Banerjee, Tathagata; Mukerjee, Rahul Optimal factorial designs for CDNA microarray experiments. (English) Zbl 1137.62074 Ann. Appl. Stat. 2, No. 1, 366-385 (2008). Summary: We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the more common orthogonal parametrization. First, analytical results are given for the \(2\times 2\) factorial. Since practical applications often involve a more complex factorial structure, we next explore general factorials and obtain a collection of optimal designs in the saturated, that is, most economic, case. This, in turn, is seen to yield an approach for finding optimal or efficient designs in the practically more important nearly saturated cases. Thereafter, the findings are extended to the more intricate situation where the underlying model incorporates dye-coloring effects, and the role of dye-swapping is critically examined. Cited in 10 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis 62K05 Optimal statistical designs 62K15 Factorial statistical designs 92C40 Biochemistry, molecular biology Keywords:admissibility; augmented design; baseline parametrization; dye-swapping; interaction; main effect; orthogonal parametrization; saturated design; weighted optimality Software:daMA × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Altman, N. S. and Hua, J. (2006). Extending the loop design for two-channel microarray experiments., Genet. Res. 88 153-163. [2] Amaratunga, D. and Cabrera, J. (2004)., Exploration and Analysis of DNA Microarray and Protein Array Data . Wiley, New York. · Zbl 1040.62096 [3] Banerjee, T. and Mukerjee, R. (2008). Supplement to “Optimal factorial designs for CDNA microarray experiments.” DOI:, 10.1214/07-AOAS144SUPP. · Zbl 1137.62074 · doi:10.1214/07-AOAS144SUPP [4] Bueno Filho, J. S. S., Gilmour, S. G. and Rosa, G. J. M. (2006). Design of microarray experiments for genetical genomics studies., Genetics 174 945-957. [5] Churchill, G. A. (2002). Fundamentals of experimental design for cDNA microarrays., Nature Genetics ( Suppl. ) 3 490-495. [6] Dey, A. and Mukerjee, R. (1999)., Fractional Factorial Plans . Wiley, New York. · Zbl 0930.62081 [7] Dobbin, K. and Simon, R. (2002). Comparison of microarray designs for class comparison and class discovery., Bioinformatics 18 1438-1445. [8] Glonek, G. F. V. and Solomon, P. J. (2004). Factorial and time course designs for cDNA microarray experiments., Biostatistics 5 89-111. · Zbl 1096.62077 · doi:10.1093/biostatistics/5.1.89 [9] Grossman, H. and Schwabe, R. (2008). The relationship between optimal designs for microarray and paired comparison experiments., [10] Gupta, S. (2006). Balanced factorial designs for cDNA microarray experiments., Comm. Statist. Theory Methods 35 1469-1476. · Zbl 1105.62110 · doi:10.1080/03610920600694587 [11] Gupta, S. and Mukerjee, R. (1989)., A Calculus for Factorial Arrangements . Springer, Berlin. · Zbl 0708.62067 [12] Kendziorski, C., Irizarry, R. A., Chen, K. S., Haag, J. D. and Gould, M. N. (2005). On the utility of pooling biological samples in microarray experiments., Proc. Natl. Acad. Sci. USA 102 4252-4257. [13] Kerr, K. F. (2006). Efficient, 2 k factorial designs for blocks of size 2 with microarray applications. J. Qual. Technol. 38 309-318. [14] Kerr, M. K. (2003). Design considerations for efficient and effective microarray studies., Biometrics 59 822-828. JSTOR: · Zbl 1218.62114 · doi:10.1111/j.0006-341X.2003.00096.x [15] Kerr, M. K. and Churchill, G. A. (2001a). Experimental design for gene expression microarrays., Biostatistics 2 183-201. · Zbl 1097.62562 · doi:10.1093/biostatistics/2.2.183 [16] Kerr, M. K. and Churchill, G. A. (2001b). Statistical design and the analysis of gene expression microarray data., Genet. Res. 77 123-128. [17] Kiefer, J. C. (1975). Construction and optimality of generalized Youden designs. In, A Survey of Statistical Design and Linear Models (J. N. Srivastava, ed.) 333-353. North-Holland, Amsterdam. · Zbl 0313.62057 [18] Landgrebe, J., Bretz, F. and Brunner, E. (2006). Efficient design and analysis of two colour factorial microarray experiments., Comput. Statist. Data Anal. 50 499-517. · Zbl 1431.62499 [19] Majumdar, D. (1996). Optimal and efficient treatment-control designs. In, Handbook of Statistics 13 (S. Ghosh and C. R. Rao, eds.) 1007-1053. North-Holland, Amsterdam. · Zbl 0911.62072 [20] Nguyen, D., Arpat, A. Wang, N. and Carroll, R. J. (2002). DNA microarray experiments: Biological and technical aspects., Biometrics 58 701-717. JSTOR: · Zbl 1210.62197 · doi:10.1111/j.0006-341X.2002.00701.x [21] Rosa, G. J. M, Steibel, J. P. and Tempelman, R. J. (2005). Reassessing design and analysis of two-color microarray experiments using mixed effects models., Comp. Funct. Genomics 6 123-131. [22] Silvey, S. D. (1980)., Optimal Design . Chapman and Hall, London. · Zbl 0468.62070 [23] Wang, P. C. (2004). Designing two-level fractional factorial experiments in blocks of size two., Sankhyā Ser. A 66 327-342. · Zbl 1193.62146 [24] Wit, E., Nobile, A. and Khanin, R. (2005). Near-optimal designs for dual-channel microarray studies., Appl. Statist. 54 817-830. JSTOR: · Zbl 1490.62385 · doi:10.1111/j.1467-9876.2005.00519.x [25] Wu, C. F. J. and Hamada, M. (2000)., Experiments : Planning , Analysis and Parameter Design Optimization . Wiley, New York. · Zbl 0964.62065 [26] Yang, Y. J., and Draper, N. R. (2003). Two-level factorial and fractional factorial designs in blocks of size two., J. Qual. Technol. 35 294-305. [27] Yang, Y. H. and Speed, T. (2002). Design issues for cDNA microarray experiments., Nature Genetics ( Suppl. ) 3 579-588. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.