Barbara Bogacka

Optimum design: 2000

Preface. Part I: Theory. Some History Leading to Design Criteria for Bayesian Prediction A.C. Atkinson, V.V. Fedorov. Optimal Designs for the Evaluation of an Extremum Point R.C.H. Cheng, et al. On Regression Experiment Design in the Presence of Systematic Error S.M. Ermakov. Grobner Basis Methods in Mixture Experiments and Generalisations B. Giglio, et al. Efficient Designs for Paired Comparisons with a Polynomial Factor H. Grossmann, et al. On Generating and Classifying All qn-m Regular Designs for Square-Free q P.J. Laycock, P.J. Rowley. Second-Order Optimal Sequential Tests M.B. Malyutov, I.I. Tsitovich. Variational Calculus in the Space of Measures and Optimal Design I. Molchanov, S. Zuyev. On the Efficiency of Generally Balanced Designs Analysed by Restricted Maximum Likelihood H. Monod. Concentration Sets, Elfving Sets and Norms in Optimum Design A. Pazman. Sequential Construction of an Experimental Design from an I.I.D. Sequence of Experiments without Replacement L. Pronzato. Optimal Characteristic Designs for Polynomial Models J.M. Rodriguez-Diaz, J. Lopez-Fidalgo. A Note on Optimal Bounded Designs M. Sahm, R. Schwabe. Construction of Constrained Optimal Designs B. Torsney, S. Mandal. Part II: Applications. Pharmaceutical Applications of a Multi-Stage Group Testing Method B. Bond, et al. Block Designs for Comparison of Two Test Treatments with a Control S.M. Bortnick, et al. Optimal Sampling Design with Random Size Clusters for a Mixed Model with Measurement Errors A. Giovagnoli, L. Martino. Optimizing a Unimodal Response Function for Binary Variables J. Hardwick, Q.F. Stout. An Optimizing Up-And-Down Design E.E. Kpamegan, N.Flournoy. Further Results on Optimal and Efficient Designs for Constrained Mixture Experiments R.J. Martin, et al. Coffee-House Designs W.G. Muller. (D,t, C)-Optimal Run Orders L. Tack, M. Vandebroek. Optimal Design in Flexible Models, including Feed-Forward Networks and Nonparametric Regression D.M. Titterington. On Optimal Designs for High Dimensional Binary Regression Models B. Torsney, N. Gunduz. Planning Herbicide Dose-Response Bioassays Using the Bootstrap S.S. Zocchi, C.G. Borges Demetrio. Photo Gallery. Optimum Design 2000: List of Participants.

Compound D - and D S -optimum designs for determining the order of a chemical reaction

Estimation of the order of a chemical reaction is often at least as important as estimation of the rate of the reaction. Locally optimum experimental designs are found for the order and the rate, separately and together. Compound D-optimum designs provide a method for designing experiments with specified efficiency for rate or order determination. A relationship between the compound designs and D-optimum designs for both rate and order aids interpretation of the plots of design efficiencies. Bayesian designs incorporating prior uncertainty are exemplified. Monte Carlo sampling of the prior is used to design an experiment for the esterification of acetic anhydride.

Compound and other optimum designs for systems of nonlinear differential equations arising in chemical kinetics

Abstract The optimum design of experiments for nonlinear models requires parameter sensitivities, that is the derivatives of the response with respect to the parameters. If the differential equations forming the kinetic model do not have an analytical solution, numerical derivatives have to be used. We describe the “direct” method for calculating the sensitivities and apply it to the design of experiments for estimating the order of chemical reactions.

D- and T-optimum designs for the kinetics of a reversible chemical reaction

Abstract The purpose of our paper is to exemplify D-optimum designs for parameter estimation in the kinetics of a reversible chemical reaction and to find T-optimum designs for model discrimination, as a method of determining the order of reaction. Although the statistical methods are similar for consecutive and reversible reactions, the designs have markedly different properties. As a chemical example we use the esterification of ethanol and acetic acid. On the basis of this example we discuss the geometrical interpretation of D-optimum designs, which is strictly connected with the course of reaction and permits instructive comparisons of reversible and consecutive chemical processes. The methods of optimum experimental design provide an alternative to conventional designs for parameter estimation and model discrimination. We show how much more efficient the optimum design can be for parameter estimation than relying on a conventional design. We calculate a sequential T-optimum design and propose a statistical test verifying a hypothesis on the order of reaction. We also present the theoretical background of information matrices for non-linear models, D-optimum designs for parameter estimation and T-optimum designs for model discrimination.

Optimum Design of Experiments for Enzyme Inhibition Kinetic Models

We find closed-form expressions for the D-optimum designs for three- and four-parameter nonlinear models arising in kinetic models for enzyme inhibition. We calculate the efficiency of designs over a range of parameter values and make recommendations for design when the parameter values are not well known. In a three-parameter experimental example, a standard design has an efficiency of 18.2% of the D-optimum design. Experimental results from a standard design with 120 trials and a D-optimum design with 21 trials give parameter estimates that are in close agreement. The estimated standard errors of these parameter estimates confirm our theoretical results on efficiency and thus on the serious savings that can be made by the use of D-optimum designs.

Optimum experimental designs for dynamic systems in the presence of correlated errors

The problem of determining an optimal measurement time schedule for identification of unknown parameters in multiresponse systems when correlations between observations occur is considered. The measurement process is performed by collecting data at discrete time instants from several outputs. An observation plan is proposed based on a scalar measure of the Fisher information matrix as the design criterion quantifying the accuracy of parameter estimators. A numerical procedure is proposed to determine approximations of optimum designs in the case of correlated measurement errors. The approach is illustrated with an example of the multi-output system of equations describing a chemical kinetic reaction.

Construction of T -Optimum Designs for Multiresponse Dynamic Models

The paper aims at developing the underlying theory and constructing an efficient procedure for determining optimal experimental conditions for discriminating between several rival multivariate statistical models where the expected response is given by ordinary differential equations. The method elaborated is validated on a simulation example.

Efficient Sampling Windows for Parameter Estimation in Mixed Effects Models

In the paper we present a method of calculating an efficient window design for parameter estimation in a non-linear mixed effects model. We define a window population design on the basis of a continuous design for such a model. The support points of the design belong to intervals whose boundaries are determined in a way which ensures that the efficiency of the design is high; also the width of the intervals is related to the dynamic system’s behaviour.

Comparison of Two Design Optimality Criteria Applied to a Nonlinear Model

Abstract In chemical kinetic or pharmacokinetic studies, many mathematical models are nonlinear with respect to the model parameters. This may cause serious problems for parameter estimation. A D-optimum design, which is very popular and effective for linear models, is not so good for nonlinear models with strong parameter curvature. In this article, we compare two optimality criteria applied to a nonlinear model. Both of them minimize the volume of the confidence ellipsoid of the parameters: D-optimality uses a linear approximation of the volume, and Q-optimality uses a quadratic approximation. We compute the relative design efficiencies and use a parameter-effect curvature measure to compute the number of observations that reduces the “curvature effect” to a specified level and improves the parameter estimation. The calculated designs differ significantly, and the Q-optimum design shows increasingly better statistical properties as the curvature increases. We present our results both graphically and as tables of numerical values.

Optimality of Generally Balanced Experimental Block Designs

The subject of optimality of block designs under the mixed model has been undertaken in the eighties. Up to today there are not many papers considering the problem, contrary to the case of the fixed model. The papers of Bagchi (1987a,b), Mukhopdhyay (1981), Khatri and Shah (1984), Bhattacharya and Shah (1984) or Jacroux (1989) deal with the optimality of block designs under mixed model of a special simple kind.