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\title{\bf iChip: A Package for Analyzing Multi-platform ChIP-chip data with Various Sample Sizes}

\author{Qianxing Mo}

\maketitle

\begin{center}
Division of Biostatistics\\
Dan L. Duncan Cancer Center\\
Baylor College of Medicine\\
{\tt qmo@bcm.edu}
\end{center}

\tableofcontents

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

This package implements the models proposed by Mo and Liang (2010a, b) for ChIP-chip data analysis. 
The package can be used to analyze ChIP-chip data from multiple platforms 
(e.g. Affymetrix, Agilent, and NimbleGen) with various genomic resolutions and various sample sizes. 
Mo and Liang (2010a,b) proposed Bayesian Hierarchical models to model ChIP-chip data in which 
the spatial dependency of the data is modeled through ferromagnetic high-order or standard Ising models.  
Briefly,  without loss of generality, the proposed methods let each probe be associated with a binary 
latent variable $X_i \in (0, 1)$,
where $i$ denotes the ID for the probe, and $X_i=1$ denotes that the probe is an enriched probe, and 0
otherwise.  In the first stage, conditioning on the latent variable, the probe enrichment measurements for 
each state (0 or 1) are modeled by normal distributions.  Here, the probe enrichment measurement could
be any appropriate measurement for comparison of IP-enriched and control samples.
For example, the measurement could be a log2 ratio of IP-enriched and control samples for
a single replicate, or a summary statistic such as t-like statistic or mean difference for
multiple replicates.  In the second stage, the latent variable is modeled by 
ferromagnetic Ising models.  The Gibbs sampler and Metropolis algorithm are used to simulate from the 
posterior distributions of the model parameters, and the posterior probabilities for the probes 
in the enriched state ($X_i = 1$) are used for statistical inference.  
A probe with a high posterior probability of the enriched state will provide strong evidence that the probe is an 
enriched probe.  For further details, we refer the user to Mo and Liang's papers. 

\section{Agilent and Affymetrix ChIP-chip Data}

A subset of the Oct4 (Boyer et al., 2005) and the p53 (Cawley et al, 2004) data are used for the purpose of illustration.
The average genomic resolutions for the Oct4 and p53 data are about 280 bps and 35 bps, respectively.  
Both the Oct4 and p53 data have been log2 transformed and quantile-normalized.  
Note iChip software doesn't provide functions for data normalization.  The users should normalize their data before using iChip software.  For one-color and two-color data, one can use the quantile method (e.g., see the function 
{\it normalize.quantiles()} in the {\bf affy} package). For two-color data, one can also use 
the \textit{loess} method (e.g., see the function \textit{normalizeWithinArrays()} in the {\bf limma} package). 
\noindent
The full Oct4 data can be obtained from \\
  \url{http://jura.wi.mit.edu/young_public/hESregulation/Data_download.html}.

\noindent
The full p53 data can be obtained from \\
\url{http://www.gingeras.org/affy_archive_data/publication/tfbs/}.

\section{Example1 --- Analyzing the Agilent Promoter Array Data}
Let's start analyzing the low resolution Oct4 data.  First, we need to calculate the enrichment measurement
for each probe.  Although the enrichment measurement could be any appropriate measurement 
for comparison of IP-enriched and control samples, we suggest using the 
empirical Bayes t-statistic for multiple replicates, which can be easily calculated using 
the {\bf limma} package (Smyth, 2004).  Here, we call the empirical Bayes t-statistic limma t-statistic.  
For the users who are not familiar with limma t-statistic, we provide a wrapper function {\bf lmtstat} 
for the calculation. \\

\noindent
There are two replicates for the Oct4 data.  
The enriched DNA was labeled with Cy5 (red) dye and the control DNA was labeled with Cy3 (green) dye.  
<<echo=TRUE,print=FALSE>>=
library(iChip)
data(oct4)
head(oct4,n=3L)
@ 

\noindent
To use the iChip1 and iChip2 function, the data must be sorted, firstly by chromosome then by genomic position.
It may be a good habit to sort the data at the beginning, although function {\bf lmtstat} doesn't require the data to
be sorted. 
<<echo=TRUE,print=FALSE>>=
oct4 = oct4[order(oct4[,1],oct4[,2]),]
@ 
\noindent
Calculate the enrichment measurements --- two-sample limma t-statistics. 
<<echo=TRUE,print=FALSE>>=
oct4lmt = lmtstat(oct4[,5:6],oct4[,3:4])
@ 

\noindent
Here, we treat the IP-enriched and control
data as independent data although both the IP-enriched and control samples were hybridized to the same array. 
This is because the quantile-normalization method was applied to the oct4 data. If the data are normalized using
\textit{loess} method, the resulting data are in log ratio format (e.g., log2(IP-enriched/control)).  In this case, 
one can calculate the paired limma t-statistics. Suppose a matrix called log2ratio are the loess-normalized data, 
where each column corresponds to a sample, the paired limma t-statistics can be calculated 
using {\bf lmtstat}(log2ratio). \\

\noindent
Prepare the data for iChip2 function. 
<<echo=TRUE,print=FALSE>>=
oct4Y = cbind(oct4[,1],oct4lmt)
@ 

\noindent 
Apply the second-order Ising model to the ChIP-chip data by setting winsize = 2. 
According to our experience, a balance between high sensitivity and low FDR can be
achieved when winsize = 2.  The critical value of the second-order Ising model is about 1.0. 
For low resolution data, the value of beta could be around the critical value.   
In general, increasing beta value will lead to less enriched regions, which amounts to 
setting a stringent criterion for detecting enriched regions. 
<<echo=TRUE,print=FALSE>>=
set.seed(777)
oct4res2 = iChip2(Y=oct4Y,burnin=2000,sampling=10000,winsize=2,
  sdcut=2,beta=1.25,verbose=FALSE)
@ 

\noindent 
Plot the model parameters to see whether they converge.  In general, the MCMC chains have converged when the parameters 
fluctuate around the modes of their distributions.  If there is an obvious trend(e.g. continuous increase or decrease), 
one should increase the number of iterations in the burn-in phase.  If this doesn't work, one can adjust 
the parameter {\bf beta} to see how it affects the results. 
\begin{center}
<<fig=TRUE,echo=TRUE>>=
par(mfrow=c(2,2), mar=c(4.1, 4.1, 2.0, 1.0))
plot(oct4res2$mu0, pch=".", xlab="Iterations", ylab="mu0")
plot(oct4res2$lambda0, pch=".", xlab="Iterations", ylab="lambda0")
plot(oct4res2$mu1, pch=".", xlab="Iterations", ylab="mu1")
plot(oct4res2$lambda1, pch=".", xlab="Iterations", ylab="lambda1")
@
\end{center}

\noindent
The histogram of the posterior probabilities should be dichotomized, either 0 or 1.  For transcription factor binding
site studies, the histogram should be dominated by 0. 
\begin{center}
<<fig=TRUE,echo=TRUE>>=
hist(oct4res2$pp)
@ 
\end{center}


\noindent
Call the enriched regions detected by iChip2 using a
posterior probability (pp) cutoff of 0.9.  
<<echo=TRUE,print=FALSE>>=
reg1 = enrichreg(pos=oct4[,1:2],enrich=oct4lmt,pp=oct4res2$pp,
  cutoff=0.9,method="ppcut",maxgap=500)
print(reg1)
@ 

\noindent
Call the enriched regions detected by iChip2 using a FDR cutoff of 0.01.  The FDR is calculated
using a direct posterior probability approach (Newton et al., 2004). 
<<echo=TRUE,print=FALSE>>=
reg2 = enrichreg(pos=oct4[,1:2],enrich=oct4lmt,pp=oct4res2$pp,
  cutoff=0.01,method="fdrcut",maxgap=500)
print(reg2)
@ 

\noindent
BED file can be easily made using the output from function {\bf enrichreg}, which can be used for motif discovery
and visualized in the UCSC genome browser.  For example, 

<<echo=TRUE,print=FALSE>>=
bed1 = data.frame(chr=paste("chr",reg2[,1],sep=""),reg2[,2:3])
print(bed1[1:2,])
@ 

\noindent
Alternatively, one may create a BED file using the peak position of the enriched regions.  For example, 

<<echo=TRUE,print=FALSE>>=
bed2 = data.frame(chr=paste("chr",reg2[,1],sep=""),gstart=reg2[,6]-100,
  gend=reg2[,6]+100)
print(bed2[1:2,])
@ 

\noindent
Model the oct4 data using the first-order Ising model. 
<<echo=TRUE,print=FALSE>>=
oct4res1 =iChip1(enrich=oct4lmt,burnin=2000,sampling=10000,sdcut=2,beta0=3,
  minbeta=0,maxbeta=10,normsd=0.1,verbose=FALSE)
@ 

\noindent 
Plot the model parameters to see whether they converge.
\begin{center}
<<fig=TRUE,echo=TRUE>>=
par(mfrow=c(2,2), mar=c(4.1, 4.1, 2.0, 1.0))
plot(oct4res1$beta, pch=".", xlab="Iterations", ylab="beta")
plot(oct4res1$mu0, pch=".", xlab="Iterations", ylab="mu0")
plot(oct4res1$mu1, pch=".", xlab="Iterations", ylab="mu1")
plot(oct4res1$lambda, pch=".", xlab="Iterations", ylab="lambda")
@
\end{center}

\noindent
Call the enriched regions detected by iChip1.
<<echo=TRUE,print=FALSE>>=
enrichreg(pos=oct4[,1:2],enrich=oct4lmt,pp=oct4res1$pp,cutoff=0.9,
          method="ppcut",maxgap=500)
enrichreg(pos=oct4[,1:2],enrich=oct4lmt,pp=oct4res1$pp,cutoff=0.01,
          method="fdrcut",maxgap=500)
@ 

\section{Example2 --- Analyzing the Affymetrix Tiling Array Data}
\noindent
Now, let's analyze the high resolution p53 data.  

<<echo=TRUE,print=FALSE>>=
data(p53)
head(p53,n=3L)
# sort the p53 data by chromosome and genomic position
p53 = p53[order(p53[,1],p53[,2]),]
p53lmt = lmtstat(p53[,9:14],p53[,3:8])
p53Y = cbind(p53[,1],p53lmt)
@ 

\noindent
For high resolution data, beta could be set to a relatively large value (e.g. 2--4).
In general, increasing beta value will lead to less enriched regions, which amounts to 
setting a stringent criterion for detecting enriched regions. 
<<echo=TRUE,print=FALSE>>=
p53res2 = iChip2(Y=p53Y,burnin=2000,sampling=10000,winsize=2,sdcut=2,beta=2.5)
@ 

\begin{center}
<<fig=TRUE,echo=TRUE>>=
par(mfrow=c(2,2), mar=c(4.1, 4.1, 2.0, 1.0))
plot(p53res2$mu0, pch=".", xlab="Iterations", ylab="mu0")
plot(p53res2$lambda0, pch=".", xlab="Iterations", ylab="lambda0")
plot(p53res2$mu1, pch=".", xlab="Iterations", ylab="mu1")
plot(p53res2$lambda1, pch=".", xlab="Iterations", ylab="lambda1")
@
\end{center}

\noindent
The histogram of the posterior probabilities should be dichotomized, either 0 or 1.  For transcription factor binding
site studies, the histogram should be dominated by 0. 
\begin{center}
<<fig=TRUE,echo=TRUE>>=
hist(p53res2$pp)
@ 
\end{center}

<<echo=TRUE,print=FALSE>>=
enrichreg(pos=p53[,1:2],enrich=p53lmt,pp=p53res2$pp,cutoff=0.9,
          method="ppcut",maxgap=500)
enrichreg(pos=p53[,1:2],enrich=p53lmt,pp=p53res2$pp,cutoff=0.01,
          method="fdrcut",maxgap=500)
@ 

\noindent
Model the p53 data using the first-order Ising model. 
<<echo=TRUE,print=FALSE>>=
p53res1 =iChip1(enrich=p53lmt,burnin=2000,sampling=10000,sdcut=2,beta0=3,
  minbeta=0,maxbeta=10,normsd=0.1,verbose=FALSE)
@ 

\begin{center}
<<fig=TRUE,echo=TRUE>>=
par(mfrow=c(2,2), mar=c(4.1, 4.1, 2.0, 1.0))
plot(p53res1$beta, pch=".", xlab="Iterations", ylab="beta")
plot(p53res1$mu0, pch=".", xlab="Iterations", ylab="mu0")
plot(p53res1$mu1, pch=".", xlab="Iterations", ylab="mu1")
plot(p53res1$lambda, pch=".", xlab="Iterations", ylab="lambda")
@
\end{center}

<<echo=TRUE,print=FALSE>>=
enrichreg(pos=p53[,1:2],enrich=p53lmt,pp=p53res1$pp,cutoff=0.9,
          method="ppcut",maxgap=500)
enrichreg(pos=p53[,1:2],enrich=p53lmt,pp=p53res1$pp,cutoff=0.01,
          method="fdrcut",maxgap=500)
@ 

\section{Tips}
\noindent
What happens when there is no enriched region?  Suppose the data are just random noises.  
<<echo=TRUE,print=FALSE>>=
randomY = cbind(p53[,1],rnorm(10000,0,1))
randomres2 = iChip2(Y=randomY,burnin=1000,sampling=5000,winsize=2,
  sdcut=2,beta=2.5,verbose=FALSE)
table(randomres2$pp)
@ 

\noindent
In this case, all the probes are only in one state.  Since there is no enriched probe, the mean and variance 
become $-\infty$ or $\infty$.  In the MCMC simulations, we relabel the outputs
according to the constraint $\mu_0 < \mu_1$, where $\mu_0$ and $\mu_1$ are the population means for the non-enriched
and enriched probes, respectively (For details, see Mo and Liang, 2010a).  That is, when $\mu_0 > \mu_1$,
$\mu_0$ will be treated as the population mean of the enriched probes.  As a result, no matter 
$\mu_1 = \infty$ or $\mu_1 = -\infty$, the posterior probabilities of the probes are all 1s or close to 1. 
Therefore, when this happens, it means there is no enriched region.  \\

\noindent
In addition, for the studies of transcription factor binding sites, if the posterior probabilities are not 
dichotomized and dominated by 0, the Ising model is not in the super-paramagnetic phase.  
Only the super-paramagnetic phase reflects the binding events on the chromosomes.  
Therefore, the user should increase the value of beta to let the phase transition occur so that
the Ising model reach the super-paramagnetic phase. \\

\noindent
The probes' states reported by iChip1 are also in the same state if there is no enriched region. 
<<echo=TRUE,print=FALSE>>=
randomres1 =iChip1(enrich=randomY[,2],burnin=1000,sampling=5000,sdcut=2,
  beta0=3,minbeta=0,maxbeta=10,normsd=0.1,verbose=FALSE)
table(randomres1$pp)
@ 

\noindent
Although the above two examples only show the analysis for the data on a single chromosome, one can 
use iChip2 and iChip1 functions to analyze data with multiple chromosomes.  Although a probe may not 
be physically close to its adjacent probes (e.g., the last probe of a chromosome and the first probe 
of the next chromosome, and the probes in the same chromosome that are adjacent but separated by 
a long genomic distance), in practice, 
it should be acceptable to consider the interactions between these adjacent and boundary probes.  
There are two reasons for this.  First, the number of these probes is quite small, 
compared to all the probes in the tiling arrays. Second, these boundary probes have a very high 
probability of being non-enriched, thus it should be reasonable to consider the interactions between them.  
If we let these boundary and adjacent probes interact with each other, 
it has little effect on the results, but significantly simply the algorithms for modeling ChIP-chip data. 
In addition, it should be noted that when the data are very noisy, the posterior mean of beta will be 
relatively small(e.g., around 1) when the iChip1 method is used, and the posterior probabilities are not
dichotomized and dominated by 0.  In this case, the user should increase the value of parameter {\bf minbeta}
or use the {\bf iChip2} method for modeling. 

\section{Parallel Computaton}
If the total number of probes is relatively small (e.g., a half million), one may analyze the data 
in a single run.  If the total number of probes are large (e.g., several millions), 
one may perform parallel computation.  For example, one can model the data chromosome by chromosome and
run many jobs simultaneously.  The following is an example of parallel computation using 
the snowfall package (\url{http://cran.r-project.org/web/packages/snowfall/}).  \\

\noindent
library(snow) \\
library(snowfall)  \\
dataList = list(oct4t=oct4lmt,p53t=p53lmt) \\
sfInit(parallel=TRUE,cpus=2,type="SOCK") \\
res=sfLapply(dataList,iChip1,burnin = 2000, sampling = 10000, sdcut = 2, \\
 beta0 = 3,minbeta = 0, maxbeta = 10, normsd = 0.1, verbose = FALSE) \\

 \noindent
 In addition, Mo (2012) has applied Ising models to analysis of
 ChIP-seq data, and provided an R script named 'iSeq.R' that can be
 used as a command line program in Unix/Linux environment.  If the
 user is interested in it, the user may modify the script to
 automate ChIP-chip data analyis.  The R script iSeq.R is available
 at \\
\url{https://sites.google.com/site/quincymobio/teaching-materials}.  
 
\section{Citing iChip}
If you use iChip2 function, please cite Mo and Liang (2010a). If you use iChip1 function,
please cite Mo and Liang (2010b). 

<<echo=TRUE,print=TRUE>>=
sessionInfo()
@ 

\begin{thebibliography}{}

\bibitem[\protect\citeauthoryear{Mo and Liang.}{2010}]{mo2010a}
Mo, Q., Liang, F. (2010a).
Bayesian Modeling of ChIP-chip data through a high-order Ising Model.  
{\it Biometrics} 66(4), 1284-1294.

\bibitem[\protect\citeauthoryear{Mo and Liang.}{2010}]{mo2010b}
Mo, Q., Liang, F. (2010b).
A hidden Ising model for ChIP-chip data analysis.  
{\it Bioinformatics} {\bf 26(6)}, 777-783.

\bibitem[\protect\citeauthoryear{Mo}{2011}]{mo2012}
Mo, Q. (2012). A fully Bayesian hidden Ising model for ChIP-seq data analysis. 
{\it Biostatistics} {\bf 13(1)}, 113-28.

\bibitem[\protect\citeauthoryear{Boyer et~al.}{2005}]{boy}
Boyer, L.A., Lee, T.I., Cole, M.F., et al. (2005).
Core transcriptional regulatory circuitry in human embryonic stem cells.
{\it Cell} {\bf 122}, 947-956.

\bibitem[\protect\citeauthoryear{Cawley et~al.}{2004}]{caw}
Cawley, S., Bekiranov, S., Ng, H.H., et al. (2004).
Unbiased mapping of transcription factor binding sites along human chromosomes 21 and 22 points to
widespread regulation of noncoding RNAs.
{\it Cell} {\bf 116}, 499-509.

\bibitem[\protect\citeauthoryear{Newton et al.}{2004}]{new04}
Newton, M., Noueiry, A., Sarkar, D., Ahlquist, P. (2004). Detecting differential gene expression with a semiparametric
hierarchical mixture method.
{\it Biostatistics} {\bf 5} , 155-176.

\bibitem[\protect\citeauthoryear{Smyth}{2004}]{smyth}
Smyth, G. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray
experiments. {\it Statistical Applications in Genetics and Molecular Biology,} {\bf 3}, Iss. 1, Article 3.

\end{thebibliography}

\end{document}
