Optimal designs for multivariable spline models

In this paper, we investigate optimal designs for multivariate additive spline regressionmodels. We assume that the knot locations are unknown, so must be estimated from thedata. In this situation, the Fisher information for the full parameter vector depends on theunknown knot locations, resulting in a non-linear design problem. We show that locally,Bayesian and maximin D-optimal designs can be found as the products of the optimaldesigns in one dimension. A similar result is proven for Q-optimality in the class of allproduct design

Maximin optimal designs for the compartmental model

For the compartmental model we determine optimal designs, which are robust against misspecifications of the unknown model parameters. We propose a maximin approach based on D-efficiencies and provide designs that are optimal with respect to the particular choice of various parameter regions. --Compartmental model,robust optimal design,maximin Doptimality,local optimality

Compound Optimal Designs for Percentile Estimation in Dose-Response Models with Restricted Design Intervals

In dose-response studies, the dose range is often restricted due to ethics concerns over drug toxicity and/or efficacy, particularly when human subjects are involved. We present locally optimal designs for the estimation of several percentiles simultaneously on restricted as well as unrestricted design intervals. Our results are applicable to most of the commonly applied link functions with respect to the model under consideration. This work is a generalization of Dai (2000) where he showed that the same results hold for the logit model using Elfving?s approach on trace optimal design (Elfving, 1952). --Dose-response model,link function,percentile estimation,compound optimal design,A-optimality

Constrained optimal discriminating designs for Fourier regression models

In this article, the problem of constructing efficient discriminating designs in a Fourier regression model is considered. We propose designs which maximize the efficiency for the estimation of the coefficient corresponding to the highest frequency subject to the constraints that the coefficients of the lower frequencies are estimated with at least some given efficiency. A complete solution is presented using the theory of canonical moments, and for the special case of equal constraints the optimal designs can be found analytically. --Constrained optimal designs,trigonometric regression,D1-optimal designs,Chebyshev polynomials,canonical moments

Geometric construction of optimal designs for dose-responsemodels with two parameters

In dose-response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We derive optimal designs for estimating the underlying dose-response curve for a restricted or unrestricted dose range with respect to a broad class of optimality criteria. The underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form. These include the fundamental binary response models – the logit and the probit as well as the skewed versions of these models. Our methodology is based on a new geometric interpretation of optimal designs with respect to Kiefer?s [Omega]p-criteria in regression models with two parameters, which is of independent interest. It provides an intuitive illustration of the number and locations of the support points of [Omega]p-optimal designs. Moreover, the geometric results generalize the classical characterization of D-optimal designs by the minimum covering ellipsoid [see Silvey (1972) or Sibson (1972)] to the class of Kiefer?s [Omega]p-criteria. The results are illustrated through the re-design of a dose ranging trial. --Binary response model,Dose ranging,Dose-response,Dual problem,Link function,Locally compound optimal design,Minimum ellipse

Optimal designs for dose-response models with restricted design spaces

In dose response studies, the dose range is often restricted due to concerns over drug toxicity and/or efficacy. We present restricted and unrestricted interval locally optimal designs with respect to a very general class of optimality criteria for estimating the underlying dose response curve. The underlying curve belongs to a diversified set of link functions suitable for the dose response studies and having a common canonical form. These include the fundamental binary response models – the logit and the probit as well as the skewed versions of these models. The results are illustrated through the re-design of a dose ranging trial conducted at the Merck Research Laboratories (Zeng and Zhu, 1997). This work is a generalization of the results of Dai and Zhu (2002) in terms of the design interval, the underlying dose response curve and the optimality criterion. --Binary response model,Dose ranging,Dose response,Link function,General Equivalence Theorem,Locally compound optimal design

Optimal Discrimination Designs for Exponential Regression Models

We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw (1995) or Gibaldi and Perrier (1982). We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory?s Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach. --Compartmental Model,Model Discrimination,Discrimination Design,Locally Optimal Design,Robust Optimal Design,Maximin Optimal Design

Some robust design strategies for percentile estimation in binary response models

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. --Binary response model,robust optimal design,c-efficiency,percentile estimation,multi-objective designs

Numerical construction of maximin optimal designs for binary response models

For the binary response model, we determine optimal designs which are robust wit respect to the misspecifications of the unknown parameters. We propose a maximin approach and provide a numerical method to identify the best two point designs for the commonly applied link functions. This method is broadly applicable and can be extended to designs with a given number (>= 2) of support points and further link functions. The results are illustrated for the logistic and probit model, for which the maximin optimal designs are found explicitly. --Binary response model,robust optimal design,maximin D-optimality,Bayesian D-optimality,prior distribution