Multiple-objective optimal designs

Implementation of maximin efficient designs in dose-finding studies

This paper considers the maximin approach for designing clinical studies. A maximin efficient design maximizes the smallest efficiency when compared with a standard design, as the parameters vary in a specified subset of the parameter space. To specify this subset of parameters in a real situation, a four-step procedure using elicitation based on expert opinions is proposed. Further, we describe why and how we extend the initially chosen subset of parameters to a much larger set in our procedure. By this procedure, the maximin approach becomes feasible for dose-finding studies. Maximin efficient designs have shown to be numerically difficult to construct. However, a new algorithm, the H-algorithm, considerably simplifies the construction of these designs. We exemplify the maximin efficient approach by considering a sigmoid Emax model describing a dose-response relationship and compare inferential precision with that obtained when using a uniform design. The design obtained is shown to be at least 15% more efficient than the uniform design.

Web-based tools for finding optimal designs in biomedical studies

Experimental costs are rising and applications of optimal design ideas are increasingly applied in many disciplines. However, the theory for constructing optimal designs can be esoteric and its implementation can be difficult. To help practitioners have easier access to optimal designs and better appreciate design issues, we present a web site at http://optimal-design.biostat.ucla.edu/optimal/ capable of generating different types of tailor-made optimal designs for popular models in the biological sciences. This site also evaluates various efficiencies of a user-specified design and so enables practitioners to appreciate robustness properties of the design before implementation.

Optimal designs for composed models in pharmacokinetic-pharmacodynamic experiments

We consider two frequently used PK/PD models and provide closed form descriptions of locally optimal designs for estimating individual parameters. In a novel way, we use these optimal designs and construct locally standardized maximin optimal designs for estimating any subset of the model parameters of interest. We do this by maximizing the minimal efficiency of the estimates across all relevant parameters so that these optimal designs are less dependent on the individual parameter or parameters of interest. Additionally, robust designs are proposed to further reduce the dependence on the nominal values of the parameters. We compare efficiencies of our proposed optimal designs with locally optimal designs and designs used in four real studies from the literature and show that our proposed designs provide advantages over those used in practice.

Design issues for the Michaelis-Menten model

We discuss design issues for the Michaelis-Menten model and use geometrical arguments to find optimal designs for estimating a subset of the model parameters, or a linear combination of the parameters. We propose multiple-objective optimal designs when the parameters have different levels of interest to the researcher. In addition, we compare six commonly used sequence designs in the biological sciences for estimating parameters and, propose optimal choices for the parameters for geometric designs using closed-form efficiency formulas.

Optimal treatment allocation in comparative biomedical studies

In clinical trials involving several treatment protocols, there are usually several objectives of different importance. A general method for finding an optimal design which reflects this practical need is discussed. In particular, we show that the graphical method of Cook and Wong can be applied when there are two objectives. Several illustrative examples are discussed, including multiple-objective designs for comparing several treatment groups with a placebo group.

A graphical method for finding maximin efficiency designs

We consider the problem of designing an experiment when there are two competing optimality criteria. Designs that maximize the minimum efficiencies under the two criteria are proposed along with a graphical method for finding these maximin designs.

Multiple-objective designs in a dose-response experiment

This article is an extension of the work of Huang and Wong (1), who found dual-objective designs for models with a continuous outcome. We consider quantal dose-response experiments with a binary outcome and develop multiple-objective designs for two or more Bayesian optimality criteria. Using the logit model as an illustrative example, we construct numerically optimal designs for estimating model parameters and percentiles, with possibly unequal interest in each of the objectives. We also show that the popular equal dosage assignment rule can be a rather inefficient design for estimating model parameters under a Bayesian setup.