Some robust design strategies for percentile estimation in binary response models

Abstract

For the problem of percentile estimation of a quantal response curve, we determine multi-objective designs which are robust with respect to misspecifications of the model assumptions. We propose a maximin approach based on efficiencies and provide designs that are simultaneously efficient with respect to the particular choice of various parameter regions and link functions. Furthermore, we deal with the problems of designing model and percentile robust experiments and give various examples of such designs, which are calculated numerically.

Robustness of Design in Dose–Response Studies

“…This question of how the designs change in response to uncertainty about the appropriate link is a question which is quite naturally answered by using the techniques of this paper. Biedermann et al (2006) addressed this question by constructing designs that were intended to be simultaneously efficient with respect to various choices of link functions and parameter regions. Their work followed on that of Zhu and Wong (2001), who constructed Bayesian optimal designs minimizing a certain linear combination of loss functions.…”

“…Huang (2002) investigated robustness, against a misspecified logistic response curve, of the choice of the numbers of doses administered at each of a selection of uniformly distributed design points. Biedermann et al (2006) studied maximin designs for percentile estimation, with the minimum efficiency evaluated over a range of plausible values of the parameters. They also obtained designs that attain a reasonable level of efficiency over a finite collection of possible link functions.…”

Compound optimal designs for percentile estimation in dose–response models with restricted design intervals

“…The problem of optimal design for percentile estimation in dose-response experiments has first been addressed by Wu (1988) who derived designs that are optimal with respect to the estimation of one percentile at a time. This approach has been extended by several authors; see, e.g., a work of Zhu and Wong (2000) who focus on Bayesian optimal design for estimating the ED50 precisely, subject to the constraint that the efficiencies for estimating the other two quartiles ED25 and ED75 are not too low, or a recent work of Biedermann, Dette and Pepelyshev (2004) where model robust designs for percentile estimation in dose-response models are derived. The above authors, however, assume that the design interval comprises the entire real axis.…”

Optimal Designs for Dose-Finding Studies

“…Section 2 introduces a motivating example from a real clinical dose finding study. Next, in Section 3, it is demonstrated that optimal design problems for MED-estimation are closely related to c-optimal design problems, which have been considered by several authors in the statistical literature (see Wu, 1988, Ford, Torsney and Wu, 1992, Pukelsheim, 1993, Chapter 2, Krewski, Smythe and Fung, 2002, Biedermann, Dette and Pepelyshev, 2006, among many others). Despite their limited practical applicability, we focus initially on local optimal designs (Chernoff, 1953), because they provide the foundation of the efficient robust designs described later in the text.…”