Title page for ETD etd-03072003-100835

Type of Document Dissertation
Author Yang, Xiao
Author's Email Address xiyang@vt.edu
URN etd-03072003-100835
Title Optimal Design of Single Factor cDNA Microarray experiments and Mixed Models for Gene Expression Data
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Hoeschele, Ina Committee Co-Chair
Ye, Keying Committee Co-Chair
Prins, Samantha C. Bates Committee Member
Smith, Eric P. Committee Member
Terrell, George R. Committee Member
  • Optimal Design
  • Microarray Experiment
  • Mixed Models
Date of Defense 2003-02-25
Availability unrestricted
Microarray experiments are used to perform gene expression profiling on a large scale. E- and

A-optimality of mixed designs 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


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.

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