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In this study, methods for efficient construction of A-, MV-, D- and E-optimal or near-optimal block designs for two-colour cDNA microarray experiments with array as the block effect are considered. Two algorithms, namely the array exchange and treatment exchange algorithms together with the complete enumeration technique are introduced. For large numbers of arrays or treatments or both, the complete enumeration method is highly computer intensive. The treatment exchange algorithm computes the optimal or near-optimal designs faster than the array exchange algorithm. The two methods however produce optimal or near-optimal designs with the same efficiency under the four optimality criteria. [ABSTRACT FROM AUTHOR]

Candidate locallyD-optimal designs for the binary two-variable logistic model with no interaction, which comprise 3 and 4 support points lying in the first quadrant of the two-dimensional Euclidean space, were introduced by Haines et al. (D-optimal designs for logistic regression in two variables. In: Lopez-Fidalgo J, Rodrigez-Diaz JM, Torsney B, editors. MODA8 – advances in model-oriented designs and analysis. Heidelberg: Physica-Verlag; 2007. p. 91–98). The authors proved algebraically the globalD-optimality of the 3-point design for the special case in which the intercept parameter is equal to−1.5434. However for other selected values of the intercept parameter, the globalD-optimality of the proposed 3- and 4-point designs was only demonstrated numerically. In this paper, we provide analytical proofs of theD-optimality of these 3- and 4-point designs for all negative and zero intercept parameters of the binary two-variable logistic model with no interaction. The results are extended to the construction ofD-optimal designs on a rectangular design space and illustrated by means of two examples of which one is a real example taken from the literature. [ABSTRACT FROM AUTHOR]

In dose-response studies, Wadley’s problem occurs when the number of organisms that survive exposure to varying doses of a treatment is observed but the number initially present is unknown. The unknown number of organisms initially treated has traditionally been modelled by a Poisson distribution, resulting in a Poisson distribution for the number of survivors with parameter proportional to the probability of survival. Data in this setting are often overdispersed. This study revisits the beta-Poisson distribution and considers its effectiveness in modelling overdispersed data from a Wadley’s problem setting. [ABSTRACT FROM PUBLISHER]

This article reports the application of the annealing algorithm to the construction of exact D-, I-, and G-optimal designs for polynomial regression of degree 5 on the interval [-1, 1] and for the second-order model in two factors on the design space [-1, 1] x [-1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and efficiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized. [ABSTRACT FROM AUTHOR]