose parameters can be correlated with the electrode processes occurring in the ETI or with the physiological state of a tissue. The EEC used in this paper is a reasonable approach for simple bio-electrodes or cell membranes, assuming ideal capacitances. We use the theory of optimal experimental design to identify the frequencies in which the impedance is measured, as well as the number of measurement repetitions, in such a way that the EEC parameters can be optimally estimated. Specifically, we calculate approximate and exact D-optimal designs by optimizing the determinant of the information matrix by adapting two of the most algorithms that are routinely used nowadays (REX random exchange algorithm and KL exchange algorithm). The D-efficiency of the optimal designs provided by the algorithms was compared with the design commonly used by experimenters and it is shown that the precision of the parameter estimates can be increased.

Finding optimal design in nonlinear mixed effect models using multiplicative algorithms

BACKGROUND AND OBJECTIVES

To optimize designs for longitudinal studies analyzed by nonlinear mixed effect models (NLMEMs), the Fisher information matrix (FIM) can be used. In this work, we focused on the multiplicative algorithms, previously applied in standard individual regression, to find optimal designs for NLMEMs.

METHODS

We extended multiplicative algorithms to mixed models and implemented the algorithm both in R and in C. Then, we applied the algorithm to find D-optimal designs in two longitudinal data examples, one with continuous and one with binary outcome.

RESULTS

For these examples, we quantified the improved speed when C is used instead of R. Design optimization using the multiplicative algorithm led to designs with D-efficiency gains between 13% and 25% compared to non-optimized designs.

CONCLUSION

We found that the multiplicative algorithm can be used efficiently to design longitudinal studies.

Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods

Algorithms that compute locally optimal continuous designs often rely on a finite design space or on the repeated solution of difficult non-linear programs. Both approaches require extensive evaluations of the Jacobian Df of the underlying model. These evaluations are a heavy computational burden. Based on the Kiefer-Wolfowitz Equivalence Theorem, we present a novel design of experiments algorithm that computes optimal designs in a continuous design space. For this iterative algorithm, we combine an adaptive Bayes-like sampling scheme with Gaussian process regression to approximate the directional derivative of the design criterion. The approximation allows us to adaptively select new design points on which to evaluate the model. The adaptive selection of the algorithm requires significantly less evaluations of Df and reduces the runtime of the computations. We show the viability of the new algorithm on two examples from chemical engineering.