%\VignetteIndexEntry{Annotation-Driven Clustering}
%\VignetteDepends{golubEsets, hu6800.db}
%\VignetteKeywords{clustering microarrays GO KEGG functional annotation}
%\VignettePackage{adSplit}

\documentclass[11pt,a4paper]{report}

\usepackage{compdiag}
\usepackage{amsmath,a4}
\SweaveOpts{eps=false}

\newcommand{\Robject}[1]{{\texttt{#1}}}
\newcommand{\Rfunction}[1]{{\texttt{#1}}}
\newcommand{\Rpackage}[1]{{\textit{#1}}}
\newcommand{\Rclass}[1]{{\textit{#1}}}
\newcommand{\Rmethod}[1]{{\textit{#1}}}
\newcommand{\Rfunarg}[1]{{\texttt{#1}}}

\title{Annotation-Driven Class Discovery  \bigskip \\
       User's Guide to the Bioconductor package \Rpackage{adSplit}}
\author{Claudio Lottaz\footnote{Corresponding author: 
        \texttt{claudio.lottaz@molgen.mpg.de}},
        Joern Toedling and Rainer Spang \bigskip \\
        \small Max Planck Institute for Molecular Genetics\\ 
         Computational Diagnostics, Department for Computational Molecular Biology \\
         Ihnestr. 63-73, D-14195 Berlin, Germany}
\reportnr{02}
\year{2005}
\abstract{
  This is the vignette of the Bioconductor compliant package
  \Rpackage{adSplit}. We describe our implementation of {\it annotation-
  driven clustering} for microarray gene expression profiling 
  studies.
}
\date{}


\begin{document}

\maketitle

<<echo=FALSE,results=hide>>=
library(golubEsets)
oldopt <- options(digits=3)
on.exit( {options(oldopt)} )
options(width=70)
if (interactive()) { 
    options(error=recover)
}
set.seed(123)
@

\chapter{Introduction}
\label{sec:intro}

 \textbf{Background:}
 Clustering algorithms are widely used in the analysis of microarrays.
 In clinical studies, they are not only used to cluster genes into groups
 of co-regulated genes, but also for clustering patients, and thereby defining
 novel disease entities based on gene expression profiles. 
 Several distance based cluster algorithms have been suggested, 
 but little attention has been paid to the choice of the metric on 
 patient space. Even when using the Euclidean metric, including and excluding 
 genes from the analysis leads to different distances between the same objects, 
 and consequently to different clustering results.

 \textbf{Methodology:}
 In this package, we implement a novel algorithm for investigating the
 dependency of clustering results on the choice of metric supporting
 genes. Our method combines expression data and functional annotation
 data. According to gene annotations, a list of candidate gene sets
 with a unique functional characterization is generated.  Each set
 defines a metric on patient space, and consequently a clustering of
 patients. Based on a novel significance measure for clusterings, this
 list is filtered. Significant clusterings are reported together with
 the underlying gene sets and their functional definition.

 \textbf{Intended results:} 
 Our method reports clusterings defined by biologically focussed sets
 of genes. In our annotation driven clusterings, we have observed
 rediscoveries of clinically relevant patient subgroups through
 biologically plausible sets of genes. Hence, we conjecture that our
 method has the potential to reveal clinically relevant classes of
 patients in an unsupervised manner.
 
 \textbf{The algorithmic concept:} 
 We suggest a systematic approach to gene selection in an unsupervised
 setting.  We describe an algorithm that produces a list of
 alternative clusterings using a variety of different metrics on
 patient space.  While all metrics are of the Euclidean type, they
 differ in the set of genes used for characterizing the patient
 profiles. We derive candidate gene sets from functional annotation
 data, and filter the list by a novel significance measure for
 clustering strength.  For practical use, it is desirable to have
 functional rationales characterizing clusterings.  For instance,
 clusterings related to proliferation or apoptosis.  To this end, we
 define candidate gene sets using functional annotations from the Gene
 Ontology \cite{ashburner00gene} and from the Kyoto Encyclopedia of
 Genes and Genomes \cite{kanehisa96toward}.

 \textbf{The algorithm in a nutshell:}
 
 Annotation-driven splits specific to the corresponding gene set are
 computed using the k-means algorithm \cite{hartigan79k-means}. We use
 functional annotations from chip-specific meta-data packages provided
 in Bioconductor \cite{gentleman04bioconductor}. The quality of any
 clusterings is assessed using the \emph{diagonal linear discriminant}
 (DLD) score \cite{heydebreck01identifying}.  In order to determine
 the statistical significance of a score, we also compute DLD scores
 for restricted metrics resulting from randomly chosen gene sets.
 Empirical p-values are calculated and false discovery rates (FDR)
 computed according to Benjamini Hochber \cite{benjamini95controlling}. Finally, we
 filter the list of clusterings for minimal subgroup size and to
 control the FDR. In a nutshell, the algorithm consists of the following steps:\\

\noindent For each biological term / pathway of interest, denoted $B_i$:
\begin{enumerate}
\item Find all $n_{B_i}$ genes annotated to $B_i$ and discard all others.
\item \label{item:cluster} Perform 2-means clustering of reduced
  expression matrix.  This yields an annotation-driven clustering
  $C_{B_i}$.
\item \label{item:score} Compute DLD score $S(C_{B_i})$ for this clustering.
\item Draw 10000 random gene sets of size $n_{B_i}$ from the set of
  all measured genes. For each of these random gene sets, compute
  steps \ref{item:cluster} and \ref{item:score}.  This yields a vector
  $\textbf{\textup{r}}_{n_{B_i}}$ of 10000 scores.
\item Assign an empirical p-value to the original clustering, denoting
  the proportion of entries of $\textbf{\textup{r}}_{n_{B_i}}$ being
  greater or equal than $S(C_{B_i})$.  
\item Correct the empirical p-values for multiple testing according to
  Benjamini-Hochberg \cite{benjamini95controlling}. The resulting
  q-values are used to control the false discovery rate of a \Rclass{splitSet}.
\end{enumerate} 

 \textbf{The structure of the vignette:}
 The described package contains functions to facilitate these
 steps. The first chapter describes, how to compute a split for a
 given term of intrest. the second shows how to compute a random
 distribution of DLD-scores to judge the significance of an
 annotation-driven split. Finally, the last chapter describes how to
 collect results for many terms of interest and illustrate the
 achieved results.

\chapter{Annotation-Driven Splits}
\label{sec:splitting}

 Before starting any analysis you have to load the \Rpackage{adSplit}
 package in your R session as follows: 
<<>>= 
library(adSplit) 
@ 
 
 For illustration of \Rpackage{adSplit} usage we use the Golub data
 set on acute leukemia \cite{golub99molecular} as it is stored in the
 \Rpackage{golubEsets} experimental data package. For
 preparing the data, issue the following commands:

<<>>=
library(golubEsets) 
data(Golub_Merge) 
@

\section{Initialize k-means with divisive hierarchical cluster centroids}

 K-means clustering critically depends on its initialization step. We
 derive an initialization based on the first split of a divisive
 hierarchical clustering (Chapter 6 in \cite{kaufman90finding}).  Of
 the resulting two clusters, we compute centroids which provide the
 starting points for the k-means algorithm \cite{macqueen67methods}.
 This has been shown to outperform standard k-means with random
 starting points \cite{milligan80stage}.  In fact, k-means is used to
 refine individual clusters and to correct inappropriate assignments
 made by the hierarchical method.
 
 We have packed this procedure into the function
 \Rfunction{diana2means} of the here described package. In addition
 this function computes DLD-scores for the generated splits using the
 implementation taken from the ISIS package
 \cite{heydebreck01identifying}. Actually,
 the determined split is only returned when return.cut is set to
 true. The following snipit of code uses the 10\% most variable genes
 in the Golub-dataset to generate a split.

<<>>=
e <- exprs(Golub_Merge)
vars <- apply(e, 1, var)
e <- e[vars > quantile(vars,0.9),]

diana2means(e)
diana2means(e, return.cut=TRUE)
@

 This function returns a single number representing the splits
 DLD-score as default, when the argument \Rfunarg{return.cut} is set
 to \texttt{FALSE}. Otherwise an object of class \Rclass{split} holding
 the list elements \texttt{cut} and \texttt{score} is returned. For
 instance, the the split attributions can be extracted as follows:
 
<<>>=
x <- diana2means(e, return.cut=TRUE)
x$cut
@

 For the computation of the DLD-score, this function takes into account
 the best scoring \Rfunarg{ngenes} genes (rows). In order to avoid
 excessive influence of single strikingly well separating genes, the
 \Rfunarg{ignore.genes} argument can be used to dismiss the strongest
 genes from the score.

\section{Annotation-driven splits}

 The central function for the generation of annotation driven splits
 is called \Rfunction{adSplit}. It calls the above described function
 \Rfunction{diana2means} on a restricted set of genes. This function
 has a series of arguments, but its basic call is as follows:

<<>>=
adSplit(Golub_Merge, "GO:0006915", "hu6800")
@

 This command generates an annotation-driven split for the term
 ''apoptosis`` encoded by the identifier ''GO:0006915``.
 The string given as the chip's name is used to load the annotation
 meta-data. Thus \Rpackage{adSplit} expects a library of the same
 name to be installed, where it looks for the hashes
 \Robject{<chip-name>GO2ALLPROBES} and \Robject{<chip-name>PATH2PROBE}
 as they are provided by Bioconductor meta data packages. If we issue
 a similar command for the term ''signal transduction`` (GO:0007165),
 the following happens:

<<>>=
adSplit(Golub_Merge, "GO:0007165", "hu6800")
@

 This term has too many associated genes. Hence, it is skipped. In
 order to generate splits related to more generic terms, we can provide
 an explicit maximum limit for the amount of annotated genes to terms
 of interest. For instance:

<<>>=
adSplit(Golub_Merge, "GO:0007165", "hu6800", max.probes=7000)
@

 This command generates the wanted split based on more than 2000
 genes. \Rfunction{adSplit} returns an object of class \Rclass{splitSet}
 with the following list elements:
 \begin{enumerate}
 \item \Robject{cuts}: a matrix of split attributions. One row per annotation
    identifier (GO term or KEGG pathway for which a split has been
    generated. One column per object in the dataset. 
 \item \Robject{score}: one score per generated split
 \item \Robject{pvalue}: one empirical p-value per generated split, or \Robject{NULL}.
 \end{enumerate}
 The object may also be empty in which case all elements are \Robject{NULL}.
  
\chapter{Empirical p-Values for Splits}
\label{sec:pvalues}

 In order to generate empirical p-values for a given annotation-driven
 gene set, we suggest to sample random gene sets of the same size and
 apply the split generation algorithm implemented in
 \Rfunction{diana2means} to all 
 of these gene sets. DLD-scores
 computed for the random gene sets are used to approximate 
 the score's null distribution.
 The fraction of the scores from this
 null distribution, which are higher than the observed score for the
 gene set with common annotation, is used as empirical p-value. Some
 details on how to compute these p-values with \Rpackage{adSplit} are
 collected in this chapter.

\section{Drawing random gene sets}

 The first step needed for the random sampling is drawing a given
 number of probe-sets measured in dataset. In order to reflect one
 obvious characteristic of annotation based gene sets, 
 once we have drawn one probe set at random, we always
 include all other probe-sets representing the same gene 
 into the random selection.
 In order to speed up the repeated drawing procedure, we
 use a hash containing one entry per EntrezGene 
 identifier holding all associated probe-sets. 
 This environment is generated from the
 meta-data package ENTREZID-hash as follows:

<<>>=
EID2PSenv <- makeEID2PROBESenv(hu6800ENTREZID)
@

 The returned hash is used as follows to draw random sets of
 probe-sets:

<<>>=
drawRandomPS(10, EID2PSenv, ls(EID2PSenv))
@

 \Rfunction{drawRandomPS} returns a named vector holding random
 probe-set identifiers. The names of this vector corresponds to the
 associated LOCUSLINK identifiers.

\section{Generating DLD-score distributions}

 The functions for drawing random sets of probe-sets described in the
 previous section are combined with \Rfunction{diana2means} to generat
 null-distributions of DLD-scores. This is implemented in the function
 \Rfunction{randomDiana2means} which is used as follows:

<<>>=
scores <- randomDiana2means(20, exprs(Golub_Merge), "hu6800", ndraws = 1000) 
@

 The form of this distribution is skewed. The parameter
 \Rfunarg{ignore.genes} changes this shape towards a more symmetric
 shape as shown in the next figure. This is intuitive, since we remove
 genes which drive DLD-scores and thus approach more closely a random
 distribution.

\setkeys{Gin}{width=15cm,height=7.5cm}
<<fig=TRUE,height=3,width=6>>=
scores2 <- randomDiana2means(20, exprs(Golub_Merge), "hu6800", 
                            ndraws = 1000, ignore.genes=5) 
par(mfrow=c(1,2))
hist(scores,  nclass=30, main="", col="grey")
hist(scores2, nclass=30, main="", col="grey")
@

 The left histogram here is the score distribution when including all
 genes, the right one results from exclusion of best scoring genes.

\section{Adding empirical p-values while generating annotation driven splits}

 Finally, we can use the distribution generated with random sets of
 probe sets to compute empirical p-values. This is done by the
 \Rfunction{adSplit} function when \Rfunarg{B} is specified, the number
 of samplings to be used.

<<>>=
glutamSplits <- adSplit(Golub_Merge, "KEGG:00251", "hu6800", B=1000) 
@

 This call returns an object of class \Rclass{splitSet} with an
 additional entry called \Robject{pvalue}. The print method for the
 \Rclass{splitSet} gives a summary on sets of splits and some
 additional information, if a split set contains only 1 split:

<<>>=
print(glutamSplits)
@

\chapter{Working with Split-Sets}
\label{sec:collect}

\section{Generating split-sets}

 The function \Rfunction{adSplit} accepst more than one annotation
 identifier in one call. In this case it generates splits for each of
 the provided identifier and collects the results into one single
 returnde object. For instance:

<<>>=
x <- adSplit(Golub_Merge, c("GO:0007165","GO:0006915"), "hu6800", max.probes=7000)
print(x)
@

 If the user doesn't want to specify few terms of interst in this
 fashion, he/she may also provide one of the following specially
 treated identifiers:
 \begin{enumerate}
 \item \texttt{GO}: all available GO terms are used as gene set candidates.
 \item \texttt{KEGG}: all available KEGG pathways are used as gene set candidates.
 \item \texttt{all}: both these sets of annotation identifiers are used.
 \end{enumerate}

 For instance, the following command determines all splits driven by
 KEGG pathways without sampleing random gene lists for significance
 analysis:

<<results=hide>>=
x <- adSplit(Golub_Merge, "KEGG", "hu6800")
@
<<>>=
print(x)
@

 However, if empirical p-values are computed by sampling random gene lists, multiple testing is an issue to be considered. We use the \Rpackage{multtest} to correct our p-values and thus computing false discovery rates by the method suggested by Benjamini-Hochberg. The corresponding q-values are stored in the result's list element called \Rfunarg{qvalues}. You may consider for illustration the precomputed object \Robject{golubKEGGSplits}:

<<>>=
data(golubKEGGSplits)
print(golubKEGGSplits)
summary(golubKEGGSplits$qvalues)
@

This object has been precomputed with the following command:

\begin{quote}
\begin{verbatim}
> golubKEGGSplits <- adSplit(Golub_Merge, "KEGG", "hu6800", B=1000)
\end{verbatim}
\end{quote}

 It thus contains all splits driven by KEGG pathways and holds
 empirical p-values deduced from 1000 random gene lists. Pathways which
 have fewer than 20 genes associated are thereby skipped from the
 analysis.

\section{Graphical illustrations}

 For showing the illustration utilities implemented in
 \Rpackage{adSplit}, we use the precomputed object
 \Robject{golubKEGGSplits} included in the \Rpackage{adSplit} package.

 The \Robject{golubKEGGSplits} object contains 70 splits and
 corresponding empirical p-values and corrected q-values. The split set
 is ordered according to p-values such that the first entries are the
 most significant ones. In order to get an overview of whether
 significant splits and how many of them are generated, the package
 \Rpackage{adSplit} offers a histogram method for objects of class
 \Rclass{splitSet} called as follows:

\setkeys{Gin}{width=12cm,height=12cm}
<<fig=TRUE,width=5,height=5>>=
data(golubKEGGSplits)
hist(golubKEGGSplits)
@

 In this histogram the empirical p-values are drawn as usual in a
 histogram. In addition, the corresponding q-values corrected for
 multiple testing are plotted as a line into the histogram. The
 corresponding scale is shown to the left of the plot.

 An \Rfunction{image} method on the same objects can be used to get an
 actual representation of all splits generated. A filter argument
 called \Rfunarg{filter.fdr} is used to focus on splits with a low false
 discovery rate. The following call requires a set of splits with less
 then 30\% expected false positives.

<<echo=FALSE,result=FALSE>>=
image(golubKEGGSplits, filter.fdr=0.3, outfile="splitSet.eps", res=300)
@

\begin{quotation}
\begin{verbatim}
image(golubKEGGSplits, filter.fdr=0.3)
\end{verbatim}
\end{quotation}

\includegraphics[width=15.5cm,height=3cm]{splitSet}

 In this image, each column corresponds to a patient and each row
 corresponds to an annotation. The colors represent to which group the
 corresponding patient is attributed with respect to the corresponding
 annotation. This image is clustered in both directions in order to
 bring similar splits as well as similar patients close together.


\section*{Acknowledgements}

This research has been supported by BMBF grant 031U117/031U217 of the
German Federal Ministry of Education and the National Genome Research
Network.

%\bibliographystyle{plain}
%\bibliography[ompdiag}
\begin{thebibliography}{1}

\bibitem{ashburner00gene}
M~Ashburner, CA~Ball, JA~Blake, D~Botstein, H~Butler, JM~Cherry, AP~Davis,
  K~Dolinski, SS~Dwight, JT~Eppig, MA~Harris, DP~Hill, L~Issel-Tarver,
  A~Kasarskis, S~Lewis, JC~Matese, JE~Richardson, M~Ringwald, GM~Rubin, and
  G~Sherlock.
\newblock Gene ontology: tool for the unification of biology. the gene ontology
  consortium.
\newblock {\em Nat Genet}, 25(1):25--29, May 2000.

\bibitem{benjamini95controlling}
Yoav Benjamini and Yosef Hochberg.
\newblock Controlling the false discovery rate: {A} practical and powerful
  approach to multiple testing.
\newblock {\em Journal of the Royal Statistical Society: Series B},
  57(1):289--300, 1995.

\bibitem{gentleman04bioconductor}
RC~Gentleman, VJ~Carey, DM~Bates, B~Bolstad, M~Dettling, S~Dudoit, B~Ellis,
  L~Gautier, Y~Ge, J~Gentry, K~Hornik, T~Hothorn, W~Huber, S~Iacus, R~Irizarry,
  F~Leisch, C~Li, M~Maechler, AJ~Rossini, G~Sawitzki, C~Smith, G~Smyth,
  L~Tierney, JY~Yang, and J~Zhang.
\newblock Bioconductor: {O}pen software development for computational biology
  and bioinformatics.
\newblock {\em Genome Biology}, 5(10):R80, 2004.

\bibitem{golub99molecular}
TR~Golub, DK~Slonim, P~Tamayo, C~Huard, M~Gaasenbeek, JP~Mesirov, H~Coller,
  ML~Loh, JR~Downing, MA~Caligiuri, CD~Bloomfield, and ES~Lander.
\newblock Molecular classification of cancer: class discovery and class
  prediction by gene expression monitoring.
\newblock {\em Science}, 286(5439):531--7, Oct 1999.

\bibitem{hartigan79k-means}
JA~Hartigan and M~A Wong.
\newblock A k-means clustering algorithm.
\newblock {\em Applied Statistics}, 28:100--4, 1979.

\bibitem{huber02variance}
W~Huber, A~von Heydebreck, H~S{\"u}ltmann, A~Poustka, and M~Vingron.
\newblock Variance stabilization applied to microarray data calibration and to
  the quantification of differential expression.
\newblock {\em Bioinformatics}, 18(Suppl 1):96--104, 2002.

\bibitem{kanehisa96toward}
M~Kanehisa.
\newblock Toward pathway engineering: a new database of genetic and molecular
  pathways.
\newblock {\em Sci \& Tech Japan}, 59:34--8, 1996.

\bibitem{heydebreck01identifying}
A~von Heydebreck, W~Huber, A~Poustka, and M~Vingron.
\newblock Identifying splits with clear separation: a new class discovery
  method for gene expression data.
\newblock {\em Bioinformatics}, 17(Suppl 1):S107--14, 2001.

\bibitem{kaufman90finding}
Kaufman L, Rousseeuw PJ (1990) Finding Groups in Data: An Introduction to
  Cluster Analysis.
\newblock New York: Wiley.

\bibitem{macqueen67methods}
MacQueen JB (1967) Some methods for classification and analysis of multivariate
  observations.
\newblock In: Symposium on Math, Statistics, and Probability. volume~1, pp.
  281--97.

\bibitem{milligan80stage}
Milligan G, Sokol L (1980) A two stage clustering algorithm with robust
  recovery characteristics.
\newblock Educational and Psychological Measurement 40:755--9.

\end{thebibliography}

\end{document} 








