A- and D-optimal row-column designs for two-colour cDNA microarray experiments using linear mixed effects models

Abstract

Microarray experiments help scientists to study the expression level of thousands of genes simultaneously. These experiments have many design challenges, such as, for example, which
mRNA samples should be co-hybridized together and which treatments should be labelled with which fluorescent dye. Therefore a carefully designed microarray experiment to obtain efficient and reliable data so as to ensure the precise estimate of comparisons of interest is required. The present paper is concerned with A- and D-optimal row-column designs for two-colour microarray experiments, with the array and dye effects treated as the column and row effects, respectively. Linear mixed effects models were used to describe experiments for which a comparison of all possible pairs of treatments is of particular interest by taking the arrays as random column effects. The results of this study show that the optimal row-column designs under the linear fixed effects model are not necessarily optimal under the linear mixed effects model setting.