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Statistical designs for two-color microarray experiments involving technical replication. (English) Zbl 1157.62542
Summary: In a two-color microarray experiment, we consider the issues of determination of which mRNA samples are to be labeled with which fluorescent dye and which mRNA samples are to be hybridized together on the same slide. Specific attention is given to the test-control experiments whose primary interest lies in comparing several test treatments with a control treatment. A statistical linear model is proposed to characterize two major sources of systematic variation: the variation among distinct slides and that between fluorescent dyes. Furthermore, the possible correlation due to technical replication is also incorporated into the model. A series of A-optimal or highly efficient designs are generated from a heuristic algorithm based on the proposed model. It is shown that the obtained designs are robust not only to the variation of the correlation because of technique replication, but also to the loss of one or two slides. In addition, the comparative experiments involving technical replication are also discussed.

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62K05 Optimal statistical designs 92C40 Biochemistry, molecular biology
daMA; nauty
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##### References:
 [1] Bechhofer, B.E.; Tamhane, A.C., Incomplete block designs for comparing treatments with a control: general theory, Technometrics, 23, 45-57, (1981) · Zbl 0472.62080 [2] Graybill, F.A., Matrices with applications in statistics, (1983), Wadsworth CA, USA · Zbl 0496.15002 [3] Glonek, G.F.; Solomon, P.J., Factorial and time course designs for cdna microarray experiments, Biostatistics, 5, 89-111, (2004) · Zbl 1096.62077 [4] Hedayat, A.S.; Jacroux, M.; Majumdar, D., Optimal designs for comparing test treatments with controls, Statist. sci., 3, 462-491, (1988) · Zbl 0955.62616 [5] Jacroux, M., The A-optimality of block designs for comparing test treatments with a control, J. amer. statist. assoc., 84, 310-317, (1989) · Zbl 0687.62062 [6] Kerr, M.K.; Churchill, G.A., Experimental design for gene expression microarrays, Biostatistics, 2, 183-201, (2001) · Zbl 1097.62562 [7] Landgrebe, J.; Bretz, F.; Brunner, E., Efficient design and analysis of two colour factorial microarray experiments, Comput. statist. data anal., 50, 499-517, (2006) · Zbl 1431.62499 [8] McKay, B., 1991. “Nauty“, “makeg” and “geng” C-programs available at $$\langle$$http://cs.anu.edu.au/people/ bdm/nauty/⟩. [9] Speed, T.P.; Yang, Y.H., Direct versus indirect designs for cdna microarray experiments, Sankhya ser. A, 64, 3, 707-721, (2002) · Zbl 1192.62240 [10] Ture, T.E., Optimal row – column designs for multiple comparisons with a control: a complete catalog, Technometrics, 36, 292-299, (1994) · Zbl 0798.62081 [11] Yang, Y.H.; Speed, T.P., Design issues for cdna microarray experiments, Nat. rev. genet., 3, 579-587, (2002)
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