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%\VignetteIndexEntry{A likelihood maximization approach to infer the clonal structure of a cancer using multiple tumor samples}
%\VignetteDepends{Clomial}
%\VignetteKeywords{Cancer, Binomial, Clones, EM}
%\VignettePackage{Clomial}
\documentclass[12pt]{article}

\usepackage{amsmath}
\usepackage{cite, hyperref}

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\author{Habil Zare }

\begin{document}
\title{Clomial: A likelihood maximization approach to infer the 
clonal structure of a cancer using multiple tumor samples}
\maketitle{}

\tableofcontents
\newpage

\section{Introduction}
Identifying the clonal decomposition of a tumor is oncologically important 
and computationally challenging.  

\subsection{Oncological motivation}
Cancers arise from successive rounds of mutation and selection, generating 
clonalpopulations that vary in size, mutational content and 
drug responsiveness.
Ascertaining the clonal composition of a tumor is therefore important both 
for prognosis and therapy. Mutation counts
and frequencies resulting from next-generation sequencing (NGS) potentially 
reflect a tumor's clonal composition; however, deconvolving NGS data to infer 
a tumor's clonal structure presents a major challenge.

\subsection{Computational methodology}
Clomial is based on a generative model for NGS data derived from multiple 
subsections of a single tumor.
The counts of alternative alleles are modeled using binomial distributions, 
and therefore, the novel method is called {\bf ``Clomial''}; 
{\bf Clo}nal decomposition using bino{\bf{mial}} models.
Unlike the previous approaches, Clomial is capable of incorporating multiple
samples in the analysis together to increase statistical power.
It uses an expectation-maximization (EM) procedure for estimating
the clonal genotypes and relative frequencies
as described in \refOne,
which demonstrates, via simulation,
the validity of Clomial approach.
As a real life example, 
this package also provides the data and code to infer the clonal composition
of a primary breast cancer and associated metastatic lymph node. 
Applying Clomial to larger numbers of tumors should cast light on the 
clonal evolution of cancers in space and time.

Please refer to \refOne for a complete  description of
the methodology, and the results on the real data set.



\section{How to run Clomial?}
\subsection{Installation}
Clomial is an R package source that can be downloaded and 
installed from BioCunductor by the followig commands in R:
\newline
$\\$
\texttt{source("http://bioconductor.org/biocLite.R")}
\newline
\texttt{biocLite("Clomial")}
$\\$

%%Alternative, if the source code is already available, 
%%the package can be installed by the following command in Linux:
%%\newline
%%$\\$
%%\texttt{R CMD INSTALL Clomial\_x.y.z.tar.gz}
%%\newline
%%$\\$
%%where x.y.z. determines the version.

\subsection{A quick overview}
The main function is \code{Clomial()} which takes as input 2 matrices 
$Dt$ and $Dc$.
They contain the counts of the alternative allele, and the total number of 
processed reads, accordingly. 
Their rows correspond to the genomic loci, and their columns correspond to 
the samples.
Also, $C$, the assumed number of clones should be provided to \code{Clomial()}.
Several models should be trained using different initial values to escape from
 local optima.
Then, the best one in terms of the likelihood can be chosen by 
choose.best() function.
Finally, the Bayesian Information Criterion (BIC) can be performed using the 
compute.bic() function
to estimate the number of clones. However, the results of BIC analysis should 
be interpreted with 
great caution for the reasons explained in \refOne.


\subsection{An example}

This example shows how Clomial can be run on counts obtained from next 
generation sequencing. 
The user might use standard tools such as BWA, Samtools, or DeepSNV to map 
the reads and compute the counts.
In the following example, we analyze ready-to-use data from a primary breast
cancer and associated metastatic lymph node,
where breastCancer is a list containing the input 2 matrices $Dt$ and $Dc$.

\begin{center}
<<example,fig=FALSE, echo=TRUE>>=
library(Clomial)
set.seed(1)
data(breastCancer)
Dc <- breastCancer$Dc
Dt <- breastCancer$Dt
Clomial2 <-Clomial(Dc=Dc,Dt=Dt,maxIt=20,C=4,binomTryNum=2)
@
\end{center}

Clomial is done and the results are stored in \code{Clomial2}. 
We are interested in \code{Clomial[["models"]]} which is a list of 
trained models.
For each trained model, $Mu$ models the matrix of genotypes, 
where rows and columns correspond to genomic loci and clones, accordingly. 
Also, \code{P} is the matrix of clonal frequency where rows and columns 
correspond to clones and samples, accordingly. For example, the trained 
parameters for the first model are given by:

\begin{center}
<<model1,fig=FALSE, echo=TRUE>>=
model1 <- Clomial2$models[[1]]
## The clonal frequencies:
round(model1$P,digits=2)
## Similarly, the genotypes is given by round(model1$Mu).
@
\end{center}

\subsection{Choosing the best model}
In practice, more models should be trained using multiple random 
initialization to escape from local optima. This can be done by,
say, \code{binomTryNum=1000} which needs longer computational time, 
in order of two hours, for this data.
For the purpose of this manual, we can use pre-computed results as follows:

\begin{center}
<<model1,fig=FALSE, echo=TRUE>>=
data(Clomial1000)
models <- Clomial1000$models
## Number of trained models:
length(models)
@
\end{center}

The best model in terms of likelihood is given by \code{choos.best()} function:
\begin{center}
<<model1,fig=FALSE, echo=TRUE>>=
chosen <- choose.best(models=models, doTalk=TRUE)
M1 <- chosen$bestModel
print("Genotypes according to the best model:")
round(M1$Mu)
print("Clone frequencies in the first sample:")
round(M1$P[,1],digits=2)
@
\end{center}

In the above demo example, the number of clones was assumed to be 4. 
For real applications, it is useful to try several clone numbers and 
compare the results using BIC.
Also, note that fitting the best set of parameters needs a large number of 
models to be trained on data
in order to escape from local optima. In practice, the suitable number of 
models depends on the assumed number of clones, number of genomic loci, 
and number on samples.

\section{Reference}
Zare et al., \textbf{
Inferring clonal composition from multiple sections of a breast cancer},
Under review.


\end{document}














