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\title{Using GO for Statistical Analyses}
\author{R. Gentleman}

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\section{Introduction}

While there are a number of different definitions of an ontology we
will use the notion of a restricted vocabulary as the basis for the
discussions here. Ontologies and related concepts are becoming
increasingly important tools for organizing and navigating
information. Initiatives in biology (our main focus) as well as the
semantic web are providing a variety of resources and interesting
problems related to ontologies.

One of the major problems facing comprehensive searching and use of
available biological information is the lack of a common set of terms
and descriptions for basic biological functions, processes and
entities. In fact, many genes have a variety of different names. For
genes and gene products the Gene Ontology Consortium, or GO,
(\url{www.geneontology.org}) is an initiative that is designed to
address this problem. GO provides a restricted vocabulary as well as
clear indications of the relationships between terms.  Readers are
referred to the GO web site for more specific definitions.

GO is clearly a valuable tool for data analysis, however its structure
(as a DAG) and the complex nature of the relationships that it
represents make appropriate use of this tool challenging. Most data
analytic software is not readily able to handle these data and much of
the organizational burden falls on the data analyst.  We have been
developing tools, as part of the Bioconductor Project, that should
greatly simplify the use of GO in a data analytic context. We consider
some of these different methods in the remainder of this paper. First
we outline some general properties and behaviors of GO. That
discussion is followed by a description of our example and finally the
different methods are applied to the data.

In this paper we will use meta-data packages from the Bioconductor
Project to carry out statistical analyses of gene expression data.
But would like to note that the potential scope of these applications
is much broader and many of the methods described here could be
applied to other types of high-throughput data. To provide context we
will make use of data from an investigation into acute lymphoblastic
leukemia (ALL) reported in \citet{Chiaretti2004}.

The outline of the paper is as follows. First we discuss and explain
what GO is, how it is structured and how genes are annotated at
specific terms within GO. Then we briefly describe the example data.
Then we consider three specific analyses. The first uses GO to help
understand sets of genes that have been selected according to specific
criteria by the data analyst. The second use of GO is to reduce the
set of probes to a manageable number before carrying out an analysis,
while the third considers some variations on the graph theoretic
themes introduced by \cite{shortestpath} and finally we discuss our
findings and make some suggestions for further exploration.


\section{The Gene Ontology}

An ontology is a restricted structured vocabulary of terms that
represent domain knowledge. In a practical sense an ontology specifies
a vocabulary that can be used to exchange queries and assertions. A
commitment to the use of the ontology is an agreement to use the
shared vocabulary in a consistent way. There is no commitment to
completeness, the commitment is to coherence and consistency.

The Gene Ontology (GO) consortium produces three independent
ontologies for gene products.  The three ontologies form the basis for
the description of the molecular function, biological process and
cellular component of gene products. The relationships between gene
products and specific terms in the three ontologies, molecular
function, biological process and cellular component, are all many to
many. Gene products are physical things such as proteins or RNA. In
the remainder of the paper the terms \textit{gene product} and
\textit{gene} will be used interchangeably (except in situations where
it is obvious that the remark pertains only to one or the other).

The \textit{molecular function} of a gene product is defined to be
biochemical activity or action of the gene product. This describes a
capability that the gene product has and there is no reference to
where or when this activity or usage actually occurs.  Examples of
terms that fall into this ontology are: "enzyme," "transporter," or
"ligand."

The term \textit{biological process} should be interpreted as a
biological objective to which the gene product contributes.  A
biological process is accomplished via one or more ordered assemblies
of molecular functions. There is generally some temporal aspect to the
process and it will often involve the transformation of some physical
thing. Examples of terms in this ontology include "cell growth and
maintenance" or "signal transduction". The concept of a pathway is
different from that of a biological process. A pathway is more complex
and has dependencies and dynamics that are not part of the concept of
a biological process.  It is not always easy to distinguish between
molecular function and biological process. The GO consortium suggests
that a process must have more than one distinct step.

A \textit{cellular component} is a component of a cell that is part of
some larger object or structure. Examples of cellular components
include ``chromosome'', ``nucleus'' and ``ribosome''.

