Collaborative research: A major leap forward: Optimal designs for correlated data, multiple objectives, and multiple covariates

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Designed experiments form an integral part of the scientific process in many areas of research, such as the biological sciences, the health sciences, the social sciences, engineering, marketing, education, and others. A well-chosen design facilitates the collection of data that maximizes the information for the scientific questions of interest at a fixed cost, or that minimizes the cost for a desired level of information. Many experiments deal with correlated data, multiple objectives, or multiple covariates, but little is known about the identification of good designs in such settings. This project establishes how to find efficient designs for these types of problems for the most commonly used statistical models. The tools developed in this project have a tremendous potential for impact on society because designed experiments are used so often to further knowledge in many different fields. Results from the project will be made available to researchers in other areas through easy-to-use software that implements algorithms that are developed. Graduate students will be trained to become researchers in design of experiments. The outcomes of this project constitute a major leap forward in understanding and knowledge of optimal design of experiments. Recent contributions by the principal investigators and others have had a significant impact on the advancement of optimal design of experiments for nonlinear and generalized linear models. However, these results have for the most part been limited to (i) independent data; (ii) use of a single optimality criterion; and (iii) use of a single covariate. While these results are arguably important in their own right, this project will extend methods and tools to problems with correlated data, multiple objectives, and multiple covariates. The latter could consist of a mix of covariates that can be chosen by the experimenter and covariates that, known or unknown at the design stage, cannot be controlled by the experimenter. Preliminary results indicate that this is an opportune time to make these challenging but critical steps. Building a framework for deriving and identifying optimal designs for these types of problems will provide a much needed addition to our collective design toolbox. Current results are very sparse and only for very specialized problems that are mostly motivated by mathematical feasibility. The project develops tools to select efficient designs for models and conditions that are far more realistic than those that have been considered so far.