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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
\end{center}
\begin{center}
  4:15 p.m., Tuesday, June 21, 2005\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
\end{center}


\begin{center}
  \textsl{Cyr Emile M'LAN, Ph.D.}\\
  Assistant Professor\\
  University of Connecticut\\
  215 Glenbrook Road, U-4120\\
Storrs, CT, 06269 \\
\end{center}
\begin{center}
  \textbf{ESTIMATING GLOBAL AND GENE-SPECIFIC PARAMETERS IN UNBALANCED
    MULTIFACTORIAL ANOVA MODEL OF MOICROARRAY DATA}
\end{center}
The ability to measure thousands of mRNA transcript expressions
simultaneously using high-throughput genomic technology has
revolutionized the field of Genetics. In our study, RNA from a
collection of Lymphoblastoid Cell Lines were hybridized onto
Affymetrix genechip arrays.  The goal of this study is to discover the
genes that are highly variable in the human population subgroups. An
ANOVA model was performed and the effect of the Population subgroups
were isolated and tested after adjusting for confounding effects such
as ChipLot, Operator, and Gender.  Here the complexity of our analysis
lies in the fact that the covariates Gender and Population subgroups
have gene-specific effects while the covariates ChipLot and Operator
have a global effect (that is, they are common to all genes). In
addition, our microarray data is highly unbalanced, therefore no
results in the microarray literature is of any help.

In this talk we discuss how multifactorial analysis of variance
containing both global and gene-specific parameters can be carried out
efficiently in spite of the large size of microarray data. We first
derive an analytical form of the solutions of the normal equations and
use these solutions to suggest a low-cost two-stage analysis. Our
procedure can be viewed as an extension of the work by Kerr et al.
(2000) for balanced (orthogonal) designs. We also review permutation
tests for both balanced and unbalanced ANOVA designs. All these
results are applied to our unbalanced microarray data. We also discuss
how to get around of the computational complexities in computing ten
of thousands of empirical p-values efficiently based on large
permutation size (more than 100,000).

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