Alexander N. Donev

Tailor-Made Split-Plot Designs for Mixture and Process Variables

The design of efficient small experiments involving mixture variables and process variables is a difficult problem. An additional complication is that such experiments are often conducted using split-plot designs and therefore lead to correlated observations. The present article demonstrates how algorithmic search can be used for constructing efficient tailor-made split-plot mixture-process variable designs, when there may be constraints on the mixture components. The D-optimality criterion is used as the main design criterion. The article also shows how to construct efficient split-plot mixture-process variable designs when replication is required for independently estimating the variance components in the split-plot model. It is argued that it is better to spread the replications over different points of the design than to concentrate them in the center.

The D-optimal design of blocked experiments with mixture components.

So far, the optimal design of blocked experiments involving mixture components has received scant attention in the literature. This paper describes the algorithmic approach to designing such experiments. For constrained and unconstrained experimental regions, the resulting experimental designs are shown to be statistically much more efficient than the orthogonally blocked design options presented in the literature. As an alternative to the algorithmic approach, a simple two-stage procedure to construct highly efficient blocked mixture experiments for unconstrained design regions in the presence of fixed and/or random blocks is presented. Finally, the similarities and differences between the design of blocked mixture experiments and mixture experiments in the presence of qualitative process variables are discussed in detail.

Non-Gaussian Berkson errors in bioassay

The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods.

Construction of experimental designs for estimating variance components

Many computer algorithms have been developed to construct experimental designs that are D-optimum for the fixed parameters of a statistical model. However, the case when the interest is in the variance components has not received much attention. This problem has similarities with that of designing experiments aiming at D-optimality for the fixed parameters of nonlinear models as its solution depends on the values of the unknown parameters that need to be estimated. An algorithm that can be used to construct locally and pseudo-Bayesian A- and D-optimum designs for the variance components in a linear mixed effects model, or for variance ratios, when there is a three-stage crossed or nested variability structure is proposed. Suitable visualizations of the results in order to help the assessment of the robustness of the designs against possible inaccuracies of the assumptions about the true values of the variance components used in the selection of the designs are recommended.

General Blending Models for Data From Mixture Experiments

We propose a new class of models providing a powerful unification and extension of existing statistical methodology for analysis of data obtained in mixture experiments. These models, which integrate models proposed by Scheffé and Becker, extend considerably the range of mixture component effects that may be described. They become complex when the studied phenomenon requires it, but remain simple whenever possible. This article has supplementary material online.

Optimal Serial Dilutions Designs For Drug Discovery Experiments

Dose-response studies are an essential part of the drug discovery process. They are typically carried out on a large number of chemical compounds using serial dilution experimental designs. This paper proposes a method of selecting the key parameters of these designs (maximum dose, dilution factor, number of concentrations and number of replicated observations for each concentration) depending on the stage of the drug discovery process where the study takes place. This is achieved by employing and extending results from optimal design theory. Population D- and D S -optimality are defined and used to evaluate the precision of estimating the potency of the tested compounds. The proposed methodology is easy to use and creates opportunities to reduce the cost of the experiments without compromising the quality of the data obtained in them.

Special issue on Design of Experiments

Research on design of experiments has contributed, and continues to contribute, to the development of Statistical Sciences and to a myriad of data-based physical sciences. CSDA has long been at the forefront of publishing work in these areas. To this end a 2014 Special Issue (eds. Gilmour and Payne) was dedicated to ‘algorithms for design of experiments’, acknowledging that computational methods play a central role in the construction and validation of designs. For the current Special Issue, contributions were invited in a wide range of topics, covering a broad spectrum of design philosophies, methodologies and applications. Some of the published papers are devoted to problems related to model uncertainty and discrimination. Dette, Melas and Shpilev (2017a) focus on Fourier regression models. McGree (2017) uses the total entropy utility function for model discrimination and parameter estimation in Bayesian design. Designs considerations when making model selection for generalised linear models are studied by Woods, McGree and Lewis (2017). Central to the study of model uncertainty is the issue of design robustness. Konstantinou, Biedermann and Kimber (2017) propose robust designs for survival trials. The robustness of various designs to missing observations is studied by Smucker, Jensen, Wu and Wang (2017) and by da Silva, Gilmour and Trinca (2017). Dette, Schorning and Konstantinou (2017b) consider further implications brought by dealing with correlated observations, and Rodŕıguez-Dı́az (2017) proposes methods for constructing c-optimal designs in such situations. Atkinson and Biswas (2017) present novel ideas for adaptive designs for clinical trials with multivariate or longitudinal responses. The work of Kobilinsky, Monod and Bailey (2017) provides solutions for computer generation for generalised regular factorial designs. The competitive algorithm of Masoudi, Holling and Wong (2017) helps to find minimax and standardised maximin optimal designs. Designing combined physical and computer experiments to maximise prediction accuracy is studied by Leatherman, Dean and Santner (2017). An application of optimal design theory in a reliability industrial experiment is described by RivasLópez, Yu, López-Fidalgo, and Ruiz (2017). All papers present valuable contributions to the statistical theory and practice of design. They illustrate the continuing role to be played by thoughtful experimentation, at a time when mere scattershot sampling of ‘big data’ is becoming all too fashionable.