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<div id="content">
<h1 class="title">Inferring Somatic Signatures from Single Nucleotide Variant Calls</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#sec-1">1. Motivation: The Concept Behind Mutational Signatures</a></li>
<li><a href="#sec-2">2. Methodology: From Mutations to Somatic Signatures</a></li>
<li><a href="#sec-3">3. Workflow and Implementation: Analysis with the SomaticSignatures Package</a></li>
<li><a href="#sec-4">4. Use case: Estimating Somatic Signatures from TCGA WES Studies</a>
<ul>
<li><a href="#sec-4-1">4.1. Data: Preproccessing of the TCGA WES Studies</a></li>
<li><a href="#sec-4-2">4.2. Motifs: Extracting the Sequence Context of Somatic Variants</a></li>
<li><a href="#sec-4-3">4.3. Decomposition: Inferring Somatic Signatures</a></li>
<li><a href="#sec-4-4">4.4. Visualization: Exploration of Signatures and Samples</a>
<ul>
<li><a href="#sec-4-4-1">4.4.1. PCA</a></li>
</ul>
</li>
<li><a href="#sec-4-5">4.5. Extensions: Normalization of Sequence Motif Frequencies and Batch Effects</a></li>
</ul>
</li>
<li><a href="#sec-5">5. Alternatives: Inferring Somatic Signatures with Different Approaches</a></li>
<li><a href="#sec-6">6. Frequently Asked Questions</a>
<ul>
<li><a href="#sec-6-1">6.1. Citing SomaticSignatures</a></li>
<li><a href="#sec-6-2">6.2. Getting help</a></li>
<li><a href="#sec-6-3">6.3. Installing the package</a></li>
<li><a href="#sec-6-4">6.4. Working with VRanges</a></li>
</ul>
</li>
<li><a href="#sec-7">7. References</a></li>
<li><a href="#sec-8">8. Session Info</a></li>
</ul>
</div>
</div>
<!--
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<p class="author-top">Julian Gehring (EMBL Heidelberg)</p>


<div id="outline-container-sec-1" class="outline-2">
<h2 id="sec-1"><span class="section-number-2">1</span> Motivation: The Concept Behind Mutational Signatures</h2>
<div class="outline-text-2" id="text-1">
<p>
Recent publications introduced the concept of identifying mutational signatures
from cancer sequencing studies and linked them to potential mutation generation
processes [<a href="#nik-zainal_mutational_2012">6</a>] [<a href="#alexandrov_signatures_2013">14</a>] [<a href="#alexandrov_deciphering_2013">11</a>].
Conceptually, this relates somatically occurring <i>single nucleotide variants</i>
(SNVs) to the surrounding sequence which will be referred to as <i>mutational</i> or
<i>somatic motifs</i> in the following.  Based on the frequency of the motifs occurring
in multiple samples, these can be decomposed mathematically into so called
<i>mutational signatures</i>.  In case of the investigation of tumors, the term
<i>somatic signatures</i> will be used here to distinguish them from germline mutations and
their generating processes.
</p>

<p>
The <code>SomaticSignatures</code> package provides an efficient and user-friendly
implementation for the extraction of somatic motifs based on a list of
somatically mutated genomic sites and the estimation of somatic signatures with
a number of statistical approaches.
</p>
</div>
</div>


<div id="outline-container-sec-2" class="outline-2">
<h2 id="sec-2"><span class="section-number-2">2</span> Methodology: From Mutations to Somatic Signatures</h2>
<div class="outline-text-2" id="text-2">
<p>
The basic idea of somatic signatures is composed of two parts:
</p>

<p>
Firstly, each somatic mutation is described in relation of the sequence context
in which it occurs.  As an example, consider a SNV, resulting in the alteration
from <code>A</code> in the normal to <code>G</code> in the tumor sample, that is embedded in the sequence
context <code>TAC</code>.  Thus, the somatic motif can be written as <code>TAC&gt;TGC</code> or <code>T.C
A&gt;G</code>.  The frequency of these motifs across multiple samples is then represented
as a matrix \(M_{ij}\), where \(i\) counts over the motifs and \(j\) over the samples.
</p>

<p>
In a second step, the matrix \(M\) is numerically decomposed into two matrices \(W\)
and \(H\)
</p>

<p>
$$M_{ij} = \sum_{k=1}^{R} W_{ik} H_{jk}$$
</p>

<p>
for a fixed number \(R\) of signatures.  While \(W\) describes the composition of
each signature in term of somatic motifs, \(H\) shows the contribution of the
signature to the alterations present in each sample.
</p>
</div>
</div>


<div id="outline-container-sec-3" class="outline-2">
<h2 id="sec-3"><span class="section-number-2">3</span> Workflow and Implementation: Analysis with the SomaticSignatures Package</h2>
<div class="outline-text-2" id="text-3">
<p>
The <code>SomaticSignatures</code> package offers a framework for inferring signatures of
SNVs in a user-friendly and efficient manner for large-scale data sets.  A tight
integration with standard data representations of the <code>Bioconductor</code> project
[<a href="#gentleman_bioconductor:_2004">1</a>] was a major design goal.  Further, it extends
the selection of multivariate statistical methods for the matrix decomposition
and allows a simple visualization of the results.
</p>

<p>
For a typical workflow, a set of variant calls and the reference sequence are
needed.  Ideally, the SNVs are represented as a <code>VRanges</code> object with the
genomic location as well as reference and alternative allele defined.  The
reference sequence can be, for example, a <code>FaFile</code> object, representing an
indexed FASTA file, a <code>BSgenome</code> object, or a <code>GmapGenome</code> object.
Alternatively, we provide functions to extract the relevant information from
other sources of inputs.  At the moment, this covers the <i>MuTect</i>
[<a href="#cibulskis_sensitive_2013">12</a>] variant caller and the <i>h5vc</i> package
[<a href="#pyl_h5vc:_2014">15</a>] [<a href="#pyl_h5vc:_2013">9</a>].
</p>

<p>
Generally, the individual steps of the analysis can be summarized as:
</p>

<ol class="org-ol">
<li>The somatic motifs for each variant are retrieved from the reference sequence
with the <code>mutationContext</code> function and converted to a matrix representation
with the <code>motifMatrix</code> function.
</li>

<li>Somatic signatures are estimated with a method of choice (currently
<code>nmfDecomposition</code> and <code>pcaDecomposition</code>).
</li>

<li>The somatic signatures and their representation in the samples are assessed
with a set of accessor and plotting functions.
</li>
</ol>

<p>
To decompose \(M\), the <code>SomaticSignatures</code> package implements two methods:
</p>

<dl class="org-dl">
<dt> Non-negative matrix factorization (NMF) </dt><dd>The NMF decomposes \(M\) with the
constraint of positive components in \(W\) and \(H\)
[<a href="#gaujoux_flexible_2010">4</a>].  The method was used
[<a href="#nik-zainal_mutational_2012">6</a>] for the identification of mutational
signatures, and can be computationally expensive for large data sets.
</dd>

<dt> Principal component analysis (PCA) </dt><dd>The PCA employs the eigenvalue
decomposition and is therefore suitable for large data sets
[<a href="#stacklies_pcamethodsbioconductor_2007">2</a>].  While this is related to the
NMF, no constraint on the sign of the elements of \(W\) and \(H\) exists.
</dd>
</dl>

<p>
Other methods can be supplied through the <code>decomposition</code> argument of the
<code>identifySignatures</code> function.
</p>
</div>
</div>


<div id="outline-container-sec-4" class="outline-2">
<h2 id="sec-4"><span class="section-number-2">4</span> Use case: Estimating Somatic Signatures from TCGA WES Studies</h2>
<div class="outline-text-2" id="text-4">
<p>
In the following, the concept of somatic signatures and the steps for inferring
these from an actual biological data set are shown.  For the example, somatic
variant calls from whole exome sequencing (WES) studies from The Cancer Genome
Atlas (TCGA) project will be used, which are part of the
<code>SomaticCancerAlterations</code> package.
</p>

<!--begin.rcode load_ss, results='hide',message=FALSE
library(SomaticSignatures)
end.rcode-->

<!--begin.rcode load_supporting_packages, results='hide',message=FALSE
library(ggplot2)
end.rcode-->


<!--begin.rcode load_data_package, results='hide',message=FALSE
library(SomaticCancerAlterations)
library(BSgenome.Hsapiens.UCSC.hg19)
end.rcode-->
</div>


<div id="outline-container-sec-4-1" class="outline-3">
<h3 id="sec-4-1"><span class="section-number-3">4.1</span> Data: Preproccessing of the TCGA WES Studies</h3>
<div class="outline-text-3" id="text-4-1">
<p>
The <code>SomaticCancerAlterations</code> package provides the somatic SNV calls for eight
WES studies, each investigating a different cancer type.  The metadata
summarizes the biological and experimental settings of each study.
</p>

<!--begin.rcode sca_metadata
sca_metadata = scaMetadata()

print(sca_metadata)
end.rcode-->

<p>
The starting point of the analysis is a <code>VRanges</code> object which describes the
somatic variants in terms of their genomic locations as well as reference and
alternative alleles.  For more details about this class and how to construct it,
please see the documentation of the <code>VariantAnnotation</code> package
[<a href="#obenchain_variantannotation:_2011">5</a>].  Since the genomic positions are given
in the <i>NCBI</i> notation and the references used later are in <i>UCSC</i> notation, the
functions <code>ucsc</code> and <code>ncbi</code> are used to easily switch between the two notations.
In this example, all mutational calls of a study will be pooled together, in
order to find signatures related to a specific cancer type.
</p>

<!--begin.rcode sca_to_vranges
sca_vr = scaSNVRanges()

head(sca_vr, 3)
end.rcode-->


<p>
To get a first impression of the data, we count the number of somatic variants
per study.
</p>

<!--begin.rcode sca_study_table
sort(table(sca_vr$study), decreasing = TRUE)
end.rcode-->
</div>
</div>



<div id="outline-container-sec-4-2" class="outline-3">
<h3 id="sec-4-2"><span class="section-number-3">4.2</span> Motifs: Extracting the Sequence Context of Somatic Variants</h3>
<div class="outline-text-3" id="text-4-2">
<p>
In a first step, the sequence motif for each variant is extracted based on the
reference sequence.  Here, the <code>BSgenomes</code> object for the human hg19 reference
is used.  However, all objects with a defined <code>getSeq</code> method can serve as the
reference, e.g. an indexed FASTA file.  Additionally, we transform all motifs to
have a pyrimidine base (<code>C</code> or <code>T</code>) as a reference base
[<a href="#alexandrov_signatures_2013">14</a>].
</p>

<!--begin.rcode sca_vr_to_motifs
sca_motifs = mutationContext(sca_vr, BSgenome.Hsapiens.UCSC.hg19, unify = TRUE)
end.rcode-->

<p>
To continue with the estimation of the somatic signatures, the matrix \(M\) of the
form {motifs &times; studies} is constructed.  The <code>normalize</code> argument specifies
that frequencies rather than the actual counts are returned.
</p>

<!--begin.rcode sca_motif_occurrence
sca_mm = motifMatrix(sca_motifs, group = "study", normalize = TRUE)

head(round(sca_mm, 4))
end.rcode-->


<p>
The observed occurrence of the motifs, also termed <i>somatic spectrum</i>, can be
visualized across studies, which gives a first impression of the data.  The
distribution of the motifs clearly varies between the studies.
</p>

<!--begin.rcode sca_mutation_spectrum, fig.cap='Mutation spectrum over studies'
plotMutationSpectrum(sca_motifs, "study")
end.rcode-->
</div>
</div>


<div id="outline-container-sec-4-3" class="outline-3">
<h3 id="sec-4-3"><span class="section-number-3">4.3</span> Decomposition: Inferring Somatic Signatures</h3>
<div class="outline-text-3" id="text-4-3">
<p>
The somatic signatures can be estimated with each of the statistical methods
implemented in the package.  Here, we will use the <code>NMF</code> and <code>PCA</code>, and compare
the results.  Prior to the estimation, the number \(R\) of signatures to obtain has to
be fixed; in this example, the data will be decomposed into 5 signatures.
</p>

<!--begin.rcode sca_nmf_pca
n_sigs = 5

sigs_nmf = identifySignatures(sca_mm, n_sigs, nmfDecomposition)

sigs_pca = identifySignatures(sca_mm, n_sigs, pcaDecomposition)
end.rcode-->

<p>
The results contains the decomposed matrices stored in a list and can be
accessed using standard R accessor functions.
</p>

<!--begin.rcode sca_explore_nmf
sigs_nmf
end.rcode-->

<!--begin.rcode sca_explore_pca
sigs_pca
end.rcode-->
</div>
</div>


<div id="outline-container-sec-4-4" class="outline-3">
<h3 id="sec-4-4"><span class="section-number-3">4.4</span> Visualization: Exploration of Signatures and Samples</h3>
<div class="outline-text-3" id="text-4-4">
<p>
To explore the results for the TCGA data set, we will use the plotting
functions.  All figures are generated with the <code>ggplot2</code> package, and thus,
their properties and appearances can also be modified at a later stage.
</p>

<p>
Focusing on the results of the NMF first, the five somatic signatures (named S1
to S5) can be visualized either as a heatmap or as a barchart.
</p>

<!--begin.rcode sca_plot_nmf_signatures_map, fig.cap='Composition of somatic signatures estimated with the NMF, represented as a heatmap.'
plotSignatureMap(sigs_nmf) + ggtitle("Somatic Signatures: NMF - Heatmap")
end.rcode-->

<!--begin.rcode sca_plot_nmf_signatures, fig.cap='Composition of somatic signatures estimated with the NMF, represented as a barchart.'
plotSignatures(sigs_nmf) + ggtitle("Somatic Signatures: NMF - Barchart")
end.rcode-->


<!--begin.rcode 
plotObservedSpectrum(sigs_nmf)
end.rcode-->


<!--begin.rcode 
plotFittedSpectrum(sigs_nmf)
end.rcode-->


<p>
Each signature represents different properties of the somatic spectrum observed
in the data.  While signature S1 is mainly characterized by selective <code>C&gt;T</code> alterations,
others as S4 and S5 show a broad distribution across the motifs.
</p>

<p>
In addition, the contribution of the signatures in each study can be represented
with the same sets of plots.  Signature S1 and S3 are strongly represented in
the GBM and SKCM study, respectively.  Other signatures show a weaker
association with a single cancer type.
</p>

<!--begin.rcode sca_plot_nmf_samples_map, fig.cap='Occurrence of signatures estimated with the NMF, represented as a heatmap.'
plotSampleMap(sigs_nmf)
end.rcode-->

<!--begin.rcode sca_plot_nmf_samples, fig.cap='Occurrence of signatures estimated with the NMF, represented as a barchart.'
plotSamples(sigs_nmf)
end.rcode-->

<p>
In the same way as before, the results of the PCA can be visualized.  In
contrast to the NMF, the signatures also contain negative values, indicating the
depletion of a somatic motif.
</p>

<p>
Comparing the results of the two methods, we can see similar characteristics
between the sets of signatures, for example S1 of the NMF and S2 of the PCA.
</p>
</div>

<div id="outline-container-sec-4-4-1" class="outline-4">
<h4 id="sec-4-4-1"><span class="section-number-4">4.4.1</span> PCA</h4>
<div class="outline-text-4" id="text-4-4-1">
<!--begin.rcode sca_plot_pca_signatures_map, fig.cap='Composition of somatic signatures estimated with the PCA, represented as a heatmap.'
plotSignatureMap(sigs_pca) + ggtitle("Somatic Signatures: PCA - Heatmap")
end.rcode-->

<!--begin.rcode sca_plot_pca_signatures, fig.cap='Composition of somatic signatures estimated with the PCA, represented as a barchart.'
plotSignatures(sigs_pca) + ggtitle("Somatic Signatures: PCA - Barchart")
end.rcode-->


<!--begin.rcode 
plotObservedSpectrum(sigs_pca)
end.rcode-->


<!--begin.rcode 
plotFittedSpectrum(sigs_pca)
end.rcode-->
</div>
</div>
</div>



<div id="outline-container-sec-4-5" class="outline-3">
<h3 id="sec-4-5"><span class="section-number-3">4.5</span> Extensions: Normalization of Sequence Motif Frequencies and Batch Effects</h3>
<div class="outline-text-3" id="text-4-5">
<p>
When investigating somatic signatures between samples from different studies,
corrections for technical confounding factors should be considered.  In our use
case of the TCGA WES studies, this is of minor influence due to
similar sequencing technology and variant calling methods across the studies.
Approaches for the identification of so termed batch effects have been proposed
[<a href="#leek_capturing_2007">3</a>] [<a href="#sun_multiple_2012">8</a>] and could be adapted to the
setting of somatic signatures with existing implementations (the <code>sva</code> and
<code>leapp</code> packages).  While this correction is not performed here, we exemplify
the usage by taking the different sequencing technologies of the studies into
account.
</p>

<!--begin.rcode sva_batch_not_run, eval=FALSE
library(sva)

df = as(sca_metadata, "data.frame") ## sample x covariable
pheno = data.frame(s = unlist(df[ ,"Sequence_Source"]), c = unlist(df[ ,"Cancer_Type"]))
rownames(pheno) = gsub("(.*)_.*", "\\1", rownames(pheno))
mod = model.matrix(~ s + c, data = pheno)
mod0 = model.matrix(~ c, data = pheno)

sv = sva(sca_mm, mod, mod0, method = "irw")
end.rcode-->

<p>
If comparisons are performed across samples or studies with different capture
targets, for example by comparing whole exome with whole genome sequencing,
further corrections for the frequency of sequence motifs can be taken into
account.  The <code>kmerFrequency</code> function provides the basis for calculating the
occurrence of k-mers over a set of ranges of a reference sequence.
</p>

<p>
As an example, we compute the frequency of 3-mers for the human chromosome 1,
based on a sample of 100'000 locations.  Analogously, the k-mer occurrence across
the human exome can be obtained easily.
</p>

<!--begin.rcode kmer_chr1, eval=FALSE
k = 3
n = 1e5
chrs = "chr1"

chr1_ranges = as(seqinfo(BSgenome.Hsapiens.UCSC.hg19), "GRanges")
chr1_ranges = keepSeqlevels(chr1_ranges, chrs)

k3_chr1 = kmerFrequency(BSgenome.Hsapiens.UCSC.hg19, n, k, chr1_ranges)

k3_chr1
end.rcode-->

<p>
With the <code>normalizeMotifs</code> function, the frequency of motifs can be adjusted.
Here, we will transform our results of the TCGA WES studies to have the same
motif distribution as of a whole-genome analysis.  The <code>kmers</code> dataset contains
the estimated frequency of 3-mers across the human genome and exome.
</p>

<!--begin.rcode normalize_motifs, eval=FALSE
head(sca_mm)

data(kmers)
norms = k3wg / k3we
head(norms)

sca_norm = normalizeMotifs(sca_mm, norms)

head(sca_norm)
end.rcode-->
</div>
</div>
</div>


<div id="outline-container-sec-5" class="outline-2">
<h2 id="sec-5"><span class="section-number-2">5</span> Alternatives: Inferring Somatic Signatures with Different Approaches</h2>
<div class="outline-text-2" id="text-5">
<p>
For the identification of somatic signatures, other methods and implementations
exist.  The original framework [<a href="#nik-zainal_mutational_2012">6</a>]
[<a href="#alexandrov_deciphering_2013">11</a>] proposed for this is based on the NMF and
available for the Matlab programming language [<a href="#alexandrov_wtsi_2012">7</a>].  In
extension, a probabilistic approach based on Poisson processes has been proposed
[<a href="#fischer_emu:_2013-1">13</a>] and implemented [<a href="#fischer_emu:_2013">10</a>].
</p>
</div>
</div>


<div id="outline-container-sec-6" class="outline-2">
<h2 id="sec-6"><span class="section-number-2">6</span> Frequently Asked Questions</h2>
<div class="outline-text-2" id="text-6">
</div><div id="outline-container-sec-6-1" class="outline-3">
<h3 id="sec-6-1"><span class="section-number-3">6.1</span> Citing SomaticSignatures</h3>
<div class="outline-text-3" id="text-6-1">
<p>
If you use the <code>SomaticSignatures</code> package in your work, please cite it:
</p>

<!--begin.rcode 
citation("SomaticSignatures")
end.rcode-->
</div>
</div>


<div id="outline-container-sec-6-2" class="outline-3">
<h3 id="sec-6-2"><span class="section-number-3">6.2</span> Getting help</h3>
<div class="outline-text-3" id="text-6-2">
<p>
We welcome emails with questions or suggestions about our software, and want to
ensure that we eliminate issues if and when they appear.  We have a few requests
to optimize the process:
</p>

<ul class="org-ul">
<li>All emails and follow-up questions should take place over the <a href="http://bioconductor.org/help/mailing-list/">Bioconductor
mailing list</a>, which serves as a repository of information.
</li>

<li>The subject line should contain <i>SomaticSignatures</i> and a few words describing
the problem.  First search the <a href="http://bioconductor.org/help/mailing-list/">Bioconductor mailing list</a>, for past threads
which might have answered your question.
</li>

<li>If you have a question about the behavior of a function, read the sections of
the manual page for this function by typing a question mark and the function
name, e.g. <code>?mutationContext</code>.  Additionally, read through the vignette to understand
the interplay between different functions of the package.  We spend a lot of
time documenting individual functions and the exact steps that the software is
performing.
</li>

<li>Include all of your R code related to the question you are asking.
</li>

<li>Include complete warning or error messages, and conclude your message with the
full output of <code>sessionInfo()</code>.
</li>
</ul>
</div>
</div>



<div id="outline-container-sec-6-3" class="outline-3">
<h3 id="sec-6-3"><span class="section-number-3">6.3</span> Installing the package</h3>
<div class="outline-text-3" id="text-6-3">
<p>
Before you want to install the <code>SomaticSignatures</code> package, please ensure that
you have the latest version of <code>R</code> and <code>Bioconductor</code> installed.  For details on
this, please have a look at the help packages for <a href="http://cran.r-project.org/">R</a> and <a href="http://bioconductor.org/install/">Bioconductor</a>.  Then you
can open <code>R</code> and run the following commands which will install the latest
release version of <code>SomaticSignatures</code>:
</p>

<!--begin.rcode eval=FALSE
source("http://bioconductor.org/biocLite.R")
biocLite("SomaticSignatures")
end.rcode-->
</div>
</div>


<div id="outline-container-sec-6-4" class="outline-3">
<h3 id="sec-6-4"><span class="section-number-3">6.4</span> Working with VRanges</h3>
<div class="outline-text-3" id="text-6-4">
<p>
A central object in the workflow of <code>SomaticSignatures</code> is the <code>VRanges</code> class
which is part of the <code>VariantAnnotation</code> package.  It builds upon the commonly
used <code>GRanges</code> class of the <code>GenomicRanges</code> package.  Essentially, each row
represents a variant in terms of its genomic location as well as its reference
and alternative allele.  
</p>

<!--begin.rcode results='hide', message=FALSE
library(VariantAnnotation)
end.rcode-->

<p>
There are multiple ways of converting its own variant calls into a <code>VRanges</code>
object.  One can for example import them from a <code>VCF</code> file with the <code>readVcf</code>
function or employ the <code>readMutect</code> function for importing variant calls from
the <code>MuTect</code> caller directly.  Further, one can also construct it from any other
format in the form of:
</p>

<!--begin.rcode 
vr = VRanges(
    seqnames = "chr1",
    ranges = IRanges(start = 1000, width = 1),
    ref = "A",
    alt = "C")

vr
end.rcode-->
</div>
</div>
</div>



<div id="outline-container-sec-7" class="outline-2">
<h2 id="sec-7"><span class="section-number-2">7</span> References</h2>
<div class="outline-text-2" id="text-7">
<div id="bibliography">
<h2>References</h2>

</div>
<table>

<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="gentleman_bioconductor:_2004">1</a>]
</td>
<td class="bibtexitem">
Robert&nbsp;C. Gentleman, Vincent&nbsp;J. Carey, Douglas&nbsp;M. Bates, Ben Bolstad, Marcel
  Dettling, Sandrine Dudoit, Byron Ellis, Laurent Gautier, Yongchao Ge, Jeff
  Gentry, Kurt Hornik, Torsten Hothorn, Wolfgang Huber, Stefano Iacus, Rafael
  Irizarry, Friedrich Leisch, Cheng Li, Martin Maechler, Anthony&nbsp;J. Rossini,
  Gunther Sawitzki, Colin Smith, Gordon Smyth, Luke Tierney, Jean&nbsp;YH Yang,
  and Jianhua Zhang.
 Bioconductor: open software development for computational biology and
  bioinformatics.
 <em>Genome Biology</em>, 5(10):R80, September 2004.
 PMID: 15461798.
[&nbsp;<a href="http://dx.doi.org/10.1186/gb-2004-5-10-r80">DOI</a>&nbsp;| 
<a href="http://genomebiology.com/2004/5/10/R80/abstract">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="stacklies_pcamethodsbioconductor_2007">2</a>]
</td>
<td class="bibtexitem">
Wolfram Stacklies, Henning Redestig, Matthias Scholz, Dirk Walther, and Joachim
  Selbig.
 pcaMethodsa bioconductor package providing PCA
  methods for incomplete data.
 <em>Bioinformatics</em>, 23(9):1164-1167, May 2007.
 PMID: 17344241.
[&nbsp;<a href="http://dx.doi.org/10.1093/bioinformatics/btm069">DOI</a>&nbsp;| 
<a href="http://bioinformatics.oxfordjournals.org/content/23/9/1164">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="leek_capturing_2007">3</a>]
</td>
<td class="bibtexitem">
Jeffrey&nbsp;T Leek and John&nbsp;D Storey.
 Capturing heterogeneity in gene expression studies by surrogate
  variable analysis.
 <em>PLoS Genet</em>, 3(9):e161, September 2007.
[&nbsp;<a href="http://dx.doi.org/10.1371/journal.pgen.0030161">DOI</a>&nbsp;| 
<a href="http://dx.plos.org/10.1371/journal.pgen.0030161">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="gaujoux_flexible_2010">4</a>]
</td>
<td class="bibtexitem">
Renaud Gaujoux and Cathal Seoighe.
 A flexible r package for nonnegative matrix factorization.
 <em>BMC Bioinformatics</em>, 11(1):367, July 2010.
 PMID: 20598126.
[&nbsp;<a href="http://dx.doi.org/10.1186/1471-2105-11-367">DOI</a>&nbsp;| 
<a href="http://www.biomedcentral.com/1471-2105/11/367/abstract">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="obenchain_variantannotation:_2011">5</a>]
</td>
<td class="bibtexitem">
Valerie Obenchain, Martin Morgan, and Michael Lawrence.
 VariantAnnotation: annotation of genetic variants, 2011.
[&nbsp;<a href="http://bioconductor.org/packages/release/bioc/html/VariantAnnotation.html">.html</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="nik-zainal_mutational_2012">6</a>]
</td>
<td class="bibtexitem">
Serena Nik-Zainal, Ludmil&nbsp;B. Alexandrov, David&nbsp;C. Wedge, Peter Van&nbsp;Loo,
  Christopher&nbsp;D. Greenman, Keiran Raine, David Jones, Jonathan Hinton, John
  Marshall, Lucy&nbsp;A. Stebbings, Andrew Menzies, Sancha Martin, Kenric Leung,
  Lina Chen, Catherine Leroy, Manasa Ramakrishna, Richard Rance, King&nbsp;Wai Lau,
  Laura&nbsp;J. Mudie, Ignacio Varela, David&nbsp;J. McBride, Graham&nbsp;R. Bignell,
  Susanna&nbsp;L. Cooke, Adam Shlien, John Gamble, Ian Whitmore, Mark Maddison,
  Patrick&nbsp;S. Tarpey, Helen&nbsp;R. Davies, Elli Papaemmanuil, Philip&nbsp;J. Stephens,
  Stuart McLaren, Adam&nbsp;P. Butler, Jon&nbsp;W. Teague, G&ouml;ran J&ouml;nsson,
  Judy&nbsp;E. Garber, Daniel Silver, Penelope Miron, Aquila Fatima, Sandrine
  Boyault, Anita Langer&oslash;d, Andrew Tutt, John&nbsp;W.M. Martens, Samuel&nbsp;A.J.R.
  Aparicio, Ake Borg, Anne&nbsp;Vincent Salomon, Gilles Thomas, Anne-Lise
  B&oslash;rresen-Dale, Andrea&nbsp;L. Richardson, Michael&nbsp;S. Neuberger, P.&nbsp;Andrew
  Futreal, Peter&nbsp;J. Campbell, and Michael&nbsp;R. Stratton.
 Mutational processes molding the genomes of 21 breast cancers.
 <em>Cell</em>, 149(5):979-993, May 2012.
[&nbsp;<a href="http://dx.doi.org/10.1016/j.cell.2012.04.024">DOI</a>&nbsp;| 
<a href="http://www.sciencedirect.com/science/article/pii/S0092867412005284">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="alexandrov_wtsi_2012">7</a>]
</td>
<td class="bibtexitem">
Ludmil Alexandrov.
 WTSI mutational signature framework, October 2012.
[&nbsp;<a href="http://www.mathworks.de/matlabcentral/fileexchange/38724-wtsi-mutational-signature-framework">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="sun_multiple_2012">8</a>]
</td>
<td class="bibtexitem">
Yunting Sun, Nancy&nbsp;R. Zhang, and Art&nbsp;B. Owen.
 Multiple hypothesis testing adjusted for latent variables, with an
  application to the AGEMAP gene expression data.
 <em>The Annals of Applied Statistics</em>, 6(4):1664-1688, December
  2012.
 Zentralblatt MATH identifier: 06141543; Mathematical Reviews number
  (MathSciNet): MR3058679.
[&nbsp;<a href="http://dx.doi.org/10.1214/12-AOAS561">DOI</a>&nbsp;| 
<a href="http://projecteuclid.org/euclid.aoas/1356629055">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="pyl_h5vc:_2013">9</a>]
</td>
<td class="bibtexitem">
Paul&nbsp;Theodor Pyl.
 h5vc: Managing alignment tallies using a hdf5 backend, 2013.
[&nbsp;<a href="http://bioconductor.org/packages/release/bioc/html/h5vc.html">.html</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="fischer_emu:_2013">10</a>]
</td>
<td class="bibtexitem">
Andrej Fischer.
 EMu: expectation-maximisation inference of mutational signatures,
  2013.
[&nbsp;<a href="http://www.sanger.ac.uk/resources/software/emu/">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="alexandrov_deciphering_2013">11</a>]
</td>
<td class="bibtexitem">
Ludmil&nbsp;B. Alexandrov, Serena Nik-Zainal, David&nbsp;C. Wedge, Peter&nbsp;J. Campbell, and
  Michael&nbsp;R. Stratton.
 Deciphering signatures of mutational processes operative in human
  cancer.
 <em>Cell Reports</em>, 3(1):246-259, January 2013.
[&nbsp;<a href="http://dx.doi.org/10.1016/j.celrep.2012.12.008">DOI</a>&nbsp;| 
<a href="http://www.sciencedirect.com/science/article/pii/S2211124712004330">http</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="cibulskis_sensitive_2013">12</a>]
</td>
<td class="bibtexitem">
Kristian Cibulskis, Michael&nbsp;S. Lawrence, Scott&nbsp;L. Carter, Andrey Sivachenko,
  David Jaffe, Carrie Sougnez, Stacey Gabriel, Matthew Meyerson, Eric&nbsp;S.
  Lander, and Gad Getz.
 Sensitive detection of somatic point mutations in impure and
  heterogeneous cancer samples.
 <em>Nature Biotechnology</em>, advance online publication, February
  2013.
[&nbsp;<a href="http://dx.doi.org/10.1038/nbt.2514">DOI</a>&nbsp;| 
<a href="http://www.nature.com/nbt/journal/vaop/ncurrent/full/nbt.2514.html">.html</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="fischer_emu:_2013-1">13</a>]
</td>
<td class="bibtexitem">
Andrej Fischer, Christopher&nbsp;Jr Illingworth, Peter&nbsp;J Campbell, and Ville
  Mustonen.
 EMu: probabilistic inference of mutational processes and their
  localization in the cancer genome.
 <em>Genome biology</em>, 14(4):R39, April 2013.
 PMID: 23628380.
[&nbsp;<a href="http://dx.doi.org/10.1186/gb-2013-14-4-r39">DOI</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="alexandrov_signatures_2013">14</a>]
</td>
<td class="bibtexitem">
Ludmil&nbsp;B. Alexandrov, Serena Nik-Zainal, David&nbsp;C. Wedge, Samuel A. J.&nbsp;R.
  Aparicio, Sam Behjati, Andrew&nbsp;V. Biankin, Graham&nbsp;R. Bignell, Niccol&ograve;
  Bolli, Ake Borg, Anne-Lise B&oslash;rresen-Dale, Sandrine Boyault, Birgit
  Burkhardt, Adam&nbsp;P. Butler, Carlos Caldas, Helen&nbsp;R. Davies, Christine Desmedt,
  Roland Eils, J&oacute;runn&nbsp;Erla Eyfj&ouml;rd, John&nbsp;A. Foekens, Mel Greaves, Fumie
  Hosoda, Barbara Hutter, Tomislav Ilicic, Sandrine Imbeaud, Marcin Imielinsk,
  Natalie J&auml;ger, David T.&nbsp;W. Jones, David Jones, Stian Knappskog, Marcel
  Kool, Sunil&nbsp;R. Lakhani, Carlos L&oacute;pez-Ot&iacute;n, Sancha Martin, Nikhil&nbsp;C.
  Munshi, Hiromi Nakamura, Paul&nbsp;A. Northcott, Marina Pajic, Elli Papaemmanuil,
  Angelo Paradiso, John&nbsp;V. Pearson, Xose&nbsp;S. Puente, Keiran Raine, Manasa
  Ramakrishna, Andrea&nbsp;L. Richardson, Julia Richter, Philip Rosenstiel, Matthias
  Schlesner, Ton&nbsp;N. Schumacher, Paul&nbsp;N. Span, Jon&nbsp;W. Teague, Yasushi Totoki,
  Andrew N.&nbsp;J. Tutt, Rafael Vald&eacute;s-Mas, Marit&nbsp;M. van Buuren, Laura
  van&nbsp;t Veer, Anne Vincent-Salomon, Nicola Waddell, Lucy&nbsp;R.
  Yates, Australian Pancreatic Cancer Genome Initiative, ICGC Breast
  Cancer Consortium, ICGC MMML-Seq Consortium, Icgc PedBrain,
  Jessica Zucman-Rossi, P.&nbsp;Andrew&nbsp;Futreal, Ultan McDermott, Peter Lichter,
  Matthew Meyerson, Sean&nbsp;M. Grimmond, Reiner Siebert, El&iacute;as Campo,
  Tatsuhiro Shibata, Stefan&nbsp;M. Pfister, Peter&nbsp;J. Campbell, and Michael&nbsp;R.
  Stratton.
 Signatures of mutational processes in human cancer.
 <em>Nature</em>, 500(7463):415-421, August 2013.
[&nbsp;<a href="http://dx.doi.org/10.1038/nature12477">DOI</a>&nbsp;| 
<a href="http://www.nature.com/nature/journal/v500/n7463/full/nature12477.html">.html</a>&nbsp;]

</td>
</tr>


<tr valign="top">
<td align="right" class="bibtexnumber">
[<a name="pyl_h5vc:_2014">15</a>]
</td>
<td class="bibtexitem">
Paul&nbsp;Theodor Pyl, Julian Gehring, Bernd Fischer, and Wolfgang Huber.
 h5vc: Scalable nucleotide tallies with HDF5.
 <em>Bioinformatics</em>, page btu026, January 2014.
 PMID: 24451629.
[&nbsp;<a href="http://dx.doi.org/10.1093/bioinformatics/btu026">DOI</a>&nbsp;| 
<a href="http://bioinformatics.oxfordjournals.org/content/early/2014/01/21/bioinformatics.btu026">http</a>&nbsp;]

</td>
</tr>
</table>
</div>
</div>


<div id="outline-container-sec-8" class="outline-2">
<h2 id="sec-8"><span class="section-number-2">8</span> Session Info</h2>
<div class="outline-text-2" id="text-8">
<!--begin.rcode echo=FALSE, results='markup'
sessionInfo()
end.rcode-->
</div>
</div>
</div>
</body>
</html>
