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Designs for two‐colour microarray experiments

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  • R. A. Bailey

Abstract

Summary. Designs for two‐colour microarray experiments can be viewed as block designs with two treatments per block. Explicit formulae for the A‐ and D‐criteria are given for the case that the number of blocks is equal to the number of treatments. These show that the A‐ and D‐optimality criteria conflict badly if there are 10 or more treatments. A similar analysis shows that designs with one or two extra blocks perform very much better, but again there is a conflict between the two optimality criteria for moderately large numbers of treatments. It is shown that this problem can be avoided by slightly increasing the number of blocks. The two colours that are used in each block effectively turn the block design into a row–column design. There is no need to use a design in which every treatment has each colour equally often: rather, an efficient row–column design should be used. For odd replication, it is recommended that the row–column design should be based on a bipartite graph, and it is proved that the optimal such design corresponds to an optimal block design for half the number of treatments. Efficient row–column designs are given for replications 3–6. It is shown how to adapt them for experiments in which some treatments have replication only 2.

Suggested Citation

  • R. A. Bailey, 2007. "Designs for two‐colour microarray experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 365-394, August.
    • Handle: RePEc:bla:jorssc:v:56:y:2007:i:4:p:365-394
    DOI: 10.1111/j.1467-9876.2007.00582.x
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    References listed on IDEAS

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    1. M. Kathleen Kerr, 2003. "Design Considerations for Efficient and Effective Microarray Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 822-828, December.
    2. Ernst Wit & Agostino Nobile & Raya Khanin, 2005. "Near‐optimal designs for dual channel microarray studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(5), pages 817-830, November.
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    1. Harman, Radoslav & Filová, Lenka, 2014. "Computing efficient exact designs of experiments using integer quadratic programming," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1159-1167.
    2. Lima Passos, Valéria & Tan, Frans E.S. & Berger, Martijn P.F., 2011. "Cost-efficiency considerations in the choice of a microarray platform for time course experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 944-954, January.
    3. Kerr Kathleen F., 2012. "Optimality Criteria for the Design of 2-Color Microarray Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(1), pages 1-9, January.
    4. Godolphin, J.D. & Warren, H.R., 2014. "An efficient procedure for the avoidance of disconnected incomplete block designs," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1134-1146.

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