Fully Bayesian Experimental Design for Pharmacokinetic Studies

Bayesian design and analysis of two-arm cluster randomized trials using assurance

We consider the design of a two-arm superiority cluster randomized controlled trial (RCT) with a continuous outcome. We detail Bayesian inference for the analysis of the trial using a linear mixed-effects model. The treatment is compared to control using the posterior distribution for the treatment effect. We develop the form of the assurance to choose the sample size based on this analysis, and its evaluation using a two loop Monte Carlo sampling scheme. We assess the proposed approach, considering the effect of different forms of prior distribution, and the number of Monte Carlo samples needed in both loops for accurate determination of the assurance and sample size. Based on this assessment, we provide general advice on each of these choices. We apply the approach to the choice of sample size for a cluster RCT into poststroke incontinence, and compare the resulting sample size to that from assurance based on a Wald test for the treatment effect. The Bayesian approach to design and analysis developed in this article can offer advantages in terms of an increase in the robustness of the chosen sample size to parameter mis-specification and reduced sample sizes if prior information indicates the treatment effect is likely to be larger than the minimal clinically important difference.

Simplified Algorithms for Adaptive Experiment Design in Parameter Estimation

Measurements to estimate parameters of a model are commonplace in the physical sciences, where the traditional approach to automation is to use a sequence of preselected settings followed by least-squares fitting of a model function to the data. This measure-then-fit approach is simple and effective and entirely appropriate for many applications but when measurement resources are limited, efficiency becomes more important. To increase efficiency, Bayesian experiment design allows measurement settings to be chosen adaptively based on accumulated data and utility, the predicted improvement in results as a function of settings. However, the calculation of utility has been judged too impractical for most applications. In this paper, we introduce computational methods and simplified algorithms that accelerate utility calculations by over an order of magnitude, with only slight degradation in measurement efficiency. The methods eliminate utility calculation as a barrier to practical application of efficient adaptive measurement.

Probabilistic Framework for Optimal Experimental Campaigns in the Presence of Operational Constraints

The predictive capability of any mathematical model is intertwined with the quality of experimental data collected for its calibration. Model-based design of experiments helps compute maximally informative campaigns for model...

Optimal experimental design for predator-prey functional response experiments

Functional response models are important in understanding predator-prey interactions. The development of functional response methodology has progressed from mechanistic models to more statistically motivated models that can account for variance and the over-dispersion commonly seen in the datasets collected from functional response experiments. However, little information seems to be available for those wishing to prepare optimal parameter estimation designs for functional response experiments. It is worth noting that optimally designed experiments may require smaller sample sizes to achieve the same statistical outcomes as non-optimally designed experiments. In this paper, we develop a model-based approach to optimal experimental design for functional response experiments in the presence of parameter uncertainty (also known as a robust optimal design approach). Further, we develop and compare new utility functions which better focus on the statistical efficiency of the designs; these utilities are generally applicable for robust optimal design in other applications (not just in functional response). The methods are illustrated using a beta-binomial functional response model for two published datasets: an experiment involving the freshwater predator Notonecta glauca (an aquatic insect) preying on Asellus aquaticus (a small crustacean), and another experiment involving a ladybird beetle (Propylea quatuordecimpunctata L.) preying on the black bean aphid (Aphis fabae Scopoli). As a by-product, we also derive necessary quantities to perform optimal design for beta-binomial regression models, which may be useful in other applications.

Bayesian Input Design for Linear Dynamical Model Discrimination

A Bayesian design of the input signal for linear dynamical model discrimination has been proposed. The discrimination task is formulated as an estimation problem, where the estimated parameter indexes particular models. As the mutual information between the parameter and model output is difficult to calculate, its lower bound has been used as a utility function. The lower bound is then maximized under the signal energy constraint. Selection between two models and the small energy limit are analyzed first. The solution of these tasks is given by the eigenvector of a certain Hermitian matrix. Next, the large energy limit is discussed. It is proved that almost all (in the sense of the Lebesgue measure) high energy signals generate the maximum available information, provided that the impulse responses of the models are different. The first illustrative example shows that the optimal signal can significantly reduce error probability, compared to the commonly-used step or square signals. In the second example, Bayesian design is compared with classical average D-optimal design. It is shown that the Bayesian design is superior to D-optimal design, at least in this example. Some extensions of the method beyond linear and Gaussian models are briefly discussed.