Optimal Design of Single Factor cDNA Microarray Experiments and Mixed Models for Gene Expression Data

(ABSTRACT) Microarray experiments are used to perform gene expression profiling on a large scale. E-and A-optimality of mixed design was established for experiments with up to 26 different varieties and with the restriction that the number of arrays available is equal to the number of varieties. Because the IBD setting only allows for a single blocking factor (arrays), the search for optimal designs was extended to the Row-Column Design (RCD) setting with blocking factors dye (row) and array (column). Relative efficiencies of these designs were further compared under analysis of variance (ANOVA) models. We also compared the performance of classification analysis for the interwoven loop and the replicated reference designs under four scenarios. The replicated reference design was favored when gene-specific sample variation was large, but the interwoven loop design was preferred for large variation among biological replicates. We applied mixed model methodology to detection and estimation of gene differential expression. For identification of differential gene expression, we favor contrasts which include both variety main effects and variety by gene interactions. In terms of t-statistics for these contrasts, we examined the equivalence between the one-and two-step analyses under both fixed and mixed effects models. We analytically established conditions for equivalence under fixed and mixed models. We investigated the difference of approximation with the two-step analysis in situations where equivalence does not hold. The significant difference between the one-and two-step mixed effects model was further illustrated through Monte Carlo simulation and three case studies. We implemented the one-step analysis for mixed models with the ASREML software. Acknowledgments I would like to thank Dr. Ina Hoeschele and Dr. Keying Ye, who have been there for me every step of the way, teaching, encouraging and helping. I greatly appreciate the time and effort that they have given to me and to my work, I have enjoyed working with them. What they have taught me in the last few years will benefit me all my life, and I am grateful to them forever. I would also like to recognize the contribution of my committee members, Dr. am so thankful to them for agreeing to serve on my committee and for those helpful and constructive suggestions. I would also like to thank Dr. John P. Morgan, my former committee member, for those stimulating discussions about design of experiment with block size two and for providing references that have greatly improved this work.