Algorithmic construction of optimal block designs for two-colour cDNA microarray experiments using the linear mixed effects model

References

• Aptech Systems, Inc. 2017. Gauss software, version 17 [Computer software manual]. Chandler, AZ. Retrieved from http://www.aptech.com/
   Google Scholar
• Bailey, R. 2007. Designs for two-colour microarray experiments. Journal of the Royal Statistical Society: Series C (Applied Statistics) 56 (4):365–94.
   Google Scholar
• Bailey, R. 2009. Designs for dose–escalation trials with quantitative responses. Statistics in medicine 28 (30):3721–38.
   Google Scholar
• Bailey, R., K. Schiffl, and R.-D. Hilgers. 2013. A note on robustness of d-optimal block designs for two-colour microarray experiments. Journal of Statistical Planning and Inference 143 (7):1195–202.
   Google Scholar
• Churchill, G. A. 2002. Fundamentals of experimental design for cdna microarrays. Nature Genetics 32:490–95.
   Google Scholar
• Dey, A. 2010. Incomplete block designs. World Scientific. Singapore.
   Google Scholar
• Fedorov, V. V. 1972. Theory of optimal experiments. Academic Press. New York.
   Google Scholar
• Gemechu, D. B., L. K. Debusho, and L. M. Haines. 2014. A-optimal designs for two-colour cDNA microarray experiments using the linear mixed effects model. In Annual Proceedings of the South African Statistical Association Conference (Vol. 2014, No. Congress 1, pp. 33–40). South African Statistical Association (SASA).
   Google Scholar
• Gemechu, D. B., L. K. Debusho, and L. M. Haines. 2015. A-and d-optional row-column designs for two-colour cdna microarray experiments using linear mixed effects models. South African Statistical Journal 49 (2):153–68.
   Google Scholar
• Haines, L. M. 2015. Introduction to linear models. In Handbook of design and analysis of experiments:63–96. Taylor & Francis/CRC Press. Boca Raton, FL.
   Google Scholar
• Haines, L. M., and A. E. Clark. 2014. The construction of optimal designs for dose-escalation studies. Statistics and Computing 24 (1):101–09.
   Google Scholar
• Huang, H. Z., H. B. Fang, and M. Tan. 2017. Experimental design for multi-drug combination studies using signalling networks. Biometrics. In Press, DOI: 10.1111/biom.12777.
   Google Scholar
• Jones, B. 1976. An algorithm for deriving optimal block designs. Technometrics 18 (4):451–58.
   Google Scholar
• Jones, B., and J. A. Eccleston. 1980. Exchange and interchange procedures to search for optimal designs. Journal of the Royal Statistical Society, Series B 42:291–97.
   Google Scholar
• Jones, B., and C. J. Nachtsheim. 2011. A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology 43:1–15.
   Google Scholar
• Kerr, M. K. 2003. Design considerations for efficient and effective microarray studies. Biometrics 59 (4):822–28.
   Google Scholar
• Kerr, M. K., and G. A. Churchill. 2001a. Experimental design for gene expression microarrays. Biostatistics 2 (2):183–201.
   Google Scholar
• Kerr, M. K., and G. A. Churchill. 2001b. Statistical design and the analysis of gene expression microarray data. Genetical Research 77:123–28.
   Google Scholar
• Landgrebe, J., F. Bretz, and E. Brunner. 2006. Efficient design and analysis of two colour factorial microarray experiments. Computational Statistics & Data Analysis 50 (2):499–517.
   Google Scholar
• Meyer, R. K., and C. J. Nachtsheim. 1995. The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37 (1):60–69.
   Google Scholar
• Nguyen, N.-K., and E. Williams. 2006. Experimental designs for 2-colour cdna microarray experiments. Applied Stochastic Models in Business and Industry 22 (5-6):631–38.
   Google Scholar
• Press, W. H., B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, and P. B. Kramer. 2007. Numerical recipes: the art of scientific computing. Cambridge University Press, New York.
   Google Scholar
• Rathore, A., R. Parsad, and V. Gupta. 2006. Computer aided search of efficient block designs for making all possible pairwise treatment comparisons. In J. Statist. Appl.: The Journal Forum Interdis. MathVol. 1. 15–33.
   Google Scholar
• Russell, K., J. Eccleston, and G. Knudsen. 1981. Algorithms for the construction of (m, s)-optimal block designs and row-column designs. Journal of Statistical Computation and Simulation 12 (2):93–105.
   Google Scholar
• Sarkar, A., R. Parsad, A. Rathore, and Y. Gupta. 2007. Efficient block designs for 2-colour microarray experiments. Journal of Indian Society of Agricultural Statistics 61 (2):227–48.
   Google Scholar
• Schiffl, K., and R.-D. Hilgers. 2012. A-optimal designs for two-color microarray experiments for treatment-control and all-to-next contrasts. Communications in Statistics-Simulation and Computation 41 (7):1142–51.
   Google Scholar
• Shah, K., and B. Sinha. 1989. Theory of optimal designs, Vol. 54 of Lecture Notes in Statistics. New York: Springer.
   Google Scholar
• Wilson, R. J. 1985. An introduction to graph theory (3rd ed.). Longman, Harlow, England.
   Google Scholar
• Wit, E., A. Nobile, and R. Khanin. 2005. Near-optimal designs for dual channel microarray studies. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (5):817–30.
   Google Scholar
• Wolfram Research, Inc. 2017. Mathematica, version 11.1 [Computer software manual]. Champaign, Illinois. Retrieved from http://www.wolfram.com/
   Google Scholar
• Yang, Y. H., and T. Speed. 2002. Design issues for cdna microarray experiments. Nature Reviews Genetics 3 (8):579–88.
   Google Scholar