Optimal designs for discriminating between dose-response models in toxicology studies

Abstract

We consider design issues for toxicology studies when we have a continuous response and the true mean response is only known to be a member of a class of nested models. This class of non-linear models was proposed by toxicologists who were concerned only with estimation problems. We develop robust and efficient designs for model discrimination and for estimating parameters in the selected model at the same time. In particular, we propose designs that maximize the minimum of D-or D1-efficiencies over all models in the given class. We show that our optimal designs are efficient for determining an appropriate model from the postulated class, quite efficient for estimating model parameters in the identified model and also robust with respect to model misspecification. To facilitate the use of optimal design ideas in practice, we have also constructed a website that freely enables practitioners to generate a variety of optimal designs for a range of models and also enables them to evaluate the efficiency of any design. This is an electronic reprint of the original article published by the ISI/BS in Bernoulli, 2010, Vol. 16, No. 4, 1164-1176. This reprint differs from the original in pagination and typographic detail. 1350-7265 c 2010 ISI/BSOptimal designs for discriminating between dose-response models 1165 include how to select the number of dose levels to observe the continuous outcome, where these levels are and how many repeated observations to take at each of these levels. This work assumes, for the sake of simplicity, that there is only one independent variable, the dose level and only non-sequential designs are considered.When we have competing models, a design should be able to discriminate among these models and select the most appropriate ones. Dette [5][6][7] found optimal discrimination designs for polynomial regression models, and Dette and Roeder [9] and Dette and Haller [10] found optimal discrimination designs for trigonometric and Fourier regression models, respectively. T -optimal designs are usually used to discriminate between homoscedastic models with normal errors [1-3, 12]. For discriminating non-linear models, only numerical results are possible; Lopez-Fidalgo et al. [16] investigated optimal designs maximizing a weighted average of two T -criterion functions and Lopez-Fidalgo et al. [17] constructed T -optimal designs for Michaelis-Menten-like models. When the design problem involves model discrimination and another optimality criterion, the problem is more complicated. Hill et al. [12] was among the first to consider studies with two goals: model discrimination and estimation of model parameters. Dette et al. [8] gave a concrete example where they wanted to discriminate between the Michaelis-Menten-model and the Emax model and estimate model parameters in an enzyme-kinetic study. A key reason for there having been so little research into such design problems for non-linear models is that there are serious technical difficulties. The motivation for this work comes from recent proposals by Pie...

Optimal Designs for Dose Finding Studies with an Active Control

“…An important problem in this context is the construction of efficient designs for model discrimination, which has been discussed for dose response models without AC in and Dette, Pepelyshev, Shpilev and Wong (2010). A promising direction consists in the construction of T -optimal designs (see Dette and Titoff (2009)) to discriminate efficiently between the linear and EMAX model that was discussed in Sections 3.4 and 3.5.…”

“…(), Dragalin et al . (), Dette, Bretz, Pepelyshev and Pinheiro () and Dette, Kiss, Bevanda and Bretz () among others). However, to our best knowledge, optimal design problems for active controlled dose finding studies have not been considered in the literature so far.…”

An equivalence theorem for design optimality with respect to a multi-objective criterion

“…In toxicology studies, we may have a continuous response and several possible models for the true mean response. As in Dette et al (2010), we assume the following rival models for the mean response of the outcome Y :…”