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\title{The \Rpackage{ENmix} User's Guide}

\date{Modified: April 9 2020.  Compiled: \today}
\begin{document}
\maketitle

\section{Introduction}

The \Rpackage{ENmix} package provides a set of quality control and data 
pre-processing tools for Illumina  
HumanMethylation450 and MethylationEPIC Beadchips. It includes ENmix background 
 correction, RELIC dye bias correction, RCP probe-type bias adjustment, 
 along with a number of additional tools.
These functions can be used to remove unwanted experimental noise and thus to
improve accuracy and reproducibility of methylation measures. 
\Rpackage{ENmix} functions 
are flexible and transparent. Users have option to choose a single pipeline 
command to finish all data pre-processing steps (including background correction, 
dye-bias adjustment, inter-array normalization and probe-type bias correction) or 
to use individual functions sequentially to perform data pre-processing in a more 
customized manner. In addition the \Rpackage{ENmix} package has selectable 
complementary functions for efficient data visualization (such as data 
distribution plots); quality control (identifing and filtering 
low quality data points, samples, probes, and outliers, along with 
imputation of missing values); identification of probes with multimodal 
distributions due to SNPs or other factors; exploration of data variance
 structure using principal component regression analysis plot; preparation
of experimental factors related surrogate control variables 
to be adjusted in downstream 
statistical analysis; an efficient algorithm oxBS-MLE to estimate
5-methylcytosine and 5-hydroxymethylcytosine level; estimation of celltype
proporitons; methlation age calculation and differentially methylated
region (DMR) analysis.

The data structure used by the \Rpackage{ENmix} package is compatible with
several other related R packages, such as \Rpackage{minfi},
\Rpackage{wateRmelon} and \Rpackage{ChAMP},
providing straightforward integration of 
ENmix-corrected datasets for subsequent data analysis. 

The software is designed to support large scale data analysis, and provides
 multi-processor parallel computing options for most functions. 

\section{Citation}

The following publications can be refered to learn more about the methods 
implemented in this package. 

Xu Z, Niu L, Li L, Taylor JA.
ENmix: a novel background correction method for Illumina
HumanMethylation450 BeadChip, Nucleic Acids Research, 2015

Niu L, Xu Z, Taylor JA.
RCP: a novel probe design bias correction method for Illumina Methylation 
BeadChip. Bioinformatics, 2016

Xu Z, Langie SA, De Boever P, Taylor JA, Niu L.
RELIC: a novel dye-bias correction method for Illumina Methylation BeadChip.
BMC Genomics. 2017

Xu Z, Taylor JA, Leung YK, Ho SM, Niu L.
oxBS-MLE: an efficient method to estimate 5-methylcytosine and 
5-hydroxymethylcytosine in paired bisulfite and oxidative 
bisulfite treated DNA.
Bioinformatics. 2016 

Xu Z, Xie C, Taylor JA, Niu L. 
ipDMR: Identification of differentially methylated regions with interval P values
in review, 2020

\section{Example Analysis}

\subsection{Example 1: using pipeline }

Pipeline function \Rfunction{mpreprocess} can be used to perform background 
correction, dye-bias adjustment, inter-array normalization, probe-type bias 
correction, as well as outlier removal and imputation in a single step. 

<<example, eval=FALSE>>=
library(ENmix)
#read in data
require(minfiData)
#data pre-processing
beta=mpreprocess(RGsetEx,nCores=6)
#or
#read in IDAT files
path <- file.path(find.package("minfiData"),"extdata")
rgSet <- readidat(path = path,recursive = TRUE)
#quality control and data pre-processing
beta=mpreprocess(rgSet,nCores=6,qc=TRUE,foutlier=TRUE,
     rmcr=TRUE,impute=TRUE)
@

\subsection{Example 2: using individual function}

This example code is basically doing the same thing as in example 1, but 
more transparent, and has more customized options. 

<<example, eval=FALSE>>=
library(ENmix)
#read in data
path <- file.path(find.package("minfiData"),"extdata")
rgSet <- readidat(path = path,recursive = TRUE)

#QC info
qc<-QCinfo(rgSet)
#background correction and dye bias correction
#if provide qc info, the low quality samples and probes 
#will be excluded before background correction
mdat<-preprocessENmix(rgSet, bgParaEst="oob", dyeCorr="RELIC", 
QCinfo=qc, nCores=6)
#low quality samples and probes can also be excluded after 
#background correction using QCfilter.
#mdat <- QCfilter(mdat,qcinfo=qc,outlier=TRUE)
#inter-array normalization
mdat<-norm.quantile(mdat, method="quantile1")
#probe-type bias adjustment
beta<-rcp(mdat,qcscore=qc)
beta <- rm.outlier(beta,qcscore=qc,impute=TRUE,rmcr=TRUE)
@


\subsection{Example 3: A more elaborated example}

This example is to demonstrate the flexibility of the package functions. 
Getting detailed information about data quality, SNP-like probes, excluding 
user specified probes and/or samples, principal component regression analysis,
outlier removal, sex prediction, cell sub-type proportion estimates and control
 surrogate variables. 

<<example, eval=FALSE>>=
library(ENmix)
#read in data
path <- file.path(find.package("minfiData"),"extdata")
rgSet <- readidat(path = path,recursive = TRUE)
sheet <- read.metharray.sheet(file.path(find.package("minfiData"),"extdata"), 
         pattern = "csv$")
rownames(sheet)=paste(sheet$Slide,sheet$Array,sep="_")
colData(rgSet)=as(sheet[colnames(rgSet),],"DataFrame")
#control plots
plotCtrl(rgSet)
#QC info
qc<-QCinfo(rgSet)
#calculate detection P values
detp=calc_detP(rgSet,detPtype = "negative")
detp2=calc_detP(rgSet,detPtype = "oob")
#get methDataSet
mraw <- getmeth(rgSet)
#get raw methyaltion beta values
beta<-getB(mraw)
#distribution plot
multifreqpoly(beta,main="Methylation Beta value distribution")
#Search for multimodal CpGs
#sample size in this example data is too small for this purpose!
#exclude low quality data first
bb=beta; bb[qc$detP>0.05 | qc$nbead<3]=NA 
nmode<-nmode.mc(bb, minN = 3, modedist=0.2, nCores = 6)
outCpG = names(nmode)[nmode>1]
#background correction and dye bias correction
mdat<-preprocessENmix(rgSet, bgParaEst="oob", dyeCorr="RELIC",
                      QCinfo=qc, exCpG=outCpG, nCores=6)
#inter-array normalization
mdat<-norm.quantile(mdat, method="quantile1")
colData(mdat)=as(sheet[colnames(mdat),],"DataFrame")
#probe-type bias adjustment
beta<-rcp(mdat,qcscore=qc)
# Principal component regression analysis plot
cov<-data.frame(group=colData(mdat)$Sample_Group,
    slide=factor(colData(mdat)$Slide))
pcrplot(beta, cov, npc=6)
#filter out low quality and outlier data points for each probe;
#rows and columns with too many missing value can be removed 
#if specify; Do imputation to fill missing data if specify.
beta <- rm.outlier(beta,qcscore=qc,rmcr=TRUE,impute=TRUE)
#Non-negative control surrogate variables
csva<-ctrlsva(rgSet)
#estimate cell type proportions
#based on rgDataset
celltype=estimateCellProp(userdata=rgSet,refdata="FlowSorted.Blood.450k",
         nonnegative = TRUE,normalize=TRUE)
#using methDataSet
celltype=estimateCellProp(userdata=mdat,refdata="FlowSorted.Blood.450k",
         nonnegative = TRUE,normalize=TRUE)
#using beta value
celltype=estimateCellProp(userdata=beta,refdata="FlowSorted.Blood.450k",
         nonnegative = TRUE,normalize=TRUE)
#predic sex based on rgDataSet or methDataset
sex=predSex(rgSet)
sex=predSex(mdat)
#Methylation age calculation
mage=methyAge(beta)
#ICC analysis, see manual
#DMR analysis, see manual
@

\section{Setting up the data}
The first step is to import array raw data files (*.idat)
 to create an object of \Robject{rgDataSet}, which is similar to 
\Robject{RGChannelSetExtended} in minfi package, but with probe annotation 
integrated into data object, and having smaller data size. User can also 
use minfi package to read in idat files and create 
\Robject{RGChannelSetExtended}. Most functions in ENmix support 
\Robject{RGChannelSetExtended} or \Robject{RGChannelSet}.

<<UnevaluatedCode, eval=FALSE>>=
library(ENmix)
rgSet <- readidat(path = "directory containing idat files",recursive = TRUE)
@
When methylation IDAT raw data files are not available, such as in many
 publically available datasets, users can use methylated (M) and unmethylated
 (U) intensity data to create an object of \Robject{MethylSet}.

<<UnevaluatedCode, eval=FALSE>>=
M<-matrix_for_methylated_intensity
U<-matrix_for_unmethylated_intensity
pheno<-as.data.frame(cbind(colnames(M), colnames(M)))
names(pheno)<-c("Basename","filenames")
rownames(pheno)<-pheno$Basename
pheno<-AnnotatedDataFrame(data=pheno)
anno<-c("IlluminaHumanMethylation450k", "ilmn12.hg19")
names(anno)<-c("array", "annotation")
mdat<-MethylSet(Meth = M, Unmeth = U, annotation=anno, 
phenoData=pheno)
@

\section{Quality Control}
\subsection{Internal control probes}
Illumina 450k chip incorporated 15 different types of internal control
probes (total of 848 probes). The control plots generated using the data 
by Illumina GenomeStudio software are very useful to inspect experimental 
process and data quality. However, GenomeStudio only works on the windows 
operating system, it is time consuming to generate these plots for larger 
dataset, and there is also no option to save the plots into file. The function
 \Rfunction{plotCtrl} can generate similar plots for each type of control.

<<ctrlplot, eval=FALSE>>=
plotCtrl(rgSet)
@
 
See Illumina Infinium HD Methylation Assay for detailed description on how to 
interpret these control figures. Here is a list of control types:

\begin{tabular}{ l c }
\toprule
\textbf{Control types} & \textbf{Number of probes} \\
\midrule
\textbf{Sample-Independent Controls} &  \\
STAINING & 4 \\
EXTENSION & 4 \\
HYBRIDIZATION & 3 \\
TARGET REMOVAL & 2 \\
RESTORATION & 1 \\
\midrule
\textbf{Sample-Dependent Controls} &   \\
BISULFITE CONVERSION I & 12 \\
BISULFITE CONVERSION II & 4 \\
SPECIFICITY I & 12 \\
SPECIFICITY II & 3 \\
NON-POLYMORPHIC & 4 \\
NORM\_A & 32 \\
NORM\_C & 61 \\
NORM\_G & 32 \\
NORM\_T & 61 \\
NEGATIVE & 613 \\
\bottomrule
\end{tabular}


\begin{figure}[!htbp]
\centerline{\includegraphics[scale=0.75]{./fig/BISULFITE_CONVERSION_I.jpg}}
\caption{Bisulfite conversion controls for type I probes}
\label{fig:bisul_I}
\end{figure}

\begin{figure}[!htbp]
\centerline{\includegraphics[scale=0.75]{./fig/NEGATIVE.jpg}}
\caption{Negative control probes}
\label{fig:negcont}
\end{figure}

\begin{figure}[!htbp]
\centerline{\includegraphics[scale=0.75]{./fig/NORM_ACGT.jpg}}
\caption{NORM ACGT control probes}
\label{fig:acgt}
\end{figure}


These controls can also be plotted in user specified order to check 
how experimental factors affect methylation measures, such as batch,
 plate, array or array location.

<<ctrlplot, eval=FALSE>>=

path <- file.path(find.package("minfiData"),"extdata")
rgSet <- readidat(path = path,recursive = TRUE)
sheet <- read.metharray.sheet(file.path(find.package("minfiData"),"extdata"),
    pattern = "csv$") 
rownames(sheet)=paste(sheet$Slide,sheet$Array,sep="_")
colData(rgSet)=as(sheet[colnames(rgSet),],"DataFrame")
#control plots
IDorder=rownames(colData(rgSet))[order(colData(rgSet)$Slide,colData(rgSet)$Array)]
plotCtrl(rgSet,IDorder)
@

\subsection{Data distribution}

Methylation intensity or beta value distribution plots are 
very useful for data summary, visual inspection and identification of 
outlier samples. Density plot is routinely generated using R function
\Rfunction{multidensity}. However, the function is computationally intensive,
 and can take several hours to produce density plots for a large methylation 
dataset. Furthermore, density plot is difficult to understand for 
many investigators, also as noted in the man page of 
\Rfunction{multidensity}, density plot may not be able to display data 
distribution accurately for some data because of the smooth function which may
lead part of the distribution to be out of range, and may obscure important 
details in data distribution. 

ENmix's frequency polygon plot provides a better alternative for inspection of data
distribution. It can accurately reflect data distribution and, like histogram 
it is easy to understand. It is also much faster, and only take a few
minutes to produce a distribution plot for >1000 samples. 

<<ctrlplot, eval=FALSE>>=
mraw <- getmeth(rgSet)
#total intensity plot is userful for data quality inspection
#and identification of outlier samples
multifreqpoly(assays(mraw)$Meth+assays(mraw)$Unmeth,
xlab="Total intensity")
#Compare frequency polygon plot and density plot
beta<-getB(mraw)
anno=rowData(mraw)
beta1=beta[anno$Infinium_Design_Type=="I",]
beta2=beta[anno$Infinium_Design_Type=="II",]
library(geneplotter)
jpeg("dist.jpg",height=900,width=600)
par(mfrow=c(3,2))
multidensity(beta,main="Multidensity")
multifreqpoly(beta,main="Multifreqpoly",xlab="Beta value")
multidensity(beta1,main="Multidensity: Infinium I")
multifreqpoly(beta1,main="Multifreqpoly: Infinium I",
xlab="Beta value")
multidensity(beta2,main="Multidensity: Infinium II")
multifreqpoly(beta2,main="Multifreqpoly: Infinium II",
xlab="Beta value")
dev.off()
@

See the following figures (Figure 4) generated from the above code. When 
type I and type II probes are plotted separately (Fig 4 bottom 4 panels) 
the difference in modes between type I and II probes can be appreciated. 
But when all probes are plotted together (Fig 4 top panels), the
multidensity plot obscures these differences, while they remain readily 
apparent in the multifreqpoly plot. In addition, the multidensity plots 
appear to suggest that probes range in value
from <0 to >1, whereas multifreqpoly correctly show the range from 0 to 1.

\begin{figure}[!htbp]
\centerline{\includegraphics[scale=0.75]{./fig/dist.jpg}}
\caption{Methylation beta value distribution plots for all probes (top 2 panels)
and for type I (middle panels) and II (bottom panels) probes separately. The
smoothing function in multidensity plots (panels on left) results in misleading
range and mode information which are more accurately depicted in the
multifreqpoly plots (panels on right)}
\label{fig:dist}
\end{figure}

\subsection{QC information, filtering of low quality samples and probes}
Data quality measures, including detection P values, number of 
beads for each methylation read and average intensities for bisulfite
conversion probes can be
 extracted using the function \Rfunction{QCinfo} from an object of
 \Robject{RGChannelSetExtended}. Based on default or user specified 
quality score thresholds, the \Rfunction{QCinfo} can also identify and 
export a list of low quality samples and CpG probes. Outlier samples based on 
total intensity or beta value distribution should be excluded before
further analysis. Such samples have been difficult to identify, but by using 
the argument outlier=TRUE, these outlier samples will be identified 
 automatically. Data quality score figures from
\Rfunction{QCinfo} can be used to guide the selection of quality score 
thresholds. Low quality samples and probes can be filtered out using 
\Rfunction{QCfilter} or \Rfunction{preprocessENmix}.

<<filter, eval=FALSE>>=
qc<-QCinfo(rgSet)
#exclude before backgroud correction
mdat<-preprocessENmix(rgSet, bgParaEst="oob", dyeCorr="RELIC", 
QCinfo=qc, nCores=6)
#Or exclude after background correction
mdat <- QCfilter(mdat,qcinfo=qc,outlier=TRUE)
@

\subsection{Filtering out outliers and low quality data values}
Outlier and low quality data values can have a large impact on association
statistical tests. Function \Rfunction{rm.outlier} can filter out these
data points and replace them as missing values. Outliers are defined as 
values smaller than 3 times IQR from the lower quartile or larger than 
3 times IQR from the upper quartile. Some statistical methods do not allow 
missing values, argument \textit{impute=TRUE} in the function can be 
specified to impute missing data using k-nearest neighbors method.

<<preprocessENmix, eval=FALSE>>=
#filter out outliers
b1=rm.outlier(beta)
#filter out low quality and outlier values
b2=rm.outlier(beta,qcscore=qcscore)
#filter out low quality and outlier values, remove rows and columns
# with too many missing values
b3=rm.outlier(beta,qcscore=qcscore,rmcr=TRUE)
#filter out low quality and outlier values, remove rows and columns
# with too many missing values, and then do imputation
b3=rm.outlier(beta,qcscore=qcscore,rmcr=TRUE,impute=TRUE)
@

\section{Background correction and dye-bias adjustment}
Function \Rfunction{preprocessENmix} incorporates a model based background
 correction method \textit{ENmix}, which models methylation signal intensities 
with a flexible exponential-normal mixture distribution, together
 with a truncated normal distribution to model background noise. 
Users can also specify a list of poor performance CpGs to be excluded
 before background correction using argument \textit{exCpG}. Argument dyeCorr 
can be used to specify a method for dye-bias correction, the default is RELIC. 

See the following papers for the detailed description of related methods:

Zongli Xu, et. al. ENmix: a novel background correction method for Illumina
HumanMethylation450 BeadChip, Nucleic Acids Research, 2015

Xu Z, Langie SA, De Boever P, Taylor JA, Niu L.
RELIC: a novel dye-bias correction method for Illumina Methylation BeadChip.
BMC Genomics. 2017

If argument QCinfo is specified, the low quality samples and probes identified 
by function \Rfunction{QCinfo} will be excluded before ENmix background correction.
Using argument \textit{exSample} and \textit{exCpG}, User can also specify a list 
of samples or probes to be excluded before background correction. 
 
<<preprocessENmix, eval=FALSE>>=
qc=QCinfo(rgSet)
mdat<-preprocessENmix(rgSet, bgParaEst="oob", dyeCorr="RELIC", 
QCinfo=qc, exCpG=NULL, nCores=6)
@

\section{Inter-array normalization}
Function \Rfunction{norm.quantile} can be used to perform quantile 
normalization on methylation intensity values.

<<normalize.quantile.450k, eval=FALSE>>=
mdat<-norm.quantile(mdat, method="quantile1")
@

\section{Probe type bias adjustment}
The majority of probes on Illumina 450K and EPIC BeadChips are type II probes.
 Although type II probes facilitate increased array genome coverage, they were
 shown to have decreased dynamic range and reproducibility compared to type I
 probes. Taking advantage of the high spatial correlation of DNA methylation 
levels along the human genome, The RCP 
(Regression on Correlated Probes) method utilizes nearby (<25 bp) type I and 
II probe pairs to derive the quantitative relationship between probe types and
 then recalibrates type II probe measurements using type I probes as referents. 

<<rcp, eval=FALSE>>=
beta<-rcp(mdat)
@

See the following publication for the detailed description of the method:

Niu L, Xu Z, Taylor JA.
RCP: a novel probe design bias correction method for Illumina Methylation
BeadChip. Bioinformatics, 2016

\section{Batch effect correction}

Function \Rfunction{ctrlsva} can be used to estimate surrogate variables for batch 
effect and unknown experimental confounders from intensity data for non-negative 
internal control probes. These variables can then be adjusted as covariables in 
downstream association analysis to remove unwanted data variation.  

<<ctrlsva, eval=FALSE>>=
sva<-ctrlsva(rgSet)
@

\section{Principal component regression analysis plot}
First, principal component analysis will be performed in standardized beta value 
matrix (standardized for each CpG), and then the specified number of top 
principal components (that explain most data variation) will be used to perform
linear regression with each specified variables, such as batch or environmental 
variables. Regression P values will be 
plotted to explore methylation data variance structure and to identify possible
 confounding variables to guide association statistical analysis.

<<pcrplot, eval=FALSE>>=
cov<-data.frame(group=colData(mdat)$Sample_Group,
    slide=factor(colData(mdat)$Slide))
pcrplot(beta, cov, npc=6)
@

\begin{figure}[!htbp]
\centerline{\includegraphics[scale=0.75]{./fig/pcr_diag.jpg}}
\caption{Example principal component regression p value plot of raw data
generated using 450K methylation data from a published study}
\label{fig:pcrdiag}
\end{figure}

\section{Multimodal CpGs}

Function \Rfunction{nmode.mc} uses an empirical approach to identify
 multimodal distributed CpGs (SNP like probes). When measured in a
population of people
 the majority of CpGs on the Illumina HumanMethylation450 BeadChip have
 unimodal distributions of DNA methylation values with relatively small
 between-person variation. However, some CpGs (typically around 10,000 in
450k array often
 seemingly the result of SNPs in the probe region) may have multimodal
 distributions of methylation values with sizeable differences between
 modes and large between-person variation. These multimodal distributed
data are usually caused by SNP effect, problematic probe design or
other unknown artifacts instead of actual methylation level and thus
should be excluded from DNA methylation analysis. Researchers
 have often excluded CpGs based on SNP annotation information. However,
because SNP annotation always depends on population origin, we found
 that this approach alone may exclude many well-distributed (unimodal)
 CpGs, while still failing to identify other multi-modal CpGs. We developed
 an empirical approach to identify CpGs that are obviously not uni-modally
 distributed,
 so that researchers can make more informed decisions about whether to
exclude them in their particular study populations and analyses.

See online supplementary materials of the following paper for  
an evaluation of the method using published EWAS data. 

Zongli Xu, Liang Niu, Leping Li and Jack A. Taylor
ENmix: a novel background correction method for Illumina
HumanMethylation450 BeadChip, Nucleic Acids Research, 2015

<<nmode.mc, eval=FALSE>>=
nmode<- nmode.mc(beta, minN = 3, modedist=0.2, nCores = 5)
@

\section{Compatibility with other related R packages}

The \Rpackage{ENmix} uses the data structure provided by R \Rpackage{minfi}
 packages as input and output, and thus is fully compatible with the minfi
 package. The same data structures were also used by several other R packages,
 such as \Rpackage{ChAMP} and \Rpackage{wateRmelon}, so the output from ENmix
 functions can be easily utilized in 
these packages for further analysis. Here are some examples:

Example 1: mixed use of minfi and ENmix functions
<<ENmixAndminfi, eval=FALSE>>=
library(ENmix)
#minfi functions to read in data
sheet <- read.metharray.sheet(file.path(find.package("minfiData"),
 "extdata"), pattern = "csv$")
rgSet <- read.metharray.exp(targets = sheet, extended = TRUE)
#ENmix function for control plot
plotCtrl(rgSet)
#minfi functions to extract methylation and annotation data
mraw <- preprocessRaw(rgSet)
beta<-getB(mraw, "Illumina")
anno=getAnnotation(rgSet)
#ENmix function for fast and accurate distribution plot
multifreqpoly(beta,main="Data distribution")
multifreqpoly(beta[anno$Type=="I",],main="Data distribution, type I")
multifreqpoly(beta[anno$Type=="II",],main="Data distribution, type II")
#ENmix background correction
mset<-preprocessENmix(rgSet, bgParaEst="oob", dyeCorr="RELIC", nCores=6)
#minfi functions for further preprocessing and analysis
gmSet <- preprocessQuantile(mset)
bumps <- bumphunter(gmSet, design = model.matrix(~ gmSet$status), B = 0,
type = "Beta", cutoff = 0.25)
@

Example 2: add ENmix background correction step into ChAMP pipeline
<<ENmixAndChAMP, eval=FALSE>>=
library(ENmix)
library(ChAMP)
testDir=system.file("extdata",package="ChAMPdata")
myLoad=champ.load(directory=testDir)
#ENmix background correction
mset<-preprocessENmix(myLoad$rgSet,bgParaEst="oob", nCores=6)
#remove probes filtered by champ.load() 
mset=mset[rownames(myLoad$beta),]
#update myLoad object with background corrected intensity data
myLoad$mset=mset
myLoad$beta=getB(mset)
myLoad$intensity=getMeth(mset)+getUnmeth(mset)
#continue ChAMP pipeline
myNorm=champ.norm()
@


\section{SessionInfo}
<<sessionInfo, results=tex, echo=FALSE>>=
toLatex(sessionInfo())
@

\section{References}
Zongli Xu, Liang Niu, Leping Li and Jack A. Taylor, ENmix: a novel background
 correction method for Illumina HumanMethylation450 BeadChip, Nucleic Acids 
Research, 2015 

Liang Niu, Zongli Xu and Jack A. Taylor, RCP: a novel probe design bias 
correction method for Illumina Methylation BeadChip, Bioinformatics 2016 

Zongli Xu, Jack A. Taylor, Yuet-Kin Leung, Shuk-Mei Ho and Liang Niu,
oxBS-MLE: An efficient method to estimate 5-methylcytosine and 
5-hydroxymethylcytosine in paired bisulfite and oxidative bisulfite 
treated DNA, under review.

Zongli Xu, Sabine A. S. Langie, Patrick De Boever, Jack A. Taylor1 and 
Liang Niu, RELIC: a novel dye-bias correction method for Illumina 
Methylation BeadChip, in review 2016

Illumina Inc., Infinium HD Assay Methylation Protocol Guide,  Illumina, Inc.
 San Diego, CA. 

Aryee MJ, Jaffe AE, Corrada-Bravo H, Ladd-Acosta C, Feinberg AP, Hansen KD 
and Irizarry RA (2014). Minfi: A flexible and comprehensive Bioconductor
 package for the analysis of Infinium DNA Methylation microarrays. 
Bioinformatics, 30(10), pp. 13631369.

Pidsley, R., CC, Y.W., Volta, M., Lunnon, K., Mill, J. and Schalkwyk, L.C.
 (2013) A data-driven approach to preprocessing Illumina 450K methylation 
array data. BMC genomics, 14, 293.

Teschendorff AE et. Al (2013). A beta-mixture quantile normalization method 
for correcting probe design bias in Illumina Infinium 450 k DNA methylation
 data. Bioinformatics.

Johnson, WE, Rabinovic, A, and Li, C (2007).  Adjusting batch effects in 
microarray expression data using Empirical Bayes methods. Biostatistics
 2007 8(1):118-127. 

\end{document}


