Comparison of robust criteria for D-optimal design

This study compared the performance of a local and three robust optimality criteria in terms of the standard error for a one-parameter and a two-parameter nonlinear model with uncertainty in the parameter values. The designs were also compared in conditions where there was misspecification in the prior parameter distribution. The impact of different correlation between parameters on the optimal design was examined in the two-parameter model. The designs and standard errors were solved analytically whenever possible and numerically otherwise.

An optimal design for screening trials

Yao, Begg, and Livingston (1996, Biometrics 52, 992-1001) considered the optimal group size for testing a series of potentially therapeutic agents to identify a promising one as soon as possible for given error rates. The number of patients to be tested with each agent was fixed as the group size. We consider a sequential design that allows early acceptance and rejection, and we provide an optimal strategy to minimize the sample sizes (patients) required using Markov decision processes. The minimization is under the constraints of the two types (false positive and false negative) of error probabilities, with the Lagrangian multipliers corresponding to the cost parameters for the two types of errors. Numerical studies indicate that there can be a substantial reduction in the number of patients required.

A review of modern computational algorithms for Bayesian optimal design

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

Active flow control bump design using hybrid Nash-game coupled to evolutionary algorithms

In this paper, the optimal design of an active flow control device; Shock Control Bump (SCB) on suction and pressure sides of transonic aerofoil to reduce transonic total drag is investigated. Two optimisation test cases are conducted using different advanced Evolutionary Algorithms (EAs); the first optimiser is the Hierarchical Asynchronous Parallel Evolutionary Algorithm (HAPMOEA) based on canonical Evolutionary Strategies (ES). The second optimiser is the HAPMOEA is hybridised with one of well-known Game Strategies; Nash-Game. Numerical results show that SCB significantly reduces the drag by 30% when compared to the baseline design. In addition, the use of a Nash-Game strategy as a pre-conditioner of global control saves computational cost up to 90% when compared to the first optimiser HAPMOEA.

A sequential Monte Carlo approach to design for population pharmacokinetics studies

Here we present a sequential Monte Carlo approach that can be used to find optimal designs. Our focus is on the design of phase III clinical trials where the derivation of sampling windows is required, along with the optimal sampling schedule. The search is conducted via a particle filter which traverses a sequence of target distributions artificially constructed via an annealed utility. The algorithm derives a catalogue of highly efficient designs which, not only contain the optimal, but can also be used to derive sampling windows. We demonstrate our approach by designing a hypothetical phase III clinical trial.

A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.