^{2}^{1}Division of Biometry, Institute of Agronomy, National Taiwan
University, Taipei, Taiwan ^{
2}Institute of Statistical Science, Academia Sinica, Taipei, TaiwanMicroarray experiments now make it possible to simultaneously monitor the mRNA expression levels of thousands of genes between different biological states. These large-scale experiments can be very costly in terms of equipment, material, consumables, time, etc. As discussed in Kerr and Churchill (2001) and Yang and Speed (2002), the most important design issue concerning the two-color cDNA microarray experiments is to determine which mRNA samples (treatments) are to be labeled with which fluorescent dye; and which are to be hybridized together on the same slide under various scientific and physical constraints. In this study, we attempt to tackle this problem via a rigorous statistical optimum design construction approach. In particular, we focus on constructing good designs for identification of the differentially expressed genes in cDNA microarray experiments under the constraint that the number of slides is fixed and the number of mRNA samples is expected to be available. We first develop a statistical model for characterizing the two major sources of systematic variation in a two-color cDNA microarray experiment, i.e. the variation between the two fluorescent dyes and the variation between distinct slides. It can be shown that the proposed model is statistically equivalent to the ANOVA model for the classical row-column design if we observe their corresponding information matrices. Conventionally, the row-column designs have been used to control two nuisance (blocking) factors in an experiment. Hence the study of the row-column v-treatment designs (2 refers to the two fluorescent dyes; the number of slides used and v the number of mRNA samples) is our main focus. We propose a heuristic algorithm to generate good row-column designs under consideration based on the proposed model and A-optimality criterion. A series of highly efficient designs (in terms of A-optimality criterion) have been tabulated to assist scientists conducting cDNA microarray experiments. Furthermore, we investigate some statistical properties for the designs obtained. It can be analytically proved that some of the designs we have obtained are A-optimal designs over the class of all possible competing designs |

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