A cross-package Bioconductor workflow for analysing methylation array data
A cross-package Bioconductor workflow for analysing methylation array data
1 Abstract
Methylation in the human genome is known to be associated with development and disease. The Illumina Infinium methylation arrays are by far the most common way to interrogate methylation across the human genome. This paper provides a Bioconductor workflow using multiple packages for the analysis of methylation array data. Specifically, we demonstrate the steps involved in a typical differential methylation analysis pipeline including: quality control, filtering, normalization, data exploration and statistical testing for probe-wise differential methylation. We further outline other analyses such as differential methylation of regions, differential variability analysis, estimating cell type composition and gene ontology testing. Finally, we provide some examples of how to visualise methylation array data.
2 Introduction
DNA methylation, the addition of a methyl group to a CG dinucleotide of the DNA, is the most extensively studied epigenetic mark due to its role in both development and disease (Bird 2002; Laird 2003). Although DNA methylation can be measured in several ways, the epigenetics community has enthusiastically embraced the Illumina HumanMethylation450 (450k) array (Bibikova et al. 2011) as a cost-effective way to assay methylation across the human genome. More recently, Illumina has increased the genomic coverage of the platform to >850,000 sites with the release of their MethylationEPIC (850k) array. As methylation arrays are likely to remain popular for measuring methylation for the foreseeable future, it is necessary to provide robust workflows for methylation array analysis.
Measurement of DNA methylation by Infinium technology (Infinium I) was first employed by Illumina on the HumanMethylation27 (27k) array (Bibikova et al. 2009), which measured methylation at approximately 27,000 CpGs, primarily in gene promoters. Like bisulfite sequencing, the Infinium assay detects methylation status at single base resolution. However, due to its relatively limited coverage the array platform was not truly considered “genome-wide” until the arrival of the 450k array. The 450k array increased the genomic coverage of the platform to over 450,000 gene-centric sites by combining the original Infinium I assay with the novel Infinium II probes. Both assay types employ 50bp probes that query a [C/T] polymorphism created by bisulfite conversion of unmethylated cytosines in the genome, however, the Infinium I and II assays differ in the number of beads required to detect methylation at a single locus. Infinium I uses two bead types per CpG, one for each of the methylated and unmethylated states (Figure 1a). In contrast, the Infinium II design uses one bead type and the methylated state is determined at the single base extension step after hybridization (Figure 1b). The 850k array also uses a combination of the Infinium I and II assays but achieves additional coverage by increasing the size of each array; a 450k slide contains 12 arrays whilst the 850k has only 8.
Figure 1: Illumina Infinium HumanMethylation450 assay, reproduced from Maksimovic, Gordon and Oshlack 2012. (a) Infinium I assay. Each individual CpG is interrogated using two bead types: methylated (M) and unmethylated (U). Both bead types will incorporate the same labeled nucleotide for the same target CpG, thereby producing the same color fluorescence. The nucleotide that is added is determined by the base downstream of the ‘C’ of the target CpG. The proportion of methylation can be calculated by comparing the intensities from the two different probes in the same color. (b) Infinium II assay. Each target CpG is interrogated using a single bead type. Methylation state is detected by single base extension at the position of the ‘C’ of the target CpG, which always results in the addition of a labeled ‘G’ or ‘A’ nucleotide, complementary to either the ‘methylated’ C or ‘unmethylated’ T, respectively. Each locus is detected in two colors, and methylation status is determined by comparing the two colors from the one position.
Regardless of the Illumina array version, for each CpG, there are two measurements: a methylated intensity (denoted by \(M\)) and an unmethylated intensity (denoted by \(U\)). These intensity values can be used to determine the proportion of methylation at each CpG locus. Methylation levels are commonly reported as either beta values (\(\beta = M/(M + U)\)) or M-values (\(Mvalue = log2(M/U)\)). For practical purposes, a small offset, \(\alpha\), can be added to the denominator of the \(\beta\) value equation to avoid dividing by small values, which is the default behaviour of the getBeta function in minfi. The default value for \(\alpha\) is 100. It may also be desirable to add a small offset to the numerator and denominator when calculating M-values to avoid dividing by zero in rare cases, however the default getM function in minfi does not do this. Beta values and M-values are related through a logit transformation. Beta values are generally preferable for describing the level of methylation at a locus or for graphical presentation because percentage methylation is easily interpretable. However, due to their distributional properties, M-values are more appropriate for statistical testing (Du et al. 2010).
In this workflow, we will provide examples of the steps involved in analysing methylation array data using R (R Core Team 2014) and Bioconductor (Huber et al. 2015), including: quality control, filtering, normalization, data exploration and probe-wise differential methylation analysis. We will also cover other approaches such as differential methylation analysis of regions, differential variability analysis, gene ontology analysis and estimating cell type composition. Finally, we will provide some examples of useful ways to visualise methylation array data.
3 Differential methylation analysis
3.1 Obtaining the data
The data required for this workflow has been bundled with the R package that contains this workflow document. Alternatively, it can be obtained from figshare. If you choose to download it seperately, once the data has been downloaded, it needs to be extracted from the archive. This will create a folder called data, which contains all the files necessary to execute the workflow.
Once the data has been downloaded and extracted, there should be a folder called data that contains all the files necessary to execute the workflow.
# set up a path to the data directory
dataDirectory <- system.file("extdata", package = "methylationArrayAnalysis")
# list the files
list.files(dataDirectory, recursive = TRUE)## [1] "48639-non-specific-probes-Illumina450k.csv"
## [2] "5975827018/5975827018_R06C02_Grn.idat"
## [3] "5975827018/5975827018_R06C02_Red.idat"
## [4] "6264509100/6264509100_R01C01_Grn.idat"
## [5] "6264509100/6264509100_R01C01_Red.idat"
## [6] "6264509100/6264509100_R01C02_Grn.idat"
## [7] "6264509100/6264509100_R01C02_Red.idat"
## [8] "6264509100/6264509100_R02C01_Grn.idat"
## [9] "6264509100/6264509100_R02C01_Red.idat"
## [10] "6264509100/6264509100_R02C02_Grn.idat"
## [11] "6264509100/6264509100_R02C02_Red.idat"
## [12] "6264509100/6264509100_R03C01_Grn.idat"
## [13] "6264509100/6264509100_R03C01_Red.idat"
## [14] "6264509100/6264509100_R03C02_Grn.idat"
## [15] "6264509100/6264509100_R03C02_Red.idat"
## [16] "6264509100/6264509100_R04C01_Grn.idat"
## [17] "6264509100/6264509100_R04C01_Red.idat"
## [18] "6264509100/6264509100_R04C02_Grn.idat"
## [19] "6264509100/6264509100_R04C02_Red.idat"
## [20] "6264509100/6264509100_R05C01_Grn.idat"
## [21] "6264509100/6264509100_R05C01_Red.idat"
## [22] "6264509100/6264509100_R05C02_Grn.idat"
## [23] "6264509100/6264509100_R05C02_Red.idat"
## [24] "6264509100/6264509100_R06C01_Grn.idat"
## [25] "6264509100/6264509100_R06C01_Red.idat"
## [26] "6264509100/6264509100_R06C02_Grn.idat"
## [27] "6264509100/6264509100_R06C02_Red.idat"
## [28] "ageData.RData"
## [29] "human_c2_v5.rdata"
## [30] "model-based-cpg-islands-hg19-chr17.txt"
## [31] "SampleSheet.csv"
## [32] "wgEncodeRegDnaseClusteredV3chr17.bed"To demonstrate the various aspects of analysing methylation data, we will be using a small, publicly available 450k methylation dataset (GSE49667)(Y. Zhang et al. 2013). The dataset contains 10 samples in total: there are 4 different sorted T-cell types (naive, rTreg, act_naive, act_rTreg, collected from 3 different individuals (M28, M29, M30). For details describing sample collection and preparation, see Y. Zhang et al. (2013). An additional birth sample (individual VICS-72098-18-B) is included from another study (GSE51180)(Cruickshank et al. 2013) to illustrate approaches for identifying and excluding poor quality samples.
There are several R Bioconductor packages available that have been developed for analysing methylation array data, including minfi (Aryee et al. 2014), missMethyl (B. Phipson, Maksimovic, and Oshlack 2016), wateRmelon (Pidsley et al. 2013), methylumi (S. Davis et al. 2015), ChAMP (Morris et al. 2014) and charm (Aryee et al. 2011). Some of the packages, such as minfi and methylumi include a framework for reading in the raw data from IDAT files and various specialised objects for storing and manipulating the data throughout the course of an analysis. Other packages provide specialised analysis methods for normalisation and statistical testing that rely on either minfi or methylumi objects. It is possible to convert between minfi and methylumi data types, however, this is not always trivial. Thus, it is advisable to consider the methods that you are interested in using and the data types that are most appropriate before you begin your analysis. Another popular method for analysing methylation array data is limma (M. E. Ritchie et al. 2015), which was originally developed for gene expression microarray analysis. As limma operates on a matrix of values, it is easily applied to any data that can be converted to a matrix in R. For a complete list of Bioconductor packages for analysing DNA methylation data, one can search for “DNAMethylation” in BiocViews (https://www.bioconductor.org/packages/release/BiocViews.html#___DNAMethylation) on the Bioconductor website.
We will begin with an example of a probe-wise differential methylation analysis using minfi and limma. By probe-wise analysis we mean each individual CpG probe will be tested for differential methylation for the comparisons of interest and p-values and moderated t-statistics (G. K. Smyth 2004) will be generated for each CpG probe.
3.2 Loading the data
It is useful to begin an analysis in R by loading all the packages that are likely to be required.
# load packages required for analysis
library(limma)
library(minfi)
library(IlluminaHumanMethylation450kanno.ilmn12.hg19)
library(IlluminaHumanMethylation450kmanifest)
library(RColorBrewer)
library(missMethyl)
library(matrixStats)
library(minfiData)
library(Gviz)
library(DMRcate)
library(stringr)The minfi, IlluminaHumanMethylation450kanno.ilmn12.hg19, IlluminaHumanMethylation450kmanifest, missMethyl, minfiData and DMRcate are methylation specific packages, while RColorBrewer and Gviz are visualisation packages. We use limma for testing differential methylation, and matrixStats and stringr have functions used in the workflow. The IlluminaHumanMethylation450kmanifest package provides the Illumina manifest as an R object which can easily be loaded into the environment. The manifest contains all of the annotation information for each of the CpG probes on the 450k array. This is useful for determining where any differentially methylated probes are located in a genomic context.
# get the 450k annotation data
ann450k = getAnnotation(IlluminaHumanMethylation450kanno.ilmn12.hg19)
head(ann450k)## DataFrame with 6 rows and 33 columns
## chr pos strand Name AddressA
## <character> <integer> <character> <character> <character>
## cg00050873 chrY 9363356 - cg00050873 32735311
## cg00212031 chrY 21239348 - cg00212031 29674443
## cg00213748 chrY 8148233 - cg00213748 30703409
## cg00214611 chrY 15815688 - cg00214611 69792329
## cg00455876 chrY 9385539 - cg00455876 27653438
## cg01707559 chrY 6778695 + cg01707559 45652402
## AddressB ProbeSeqA
## <character> <character>
## cg00050873 31717405 ACAAAAAAACAACACACAACTATAATAATTTTTAAAATAAATAAACCCCA
## cg00212031 38703326 CCCAATTAACCACAAAAACTAAACAAATTATACAATCAAAAAAACATACA
## cg00213748 36767301 TTTTAACACCTAACACCATTTTAACAATAAAAATTCTACAAAAAAAAACA
## cg00214611 46723459 CTAACTTCCAAACCACACTTTATATACTAAACTACAATATAACACAAACA
## cg00455876 69732350 AACTCTAAACTACCCAACACAAACTCCAAAAACTTCTCAAAAAAAACTCA
## cg01707559 64689504 ACAAATTAAAAACACTAAAACAAACACAACAACTACAACAACAAAAAACA
## ProbeSeqB Type
## <character> <character>
## cg00050873 ACGAAAAAACAACGCACAACTATAATAATTTTTAAAATAAATAAACCCCG I
## cg00212031 CCCAATTAACCGCAAAAACTAAACAAATTATACGATCGAAAAAACGTACG I
## cg00213748 TTTTAACGCCTAACACCGTTTTAACGATAAAAATTCTACAAAAAAAAACG I
## cg00214611 CTAACTTCCGAACCGCGCTTTATATACTAAACTACAATATAACGCGAACG I
## cg00455876 AACTCTAAACTACCCGACACAAACTCCAAAAACTTCTCGAAAAAAACTCG I
## cg01707559 GCGAATTAAAAACACTAAAACGAACGCGACGACTACAACGACAAAAAACG I
## NextBase Color Probe_rs Probe_maf CpG_rs
## <character> <character> <character> <numeric> <character>
## cg00050873 A Red NA NA NA
## cg00212031 T Red NA NA NA
## cg00213748 A Red NA NA NA
## cg00214611 A Red NA NA NA
## cg00455876 A Red NA NA NA
## cg01707559 A Red NA NA NA
## CpG_maf SBE_rs SBE_maf Islands_Name
## <numeric> <character> <numeric> <character>
## cg00050873 NA NA NA chrY:9363680-9363943
## cg00212031 NA NA NA chrY:21238448-21240005
## cg00213748 NA NA NA chrY:8147877-8148210
## cg00214611 NA NA NA chrY:15815488-15815779
## cg00455876 NA NA NA chrY:9385471-9385777
## cg01707559 NA NA NA chrY:6778574-6780028
## Relation_to_Island
## <character>
## cg00050873 N_Shore
## cg00212031 Island
## cg00213748 S_Shore
## cg00214611 Island
## cg00455876 Island
## cg01707559 Island
## Forward_Sequence
## <character>
## cg00050873 TATCTCTGTCTGGCGAGGAGGCAACGCACAACTGTGGTGGTTTTTGGAGTGGGTGGACCC[CG]GCCAAGACGGCCTGGGCTGACCAGAGACGGGAGGCAGAAAAAGTGGGCAGGTGGTTGCAG
## cg00212031 CCATTGGCCCGCCCCAGTTGGCCGCAGGGACTGAGCAAGTTATGCGGTCGGGAAGACGTG[CG]TTAAAGGGCTGAAGGGGAGGGACGGAACTGACAGTCTCTGTGACAGCTCTGAGGTGGGAG
## cg00213748 TCTGTGGGACCATTTTAACGCCTGGCACCGTTTTAACGATGGAGGTTCTGCAGGAGGGGG[CG]ACCTGGGGTAGGAGGCGTGCTAGTGGTGGATGACATTGTGGCAGAGATGGAGGTGGTGGC
## cg00214611 GCGCCGGCAGGACTAGCTTCCGGGCCGCGCTTTGTGTGCTGGGCTGCAGTGTGGCGCGGG[CG]AGGAAGCTGGTAGGGCGGTTGTCGCAAGCTCCAGCTGCAGCCTCCGCCTACGTGAGAAGA
## cg00455876 CGCGTGTGCCTGGACTCTGAGCTACCCGGCACAAGCTCCAAGGGCTTCTCGGAGGAGGCT[CG]GGGACGGAAGGCGTGGGGTGAGTGGGCTGGAGATGCAGGCGCGCCCGTGGCTGTGCAGCC
## cg01707559 AGCGGCCGCTCCCAGTGGTGGTCACCGCCAGTGCCAATCCCTTGCGCCGCCGTGCAGTCC[CG]CCCTCTGTCGCTGCAGCCGCCGCGCCCGCTCCAGTGCCCCCAATTCGCGCTCGGGAGTGA
## SourceSeq Random_Loci
## <character> <character>
## cg00050873 CGGGGTCCACCCACTCCAAAAACCACCACAGTTGTGCGTTGCCTCCTCGC
## cg00212031 CGCACGTCTTCCCGACCGCATAACTTGCTCAGTCCCTGCGGCCAACTGGG
## cg00213748 CGCCCCCTCCTGCAGAACCTCCATCGTTAAAACGGTGCCAGGCGTTAAAA
## cg00214611 CGCCCGCGCCACACTGCAGCCCAGCACACAAAGCGCGGCCCGGAAGCTAG
## cg00455876 GACTCTGAGCTACCCGGCACAAGCTCCAAGGGCTTCTCGGAGGAGGCTCG
## cg01707559 CGCCCTCTGTCGCTGCAGCCGCCGCGCCCGCTCCAGTGCCCCCAATTCGC
## Methyl27_Loci UCSC_RefGene_Name UCSC_RefGene_Accession
## <character> <character> <character>
## cg00050873 TSPY4;FAM197Y2 NM_001164471;NR_001553
## cg00212031 TTTY14 NR_001543
## cg00213748
## cg00214611 TMSB4Y;TMSB4Y NM_004202;NM_004202
## cg00455876
## cg01707559 TBL1Y;TBL1Y;TBL1Y NM_134259;NM_033284;NM_134258
## UCSC_RefGene_Group Phantom DMR Enhancer
## <character> <character> <character> <character>
## cg00050873 Body;TSS1500
## cg00212031 TSS200
## cg00213748
## cg00214611 1stExon;5'UTR
## cg00455876
## cg01707559 TSS200;TSS200;TSS200
## HMM_Island Regulatory_Feature_Name
## <character> <character>
## cg00050873 Y:9973136-9976273
## cg00212031 Y:19697854-19699393
## cg00213748 Y:8207555-8208234
## cg00214611 Y:14324883-14325218 Y:15815422-15815706
## cg00455876 Y:9993394-9995882
## cg01707559 Y:6838022-6839951
## Regulatory_Feature_Group DHS
## <character> <character>
## cg00050873
## cg00212031
## cg00213748
## cg00214611 Promoter_Associated_Cell_type_specific
## cg00455876
## cg01707559As for their many other BeadArray platforms, Illumina methylation data is usually obtained in the form of Intensity Data (IDAT) Files. This is a proprietary format that is output by the scanner and stores summary intensities for each probe on the array. However, there are Bioconductor packages available that facilitate the import of data from IDAT files into R (Smith et al. 2013). Typically, each IDAT file is approximately 8MB in size. The simplest way to import the raw methylation data into R is using the minfi function read.metharray.sheet, along with the path to the IDAT files and a sample sheet. The sample sheet is a CSV (comma-separated) file containing one line per sample, with a number of columns describing each sample. The format expected by the read.metharray.sheet function is based on the sample sheet file that usually accompanies Illumina methylation array data. It is also very similar to the targets file described by the limma package. Importing the sample sheet into R creates a data.frame with one row for each sample and several columns. The read.metharray.sheet function uses the specified path and other information from the sample sheet to create a column called Basename which specifies the location of each individual IDAT file in the experiment.
# read in the sample sheet for the experiment
targets <- read.metharray.sheet(dataDirectory, pattern="SampleSheet.csv")
targetsNow that we have imported the information about the samples and where the data is located, we can read the raw intensity signals into R from the IDAT files using the read.metharray.exp function. This creates an RGChannelSet object that contains all the raw intensity data, from both the red and green colour channels, for each of the samples. At this stage, it can be useful to rename the samples with more descriptive names.
# read in the raw data from the IDAT files
rgSet <- read.metharray.exp(targets=targets)
rgSet## class: RGChannelSet
## dim: 622399 11
## metadata(0):
## assays(2): Green Red
## rownames(622399): 10600313 10600322 ... 74810490 74810492
## rowData names(0):
## colnames(11): 6264509100_R01C01 6264509100_R02C01 ...
## 6264509100_R04C02 5975827018_R06C02
## colData names(10): Sample_Name Sample_Well ... Basename filenames
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg19# give the samples descriptive names
targets$ID <- paste(targets$Sample_Group,targets$Sample_Name,sep=".")
sampleNames(rgSet) <- targets$ID
rgSet## class: RGChannelSet
## dim: 622399 11
## metadata(0):
## assays(2): Green Red
## rownames(622399): 10600313 10600322 ... 74810490 74810492
## rowData names(0):
## colnames(11): naive.1 rTreg.2 ... act_rTreg.10 birth.11
## colData names(10): Sample_Name Sample_Well ... Basename filenames
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg193.3 Quality control
Once the data has been imported into R, we can evaluate its quality. Firstly, we need to calculate detection p-values. We can generate a detection p-value for every CpG in every sample, which is indicative of the quality of the signal. The method used by minfi to calculate detection p-values compares the total signal \((M + U)\) for each probe to the background signal level, which is estimated from the negative control probes. Very small p-values are indicative of a reliable signal whilst large p-values, for example >0.01, generally indicate a poor quality signal.
Plotting the mean detection p-value for each sample allows us to gauge the general quality of the samples in terms of the overall signal reliability (Figure 2). Samples that have many failed probes will have relatively large mean detection p-values.
# calculate the detection p-values
detP <- detectionP(rgSet)
head(detP)## naive.1 rTreg.2 act_naive.3 naive.4 act_naive.5 act_rTreg.6
## cg00050873 0 0 0.000000e+00 0 0.00000e+00 0
## cg00212031 0 0 0.000000e+00 0 0.00000e+00 0
## cg00213748 0 0 1.181832e-12 0 8.21565e-15 0
## cg00214611 0 0 0.000000e+00 0 0.00000e+00 0
## cg00455876 0 0 0.000000e+00 0 0.00000e+00 0
## cg01707559 0 0 0.000000e+00 0 0.00000e+00 0
## naive.7 rTreg.8 act_naive.9 act_rTreg.10 birth.11
## cg00050873 0 0.000000e+00 0 0.000000e+00 0.0000000
## cg00212031 0 0.000000e+00 0 0.000000e+00 0.0000000
## cg00213748 0 1.469801e-05 0 1.365951e-08 0.6735224
## cg00214611 0 0.000000e+00 0 0.000000e+00 0.7344451
## cg00455876 0 0.000000e+00 0 0.000000e+00 0.0000000
## cg01707559 0 0.000000e+00 0 0.000000e+00 0.0000000# examine mean detection p-values across all samples to identify any failed samples
pal <- brewer.pal(8,"Dark2")
par(mfrow=c(1,2))
barplot(colMeans(detP), col=pal[factor(targets$Sample_Group)], las=2,
cex.names=0.8, ylab="Mean detection p-values")
abline(h=0.05,col="red")
legend("topleft", legend=levels(factor(targets$Sample_Group)), fill=pal,
bg="white")
barplot(colMeans(detP), col=pal[factor(targets$Sample_Group)], las=2,
cex.names=0.8, ylim=c(0,0.002), ylab="Mean detection p-values")
abline(h=0.05,col="red")
legend("topleft", legend=levels(factor(targets$Sample_Group)), fill=pal,
bg="white")
Mean detection p-values summarise the quality of the signal across all the probes in each sample. The plot on the right is a zoomed in version of the plot on the left.
Figure 2: Mean detection p-values summarise the quality of the signal across all the probes in each sample. The plot on the right is a zoomed in version of the plot on the left.
The minfi qcReport function generates many other useful quality control plots. The minfi vignette describes the various plots and how they should be interpreted in detail. Generally, samples that look poor based on mean detection p-value will also look poor using other metrics and it is usually advisable to exclude them from further analysis.
qcReport(rgSet, sampNames=targets$ID, sampGroups=targets$Sample_Group,
pdf="qcReport.pdf")Poor quality samples can be easily excluded from the analysis using a detection p-value cutoff, for example >0.05. For this particular dataset, the birth sample shows a very high mean detection p-value, and hence it is excluded from subsequent analysis (Figure 2).
# remove poor quality samples
keep <- colMeans(detP) < 0.05
rgSet <- rgSet[,keep]
rgSet## class: RGChannelSet
## dim: 622399 10
## metadata(0):
## assays(2): Green Red
## rownames(622399): 10600313 10600322 ... 74810490 74810492
## rowData names(0):
## colnames(10): naive.1 rTreg.2 ... act_naive.9 act_rTreg.10
## colData names(10): Sample_Name Sample_Well ... Basename filenames
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg19# remove poor quality samples from targets data
targets <- targets[keep,]
targets[,1:5]## Sample_Name Sample_Well Sample_Source Sample_Group Sample_Label
## 1 1 A1 M28 naive naive
## 2 2 B1 M28 rTreg rTreg
## 3 3 C1 M28 act_naive act_naive
## 4 4 D1 M29 naive naive
## 5 5 E1 M29 act_naive act_naive
## 6 6 F1 M29 act_rTreg act_rTreg
## 7 7 G1 M30 naive naive
## 8 8 H1 M30 rTreg rTreg
## 9 9 A2 M30 act_naive act_naive
## 10 10 B2 M30 act_rTreg act_rTreg# remove poor quality samples from detection p-value table
detP <- detP[,keep]
dim(detP)## [1] 485512 103.4 Normalisation
To minimise the unwanted variation within and between samples, various data normalisations can be applied. Many different types of normalisation have been developed for methylation arrays and it is beyond the scope of this workflow to compare and contrast all of them (Fortin et al. 2014; M. C. Wu et al. 2014; Sun et al. 2011; D. Wang et al. 2012; Maksimovic, Gordon, and Oshlack 2012; Mancuso et al. 2011; Touleimat and Tost 2012; Teschendorff et al. 2013; Pidsley et al. 2013; T. J. Triche et al. 2013). Several methods have been built into minfi and can be directly applied within its framework (Fortin et al. 2014; T. J. Triche et al. 2013; Maksimovic, Gordon, and Oshlack 2012; Touleimat and Tost 2012), whilst others are methylumi-specific or require custom data types (M. C. Wu et al. 2014; Sun et al. 2011; D. Wang et al. 2012; Mancuso et al. 2011; Teschendorff et al. 2013; Pidsley et al. 2013). Although there is no single normalisation method that is universally considered best, a recent study by Fortin et al. (2014) has suggested that a good rule of thumb within the minfi framework is that the preprocessFunnorm (Fortin et al. 2014) function is most appropriate for datasets with global methylation differences such as cancer/normal or vastly different tissue types, whilst the preprocessQuantile function (Touleimat and Tost 2012) is more suited for datasets where you do not expect global differences between your samples, for example a single tissue. Further discussion on appropriate choice of normalisation can be found in (Hicks and Irizarry 2015), and the accompanying quantro package includes data-driven tests for the assumptions of quantile normalisation. As we are comparing different blood cell types, which are globally relatively similar, we will apply the preprocessQuantile method to our data (Figure 3). This function implements a stratified quantile normalisation procedure which is applied to the methylated and unmethylated signal intensities separately, and takes into account the different probe types. Note that after normalisation, the data is housed in a GenomicRatioSet object. This is a much more compact representation of the data as the colour channel information has been discarded and the \(M\) and \(U\) intensity information has been converted to M-values and beta values, together with associated genomic coordinates. Note, running the preprocessQuantile function on this dataset produces the warning: ‘An inconsistency was encountered while determining sex’; this can be ignored as it is due to all the samples being from male donors.
# normalize the data; this results in a GenomicRatioSet object
mSetSq <- preprocessQuantile(rgSet) ## [preprocessQuantile] Mapping to genome.## [preprocessQuantile] Fixing outliers.## Warning in .getSex(CN = CN, xIndex = xIndex, yIndex = yIndex, cutoff
## = cutoff): An inconsistency was encountered while determining sex. One
## possibility is that only one sex is present. We recommend further checks,
## for example with the plotSex function.## [preprocessQuantile] Quantile normalizing.# create a MethylSet object from the raw data for plotting
mSetRaw <- preprocessRaw(rgSet)# visualise what the data looks like before and after normalisation
par(mfrow=c(1,2))
densityPlot(rgSet, sampGroups=targets$Sample_Group,main="Raw", legend=FALSE)
legend("top", legend = levels(factor(targets$Sample_Group)),
text.col=brewer.pal(8,"Dark2"))
densityPlot(getBeta(mSetSq), sampGroups=targets$Sample_Group,
main="Normalized", legend=FALSE)
legend("top", legend = levels(factor(targets$Sample_Group)),
text.col=brewer.pal(8,"Dark2"))
The density plots show the distribution of the beta values for each sample before and after normalisation.
Figure 3: The density plots show the distribution of the beta values for each sample before and after normalisation.
3.5 Data exploration
Multi-dimensional scaling (MDS) plots are excellent for visualising data, and are usually some of the first plots that should be made when exploring the data. MDS plots are based on principal components analysis and are an unsupervised method for looking at the similarities and differences between the various samples. Samples that are more similar to each other should cluster together, and samples that are very different should be further apart on the plot. Dimension one (or principal component one) captures the greatest source of variation in the data, dimension two captures the second greatest source of variation in the data and so on. Colouring the data points or labels by known factors of interest can often highlight exactly what the greatest sources of variation are in the data. It is also possible to use MDS plots to decipher sample mix-ups.
# MDS plots to look at largest sources of variation
par(mfrow=c(1,2))
plotMDS(getM(mSetSq), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Group)])
legend("top", legend=levels(factor(targets$Sample_Group)), text.col=pal,
bg="white", cex=0.7)
plotMDS(getM(mSetSq), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Source)])
legend("top", legend=levels(factor(targets$Sample_Source)), text.col=pal,
bg="white", cex=0.7)
Multi-dimensional scaling plots are a good way to visualise the relationships between the samples in an experiment.
Figure 4: Multi-dimensional scaling plots are a good way to visualise the relationships between the samples in an experiment.
Examining the MDS plots for this dataset demonstrates that the largest source of variation is the difference between individuals (Figure 4). The higher dimensions reveal that the differences between cell types are largely captured by the third and fourth principal components (Figure 5). This type of information is useful in that it can inform downstream analysis. If obvious sources of unwanted variation are revealed by the MDS plots, we can include them in our statistical model to account for them. In the case of this particular dataset, we will include individual to individual variation in our statistical model.
# Examine higher dimensions to look at other sources of variation
par(mfrow=c(1,3))
plotMDS(getM(mSetSq), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Group)], dim=c(1,3))
legend("top", legend=levels(factor(targets$Sample_Group)), text.col=pal,
cex=0.7, bg="white")
plotMDS(getM(mSetSq), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Group)], dim=c(2,3))
legend("topleft", legend=levels(factor(targets$Sample_Group)), text.col=pal,
cex=0.7, bg="white")
plotMDS(getM(mSetSq), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Group)], dim=c(3,4))
legend("topright", legend=levels(factor(targets$Sample_Group)), text.col=pal,
cex=0.7, bg="white")
Examining the higher dimensions of an MDS plot can reaveal significant sources of variation in the data.
Figure 5: xamining the higher dimensions of an MDS plot can reaveal significant sources of variation in the data.
3.6 Filtering
Poor performing probes are generally filtered out prior to differential methylation analysis. As the signal from these probes is unreliable, by removing them we perform fewer statistical tests and thus incur a reduced multiple testing penalty. We filter out probes that have failed in one or more samples based on detection p-value.
# ensure probes are in the same order in the mSetSq and detP objects
detP <- detP[match(featureNames(mSetSq),rownames(detP)),]
# remove any probes that have failed in one or more samples
keep <- rowSums(detP < 0.01) == ncol(mSetSq)
table(keep)## keep
## FALSE TRUE
## 977 484535mSetSqFlt <- mSetSq[keep,]
mSetSqFlt## class: GenomicRatioSet
## dim: 484535 10
## metadata(0):
## assays(2): M CN
## rownames(484535): cg13869341 cg14008030 ... cg08265308 cg14273923
## rowData names(0):
## colnames(10): naive.1 rTreg.2 ... act_naive.9 act_rTreg.10
## colData names(11): Sample_Name Sample_Well ... filenames
## predictedSex
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg19
## Preprocessing
## Method: Raw (no normalization or bg correction)
## minfi version: 1.22.1
## Manifest version: 0.4.0Depending on the nature of your samples and your biological question you may also choose to filter out the probes from the X and Y chromosomes or probes that are known to have common SNPs at the CpG site. As the samples in this dataset were all derived from male donors, we will not be removing the sex chromosome probes as part of this analysis, however example code is provided below. A different dataset, which contains both male and female samples, is used to demonstrate a Differential Variability analysis and provides an example of when sex chromosome removal is necessary (Figure 13).
# if your data includes males and females, remove probes on the sex chromosomes
keep <- !(featureNames(mSetSqFlt) %in% ann450k$Name[ann450k$chr %in%
c("chrX","chrY")])
table(keep)
mSetSqFlt <- mSetSqFlt[keep,]There is a function in minfi that provides a simple interface for the removal of probes where common SNPs may affect the CpG. You can either remove all probes affected by SNPs (default), or only those with minor allele frequencies greater than a specified value.
# remove probes with SNPs at CpG site
mSetSqFlt <- dropLociWithSnps(mSetSqFlt)
mSetSqFlt## class: GenomicRatioSet
## dim: 467351 10
## metadata(0):
## assays(2): M CN
## rownames(467351): cg13869341 cg14008030 ... cg08265308 cg14273923
## rowData names(0):
## colnames(10): naive.1 rTreg.2 ... act_naive.9 act_rTreg.10
## colData names(11): Sample_Name Sample_Well ... filenames
## predictedSex
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg19
## Preprocessing
## Method: Raw (no normalization or bg correction)
## minfi version: 1.22.1
## Manifest version: 0.4.0We will also filter out probes that have shown to be cross-reactive, that is, probes that have been demonstrated to map to multiple places in the genome. This list was originally published by Chen et al. (2013) and can be obtained from the authors’ website.
# exclude cross reactive probes
xReactiveProbes <- read.csv(file=paste(dataDirectory,
"48639-non-specific-probes-Illumina450k.csv",
sep="/"), stringsAsFactors=FALSE)
keep <- !(featureNames(mSetSqFlt) %in% xReactiveProbes$TargetID)
table(keep)## keep
## FALSE TRUE
## 27433 439918mSetSqFlt <- mSetSqFlt[keep,]
mSetSqFlt## class: GenomicRatioSet
## dim: 439918 10
## metadata(0):
## assays(2): M CN
## rownames(439918): cg13869341 cg24669183 ... cg08265308 cg14273923
## rowData names(0):
## colnames(10): naive.1 rTreg.2 ... act_naive.9 act_rTreg.10
## colData names(11): Sample_Name Sample_Well ... filenames
## predictedSex
## Annotation
## array: IlluminaHumanMethylation450k
## annotation: ilmn12.hg19
## Preprocessing
## Method: Raw (no normalization or bg correction)
## minfi version: 1.22.1
## Manifest version: 0.4.0Once the data has been filtered and normalised, it is often useful to re-examine the MDS plots to see if the relationship between the samples has changed. It is apparent from the new MDS plots that much of the inter-individual variation has been removed as this is no longer the first principal component (Figure 6), likely due to the removal of the SNP-affected CpG probes. However, the samples do still cluster by individual in the second dimension (Figure 6 and Figure 7) and thus a factor for individual should still be included in the model.
par(mfrow=c(1,2))
plotMDS(getM(mSetSqFlt), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Group)], cex=0.8)
legend("right", legend=levels(factor(targets$Sample_Group)), text.col=pal,
cex=0.65, bg="white")
plotMDS(getM(mSetSqFlt), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Source)])
legend("right", legend=levels(factor(targets$Sample_Source)), text.col=pal,
cex=0.7, bg="white")
Removing SNP-affected CpGs probes from the data changes the sample clustering in the MDS plots.
Figure 6: Removing SNP-affected CpGs probes from the data changes the sample clustering in the MDS plots.
par(mfrow=c(1,3))
# Examine higher dimensions to look at other sources of variation
plotMDS(getM(mSetSqFlt), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Source)], dim=c(1,3))
legend("right", legend=levels(factor(targets$Sample_Source)), text.col=pal,
cex=0.7, bg="white")
plotMDS(getM(mSetSqFlt), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Source)], dim=c(2,3))
legend("topright", legend=levels(factor(targets$Sample_Source)), text.col=pal,
cex=0.7, bg="white")
plotMDS(getM(mSetSqFlt), top=1000, gene.selection="common",
col=pal[factor(targets$Sample_Source)], dim=c(3,4))
legend("right", legend=levels(factor(targets$Sample_Source)), text.col=pal,
cex=0.7, bg="white")
Examining the higher dimensions of the MDS plots shows that significant inter-individual variation still exists in the second and third principal components.
Figure 7: Examining the higher dimensions of the MDS plots shows that significant inter-individual variation still exists in the second and third principal components.
The next step is to calculate M-values and beta values (Figure 8). As previously mentioned, M-values have nicer statistical properties and are thus better for use in statistical analysis of methylation data whilst beta values are easy to interpret and are thus better for displaying data. A detailed comparison of M-values and beta values was published by Du et al. (2010).
# calculate M-values for statistical analysis
mVals <- getM(mSetSqFlt)
head(mVals[,1:5])## naive.1 rTreg.2 act_naive.3 naive.4 act_naive.5
## cg13869341 2.421276 2.515948 2.165745 2.286314 2.109441
## cg24669183 2.169414 2.235964 2.280734 1.632309 2.184435
## cg15560884 1.761176 1.577578 1.597503 1.777486 1.764999
## cg01014490 -3.504268 -3.825119 -5.384735 -4.537864 -4.296526
## cg17505339 3.082191 3.924931 4.163206 3.255373 3.654134
## cg11954957 1.546401 1.912204 1.727910 2.441267 1.618331bVals <- getBeta(mSetSqFlt)
head(bVals[,1:5])## naive.1 rTreg.2 act_naive.3 naive.4 act_naive.5
## cg13869341 0.84267937 0.85118462 0.8177504 0.82987650 0.81186174
## cg24669183 0.81812908 0.82489238 0.8293297 0.75610281 0.81967323
## cg15560884 0.77219626 0.74903910 0.7516263 0.77417882 0.77266205
## cg01014490 0.08098986 0.06590459 0.0233755 0.04127262 0.04842397
## cg17505339 0.89439216 0.93822870 0.9471357 0.90520570 0.92641305
## cg11954957 0.74495496 0.79008516 0.7681146 0.84450764 0.75431167par(mfrow=c(1,2))
densityPlot(bVals, sampGroups=targets$Sample_Group, main="Beta values",
legend=FALSE, xlab="Beta values")
legend("top", legend = levels(factor(targets$Sample_Group)),
text.col=brewer.pal(8,"Dark2"))
densityPlot(mVals, sampGroups=targets$Sample_Group, main="M-values",
legend=FALSE, xlab="M values")
legend("topleft", legend = levels(factor(targets$Sample_Group)),
text.col=brewer.pal(8,"Dark2"))
The distributions of beta and M-values are quite different; beta values are constrained between 0 and 1 whilst M-values range between -Inf and Inf.
Figure 8: The distributions of beta and M-values are quite different; beta values are constrained between 0 and 1 whilst M-values range between -Inf and Inf.
3.7 Probe-wise differential methylation analysis
The biological question of interest for this particular dataset is to discover differentially methylated probes between the different cell types. However, as was apparent in the MDS plots, there is another factor that we need to take into account when we perform the statistical analysis. In the targets file, there is a column called Sample_Source, which refers to the individuals that the samples were collected from. In this dataset, each of the individuals contributes more than one cell type. For example, individual M28 contributes naive, rTreg and act_naive samples. Hence, when we specify our design matrix, we need to include two factors: individual and cell type. This style of analysis is called a paired analysis; differences between cell types are calculated within each individual, and then these differences are averaged across individuals to determine whether there is an overall significant difference in the mean methylation level for each CpG site. The limma User’s Guide extensively covers the different types of designs that are commonly used for microarray experiments and how to analyse them in R.
We are interested in pairwise comparisons between the four cell types, taking into account individual to individual variation. We perform this analysis on the matrix of M-values in limma, obtaining moderated t-statistics and associated p-values for each CpG site. A convenient way to set up the model when the user has many comparisons of interest that they would like to test is to use a contrasts matrix in conjunction with the design matrix. A contrasts matrix will take linear combinations of the columns of the design matrix corresponding to the comparisons of interest.
Since we are performing hundreds of thousands of hypothesis tests, we need to adjust the p-values for multiple testing. A common procedure for assessing how statistically significant a change in mean levels is between two groups when a very large number of tests is being performed is to assign a cut-off on the false discovery rate (Benjamini and Hochberg 1995), rather than on the unadjusted p-value. Typically 5% FDR is used, and this is interpreted as the researcher willing to accept that from the list of significant differentially methylated CpG sites, 5% will be false discoveries. If the p-values are not adjusted for multiple testing, the number of false discoveries will be unacceptably high. For this dataset, assuming a Type I error rate of 5%, we would expect to see 0.05*439918=21996 statistical significant results for a given comparison, even if there were truly no differentially methylated CpG sites.
Based on a false discovery rate of 5%, there are 3021 significantly differentially methylated CpGs in the naïve vs rTreg comparison, while rTreg vs act_rTreg doesn’t show any significant differential methylation.
# this is the factor of interest
cellType <- factor(targets$Sample_Group)
# this is the individual effect that we need to account for
individual <- factor(targets$Sample_Source)
# use the above to create a design matrix
design <- model.matrix(~0+cellType+individual, data=targets)
colnames(design) <- c(levels(cellType),levels(individual)[-1])
# fit the linear model
fit <- lmFit(mVals, design)
# create a contrast matrix for specific comparisons
contMatrix <- makeContrasts(naive-rTreg,
naive-act_naive,
rTreg-act_rTreg,
act_naive-act_rTreg,
levels=design)
contMatrix## Contrasts
## Levels naive - rTreg naive - act_naive rTreg - act_rTreg
## act_naive 0 -1 0
## act_rTreg 0 0 -1
## naive 1 1 0
## rTreg -1 0 1
## M29 0 0 0
## M30 0 0 0
## Contrasts
## Levels act_naive - act_rTreg
## act_naive 1
## act_rTreg -1
## naive 0
## rTreg 0
## M29 0
## M30 0# fit the contrasts
fit2 <- contrasts.fit(fit, contMatrix)
fit2 <- eBayes(fit2)
# look at the numbers of DM CpGs at FDR < 0.05
summary(decideTests(fit2))## naive - rTreg naive - act_naive rTreg - act_rTreg act_naive - act_rTreg
## -1 1618 400 0 559
## 0 436897 439291 439918 438440
## 1 1403 227 0 919We can extract the tables of differentially expressed CpGs for each comparison, ordered by B-statistic by default, using the topTable function in limma. The B-statistic is the log-odds of differential methylation, first published by Lonnstedt and Speed (Lonnstedt and Speed 2002). To order by p-value, the user can specify sort.by="p"; and in most cases, the ordering based on the p-value and ordering based on the B-statistic will be identical.The results of the analysis for the first comparison, naive vs. rTreg, can be saved as a data.frame by setting coef=1. The coef parameter explicitly refers to the column in the contrasts matrix which corresponds to the comparison of interest.
# get the table of results for the first contrast (naive - rTreg)
ann450kSub <- ann450k[match(rownames(mVals),ann450k$Name),
c(1:4,12:19,24:ncol(ann450k))]
DMPs <- topTable(fit2, num=Inf, coef=1, genelist=ann450kSub)
head(DMPs)## chr pos strand Name Probe_rs Probe_maf CpG_rs
## cg07499259 chr1 12188502 + cg07499259 <NA> NA <NA>
## cg26992245 chr8 29848579 - cg26992245 <NA> NA <NA>
## cg09747445 chr15 70387268 - cg09747445 <NA> NA <NA>
## cg18808929 chr8 61825469 - cg18808929 <NA> NA <NA>
## cg25015733 chr2 99342986 - cg25015733 <NA> NA <NA>
## cg21179654 chr3 114057297 + cg21179654 <NA> NA <NA>
## CpG_maf SBE_rs SBE_maf Islands_Name
## cg07499259 NA <NA> NA
## cg26992245 NA <NA> NA
## cg09747445 NA <NA> NA chr15:70387929-70393206
## cg18808929 NA <NA> NA chr8:61822358-61823028
## cg25015733 NA <NA> NA chr2:99346882-99348177
## cg21179654 NA <NA> NA
## Relation_to_Island
## cg07499259 OpenSea
## cg26992245 OpenSea
## cg09747445 N_Shore
## cg18808929 S_Shelf
## cg25015733 N_Shelf
## cg21179654 OpenSea
## UCSC_RefGene_Name
## cg07499259 TNFRSF8;TNFRSF8
## cg26992245
## cg09747445 TLE3;TLE3;TLE3
## cg18808929
## cg25015733 MGAT4A
## cg21179654 ZBTB20;ZBTB20;ZBTB20;ZBTB20;ZBTB20;ZBTB20;ZBTB20
## UCSC_RefGene_Accession
## cg07499259 NM_152942;NM_001243
## cg26992245
## cg09747445 NM_001105192;NM_020908;NM_005078
## cg18808929
## cg25015733 NM_012214
## cg21179654 NM_001164343;NM_001164346;NM_001164345;NM_001164342;NM_001164344;NM_001164347;NM_015642
## UCSC_RefGene_Group Phantom DMR Enhancer
## cg07499259 5'UTR;Body
## cg26992245 TRUE
## cg09747445 Body;Body;Body
## cg18808929 TRUE
## cg25015733 5'UTR
## cg21179654 3'UTR;3'UTR;3'UTR;3'UTR;3'UTR;3'UTR;3'UTR
## HMM_Island Regulatory_Feature_Name
## cg07499259 1:12111023-12111225
## cg26992245
## cg09747445
## cg18808929
## cg25015733
## cg21179654 3:114057192-114057775
## Regulatory_Feature_Group DHS logFC AveExpr
## cg07499259 3.654104 2.46652171
## cg26992245 4.450696 -0.09180715
## cg09747445 -3.337299 -0.25201484
## cg18808929 -2.990263 0.77522878
## cg25015733 -3.054336 0.83280190
## cg21179654 Unclassified_Cell_type_specific 2.859016 1.32460816
## t P.Value adj.P.Val B
## cg07499259 18.73131 7.267204e-08 0.005067836 7.453206
## cg26992245 18.32674 8.615461e-08 0.005067836 7.359096
## cg09747445 -18.24438 8.923101e-08 0.005067836 7.339443
## cg18808929 -17.90181 1.034217e-07 0.005067836 7.255825
## cg25015733 -17.32615 1.333546e-07 0.005067836 7.108231
## cg21179654 17.27804 1.362674e-07 0.005067836 7.095476The resulting data.frame can easily be written to a CSV file, which can be opened in Excel.
write.table(DMPs, file="DMPs.csv", sep=",", row.names=FALSE)It is always useful to plot sample-wise methylation levels for the top differentially methylated CpG sites to quickly ensure the results make sense (Figure 9). If the plots do not look as expected, it is usually an indication of an error in the code, or in setting up the design matrix. It is easier to interpret methylation levels on the beta value scale, so although the analysis is performed on the M-value scale, we visualise data on the beta value scale. The plotCpg function in minfi is a convenient way to plot the sample-wise beta values stratified by the grouping variable.
# plot the top 4 most significantly differentially methylated CpGs
par(mfrow=c(2,2))
sapply(rownames(DMPs)[1:4], function(cpg){
plotCpg(bVals, cpg=cpg, pheno=targets$Sample_Group, ylab = "Beta values")
})
Plotting the top few differentially methylated CpGs is a good way to check whether the results make sense.
## $cg07499259
## NULL
##
## $cg26992245
## NULL
##
## $cg09747445
## NULL
##
## $cg18808929
## NULLFigure 9: Plotting the top few differentially methylated CpGs is a good way to check whether the results make sense.
3.8 Differential methylation analysis of regions
Although performing a probe-wise analysis is useful and informative, sometimes we are interested in knowing whether several proximal CpGs are concordantly differentially methylated, that is, we want to identify differentially methylated regions. There are several Bioconductor packages that have functions for identifying differentially methylated regions from 450k data. Some of the most popular are the dmrFind function in the charm package, which has been somewhat superseded for 450k arrays by the bumphunter function in minfi(Jaffe et al. 2012; Aryee et al. 2014), and, the recently published dmrcate in the DMRcate package (Peters et al. 2015). They are each based on different statistical methods. In our experience, the bumphunter and dmrFind functions can be somewhat slow to run unless you have the computer infrastructure to parallelise them, as they use permutations to assign significance. In this workflow, we will perform an analysis using the dmrcate. As it is based on limma, we can directly use the design and contMatrix we previously defined.
Firstly, our matrix of M-values is annotated with the relevant information about the probes such as their genomic position, gene annotation, etc. By default, this is done using the ilmn12.hg19 annotation, but this can be substituted for any argument compatible with the interface provided by the minfi package. The limma pipeline is then used for differential methylation analysis to calculate moderated t-statistics.
myAnnotation <- cpg.annotate(object = mVals, datatype = "array", what = "M",
analysis.type = "differential", design = design,
contrasts = TRUE, cont.matrix = contMatrix,
coef = "naive - rTreg", arraytype = "450K")## Your contrast returned 3021 individually significant probes. We recommend the default setting of pcutoff in dmrcate().str(myAnnotation)## List of 7
## $ ID : Factor w/ 439918 levels "cg00000029","cg00000108",..: 232388 391918 260351 19418 289954 202723 379224 278730 105471 57735 ...
## $ stat : num [1:439918] 0.0489 -2.0773 0.7711 -0.0304 -0.764 ...
## $ CHR : Factor w/ 24 levels "chr1","chr10",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ pos : int [1:439918] 15865 534242 710097 714177 720865 758829 763119 779995 805102 805338 ...
## $ betafc: num [1:439918] 0.00039 -0.04534 0.01594 0.00251 -0.00869 ...
## $ indfdr: num [1:439918] 0.994 0.565 0.872 0.997 0.873 ...
## $ is.sig: logi [1:439918] FALSE FALSE FALSE FALSE FALSE FALSE ...
## - attr(*, "row.names")= int [1:439918] 1 2 3 4 5 6 7 8 9 10 ...
## - attr(*, "class")= chr "annot"Once we have the relevant statistics for the individual CpGs, we can then use the dmrcate function to combine them to identify differentially methylated regions. The main output table DMRs$results contains all of the regions found, along with their genomic annotations and p-values.
#endif /* NEWSTUFF */
DMRs <- dmrcate(myAnnotation, lambda=1000, C=2)
head(DMRs$results)## coord no.cpgs minfdr Stouffer
## 452 chr17:57915665-57918682 12 4.957890e-91 6.639928e-10
## 723 chr3:114012316-114012912 5 1.622885e-180 1.515378e-07
## 464 chr17:74639731-74640078 6 9.516873e-90 1.527961e-07
## 1053 chrX:49121205-49122718 6 6.753751e-84 2.936984e-07
## 487 chr18:21452730-21453131 7 5.702319e-115 7.674943e-07
## 186 chr10:135202522-135203200 6 1.465070e-65 7.918224e-07
## maxbetafc meanbetafc
## 452 0.3982862 0.3131611
## 723 0.5434277 0.4251622
## 464 -0.2528645 -0.1951904
## 1053 0.4529088 0.3006242
## 487 -0.3867474 -0.2546089
## 186 0.2803157 0.2293419As for the probe-wise analysis, it is advisable to visualise the results to ensure that they make sense. The regions can easily be viewed using the DMR.plot function provided in the DMRcate package (Figure 10).
# convert the regions to annotated genomic ranges
data(dmrcatedata)
results.ranges <- extractRanges(DMRs, genome = "hg19")
# set up the grouping variables and colours
groups <- pal[1:length(unique(targets$Sample_Group))]
names(groups) <- levels(factor(targets$Sample_Group))
cols <- groups[as.character(factor(targets$Sample_Group))]
samps <- 1:nrow(targets)# draw the plot for the top DMR
par(mfrow=c(1,1))
DMR.plot(ranges=results.ranges, dmr=1, CpGs=bVals, phen.col=cols, what = "Beta",
arraytype = "450K", pch=16, toscale=TRUE, plotmedians=TRUE,
genome="hg19", samps=samps)
The DMRcate “DMR.plot” function allows you to quickly visualise DMRs in their genomic context. By default, the plot shows the location of the DMR in the genome, the position of any genes that are nearby, the base pair positions of the CpG probes, the methylation levels of the individual samples as a heatmap and the mean methylation levels for the various sample groups in the experiment. This plot shows the top ranked DMR identified by the DMRcate analysis.
Figure 10: The DMRcate DMR.plot function allows you to quickly visualise DMRs in their genomic context. By default, the plot shows the location of the DMR in the genome, the position of any genes that are nearby, the base pair positions of the CpG probes, the methylation levels of the individual samples as a heatmap and the mean methylation levels for the various sample groups in the experiment. This plot shows the top ranked DMR identified by the DMRcate analysis.
3.9 Customising visualisations of methylation data
The Gviz package offers powerful functionality for plotting methylation data in its genomic context. The package vignette is very extensive and covers the various types of plots that can be produced using the Gviz framework. We will plot one of the differentially methylated regions from the DMRcate analysis to demonstrate the type of visualisations that can be created (Figure 11).
We will first set up the genomic region we would like to plot by extracting the genomic coordinates of one of the differentially methylated regions.
# indicate which genome is being used
gen <- "hg19"
# the index of the DMR that we will plot
dmrIndex <- 1
# extract chromosome number and location from DMR results
coords <- strsplit2(DMRs$results$coord[dmrIndex],":")
chrom <- coords[1]
start <- as.numeric(strsplit2(coords[2],"-")[1])
end <- as.numeric(strsplit2(coords[2],"-")[2])
# add 25% extra space to plot
minbase <- start - (0.25*(end-start))
maxbase <- end + (0.25*(end-start))Next, we will add some genomic annotations of interest such as the locations of CpG islands and DNAseI hypersensitive sites; this can be any feature or genomic annotation of interest that you have data available for. The CpG islands data was generated using the method published by H. Wu et al. (2010); the DNaseI hypersensitive site data was obtained from the UCSC Genome Browser.
# CpG islands
islandHMM <- read.csv(paste0(dataDirectory,
"/model-based-cpg-islands-hg19-chr17.txt"),
sep="\t", stringsAsFactors=FALSE, header=FALSE)
head(islandHMM)## V1 V2 V3 V4 V5 V6 V7 V8
## 1 chr17_ctg5_hap1 8935 10075 1141 129 815 0.714 0.887
## 2 chr17_ctg5_hap1 64252 64478 227 30 165 0.727 1.014
## 3 chr17_ctg5_hap1 87730 89480 1751 135 1194 0.682 0.663
## 4 chr17_ctg5_hap1 98265 98591 327 29 226 0.691 0.744
## 5 chr17_ctg5_hap1 120763 125451 4689 359 3032 0.647 0.733
## 6 chr17_ctg5_hap1 146257 146607 351 19 231 0.658 0.500islandData <- GRanges(seqnames=Rle(islandHMM[,1]),
ranges=IRanges(start=islandHMM[,2], end=islandHMM[,3]),
strand=Rle(strand(rep("*",nrow(islandHMM)))))
islandData## GRanges object with 3456 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr17_ctg5_hap1 [ 8935, 10075] *
## [2] chr17_ctg5_hap1 [ 64252, 64478] *
## [3] chr17_ctg5_hap1 [ 87730, 89480] *
## [4] chr17_ctg5_hap1 [ 98265, 98591] *
## [5] chr17_ctg5_hap1 [120763, 125451] *
## ... ... ... ...
## [3452] chr17 [81147380, 81147511] *
## [3453] chr17 [81147844, 81148321] *
## [3454] chr17 [81152612, 81153665] *
## [3455] chr17 [81156194, 81156512] *
## [3456] chr17 [81162945, 81165532] *
## -------
## seqinfo: 5 sequences from an unspecified genome; no seqlengths# DNAseI hypersensitive sites
dnase <- read.csv(paste0(dataDirectory,"/wgEncodeRegDnaseClusteredV3chr17.bed"),
sep="\t",stringsAsFactors=FALSE,header=FALSE)
head(dnase)## V1 V2 V3 V4 V5 V6 V7
## 1 chr17 125 335 7 444 7 84,83,88,90,77,87,89,
## 2 chr17 685 835 1 150 1 80,
## 3 chr17 2440 2675 13 410 13 0,30,102,104,38,47,61,68,122,1,51,73,75,
## 4 chr17 3020 3170 1 247 1 120,
## 5 chr17 3740 3890 2 161 2 71,73,
## 6 chr17 5520 6110 4 241 5 17,19,25,16,16,
## V8
## 1 328,208,444,218,109,171,191,
## 2 150,
## 3 204,410,301,206,46,48,84,164,85,12,98,215,146,
## 4 247,
## 5 108,161,
## 6 241,185,239,26,52,dnaseData <- GRanges(seqnames=dnase[,1],
ranges=IRanges(start=dnase[,2], end=dnase[,3]),
strand=Rle(rep("*",nrow(dnase))),
data=dnase[,5])
dnaseData## GRanges object with 74282 ranges and 1 metadata column:
## seqnames ranges strand | data
## <Rle> <IRanges> <Rle> | <integer>
## [1] chr17 [ 125, 335] * | 444
## [2] chr17 [ 685, 835] * | 150
## [3] chr17 [2440, 2675] * | 410
## [4] chr17 [3020, 3170] * | 247
## [5] chr17 [3740, 3890] * | 161
## ... ... ... ... . ...
## [74278] chr17 [81153140, 81153350] * | 574
## [74279] chr17 [81153580, 81153810] * | 208
## [74280] chr17 [81185540, 81185750] * | 326
## [74281] chr17 [81188880, 81189090] * | 209
## [74282] chr17 [81194900, 81195115] * | 185
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengthsNow, set up the ideogram, genome and RefSeq tracks that will provide context for our methylation data.
iTrack <- IdeogramTrack(genome = gen, chromosome = chrom, name="")
gTrack <- GenomeAxisTrack(col="black", cex=1, name="", fontcolor="black")
rTrack <- UcscTrack(genome=gen, chromosome=chrom, track="refGene",
from=minbase, to=maxbase, trackType="GeneRegionTrack",
rstarts="exonStarts", rends="exonEnds", gene="name",
symbol="name2", transcript="name", strand="strand",
fill="darkblue",stacking="squish", name="RefSeq",
showId=TRUE, geneSymbol=TRUE)Ensure that the methylation data is ordered by chromosome and base position.
ann450kOrd <- ann450kSub[order(ann450kSub$chr,ann450kSub$pos),]
head(ann450kOrd)## DataFrame with 6 rows and 22 columns
## chr pos strand Name Probe_rs
## <character> <integer> <character> <character> <character>
## cg13869341 chr1 15865 + cg13869341 NA
## cg24669183 chr1 534242 - cg24669183 rs6680725
## cg15560884 chr1 710097 + cg15560884 NA
## cg01014490 chr1 714177 - cg01014490 NA
## cg17505339 chr1 720865 - cg17505339 NA
## cg11954957 chr1 758829 + cg11954957 rs115498424
## Probe_maf CpG_rs CpG_maf SBE_rs SBE_maf
## <numeric> <character> <numeric> <character> <numeric>
## cg13869341 NA NA NA NA NA
## cg24669183 0.108100 NA NA NA NA
## cg15560884 NA NA NA NA NA
## cg01014490 NA NA NA NA NA
## cg17505339 NA NA NA NA NA
## cg11954957 0.029514 NA NA NA NA
## Islands_Name Relation_to_Island UCSC_RefGene_Name
## <character> <character> <character>
## cg13869341 OpenSea WASH5P
## cg24669183 chr1:533219-534114 S_Shore
## cg15560884 chr1:713984-714547 N_Shelf
## cg01014490 chr1:713984-714547 Island
## cg17505339 OpenSea
## cg11954957 chr1:762416-763445 N_Shelf
## UCSC_RefGene_Accession UCSC_RefGene_Group Phantom
## <character> <character> <character>
## cg13869341 NR_024540 Body
## cg24669183
## cg15560884
## cg01014490
## cg17505339
## cg11954957
## DMR Enhancer HMM_Island Regulatory_Feature_Name
## <character> <character> <character> <character>
## cg13869341
## cg24669183 1:523025-524193
## cg15560884
## cg01014490 1:703784-704410 1:713802-715219
## cg17505339
## cg11954957
## Regulatory_Feature_Group DHS
## <character> <character>
## cg13869341
## cg24669183
## cg15560884
## cg01014490 Promoter_Associated
## cg17505339
## cg11954957bValsOrd <- bVals[match(ann450kOrd$Name,rownames(bVals)),]
head(bValsOrd)## naive.1 rTreg.2 act_naive.3 naive.4 act_naive.5
## cg13869341 0.84267937 0.85118462 0.8177504 0.82987650 0.81186174
## cg24669183 0.81812908 0.82489238 0.8293297 0.75610281 0.81967323
## cg15560884 0.77219626 0.74903910 0.7516263 0.77417882 0.77266205
## cg01014490 0.08098986 0.06590459 0.0233755 0.04127262 0.04842397
## cg17505339 0.89439216 0.93822870 0.9471357 0.90520570 0.92641305
## cg11954957 0.74495496 0.79008516 0.7681146 0.84450764 0.75431167
## act_rTreg.6 naive.7 rTreg.8 act_naive.9 act_rTreg.10
## cg13869341 0.8090798 0.8891851 0.88537940 0.90916748 0.88334231
## cg24669183 0.8187838 0.7903763 0.85304116 0.80930568 0.80979554
## cg15560884 0.7721528 0.7658623 0.75909061 0.78099397 0.78569274
## cg01014490 0.0644404 0.0245281 0.02832358 0.07740468 0.04640659
## cg17505339 0.9286016 0.8889361 0.87205348 0.90099782 0.93508348
## cg11954957 0.8116911 0.7832207 0.84929777 0.84719430 0.83350220Create the data tracks using the appropriate track type for each data type.
# create genomic ranges object from methylation data
cpgData <- GRanges(seqnames=Rle(ann450kOrd$chr),
ranges=IRanges(start=ann450kOrd$pos, end=ann450kOrd$pos),
strand=Rle(rep("*",nrow(ann450kOrd))),
betas=bValsOrd)
# extract data on CpGs in DMR
cpgData <- subsetByOverlaps(cpgData, results.ranges[dmrIndex])
# methylation data track
methTrack <- DataTrack(range=cpgData, groups=targets$Sample_Group,genome = gen,
chromosome=chrom, ylim=c(-0.05,1.05), col=pal,
type=c("a","p"), name="DNA Meth.\n(beta value)",
background.panel="white", legend=TRUE, cex.title=0.8,
cex.axis=0.8, cex.legend=0.8)
# CpG island track
islandTrack <- AnnotationTrack(range=islandData, genome=gen, name="CpG Is.",
chromosome=chrom,fill="darkgreen")
# DNaseI hypersensitive site data track
dnaseTrack <- DataTrack(range=dnaseData, genome=gen, name="DNAseI",
type="gradient", chromosome=chrom)
# DMR position data track
dmrTrack <- AnnotationTrack(start=start, end=end, genome=gen, name="DMR",
chromosome=chrom,fill="darkred")Set up the track list and indicate the relative sizes of the different tracks. Finally, draw the plot using the plotTracks function (Figure 11).
tracks <- list(iTrack, gTrack, methTrack, dmrTrack, islandTrack, dnaseTrack,
rTrack)
sizes <- c(2,2,5,2,2,2,3) # set up the relative sizes of the tracks
plotTracks(tracks, from=minbase, to=maxbase, showTitle=TRUE, add53=TRUE,
add35=TRUE, grid=TRUE, lty.grid=3, sizes=sizes, length(tracks))
Figure 11: The Gviz package provides extensive functionality for customising plots of genomic regions. This plot shows the top ranked DMR identified by the DMRcate analysis.
4 Additional analyses
4.1 Gene ontology testing
Once you have performed a differential methylation analysis, there may be a very long list of significant CpG sites to interpret. One question a researcher may have is, “which gene pathways are over-represented for differentially methylated CpGs?” In some cases it is relatively straightforward to link the top differentially methylated CpGs to genes that make biological sense in terms of the cell types or samples being studied, but there may be many thousands of CpGs significantly differentially methylated. In order to gain an understanding of the biological processes that the differentially methylated CpGs may be involved in, we can perform gene ontology or KEGG pathway analysis using the gometh function in the missMethyl package (B. Phipson, Maksimovic, and Oshlack 2016).
Let us consider the first comparison, naive vs rTreg, with the results of the analysis in the DMPs table. The gometh function takes as input a character vector of the names (e.g. cg20832020) of the significant CpG sites, and optionally, a character vector of all CpGs tested. This is recommended particularly if extensive filtering of the CpGs has been performed prior to analysis. For gene ontology testing (default), the user can specify collection="GO”. For testing KEGG pathways, specify collection="KEGG”. In the DMPs table, the Name column corresponds to the CpG name. We will select all CpG sites that have adjusted p-value of less than 0.05.
# Get the significant CpG sites at less than 5% FDR
sigCpGs <- DMPs$Name[DMPs$adj.P.Val<0.05]
# First 10 significant CpGs
sigCpGs[1:10]## [1] "cg07499259" "cg26992245" "cg09747445" "cg18808929" "cg25015733"
## [6] "cg21179654" "cg26280976" "cg16943019" "cg10898310" "cg25130381"# Total number of significant CpGs at 5% FDR
length(sigCpGs)## [1] 3021# Get all the CpG sites used in the analysis to form the background
all <- DMPs$Name
# Total number of CpG sites tested
length(all)## [1] 439918The gometh function takes into account the varying numbers of CpGs associated with each gene on the Illumina methylation arrays. For the 450k array, the numbers of CpGs mapping to genes can vary from as few as 1 to as many as 1200. The genes that have more CpGs associated with them will have a higher probability of being identified as differentially methylated compared to genes with fewer CpGs. We can look at this bias in the data by specifying plot=TRUE in the call to gometh (Figure 12).
par(mfrow=c(1,1))
gst <- gometh(sig.cpg=sigCpGs, all.cpg=all, plot.bias=TRUE)## Warning in alias2SymbolTable(flat$symbol): Multiple symbols ignored for one
## or more aliases
Bias resulting from different numbers of CpG probes in different genes.
Figure 12: Bias resulting from different numbers of CpG probes in different genes.
The gst object is a data.frame with each row corresponding to the GO category being tested. Note that the warning regarding multiple symbols will always be displayed as there are genes that have more than one alias, however it is not a cause for concern.
The top 20 gene ontology categories can be displayed using the topGO function. For KEGG pathway analysis, the topKEGG function can be called to display the top 20 enriched pathways.
# Top 10 GO categories
topGO(gst, number=10)## Term Ont N DE
## GO:0002376 immune system process BP 2589 372
## GO:0006955 immune response BP 1794 251
## GO:0046649 lymphocyte activation BP 594 123
## GO:0002682 regulation of immune system process BP 1284 201
## GO:0042110 T cell activation BP 431 98
## GO:0001775 cell activation BP 1270 197
## GO:0002684 positive regulation of immune system process BP 897 147
## GO:0007166 cell surface receptor signaling pathway BP 2569 358
## GO:0006954 inflammatory response BP 638 108
## GO:0006952 defense response BP 1412 191
## P.DE FDR
## GO:0002376 6.043095e-29 1.318241e-24
## GO:0006955 3.609892e-21 3.937309e-17
## GO:0046649 8.114628e-20 5.900416e-16
## GO:0002682 4.749381e-19 2.416625e-15
## GO:0042110 5.539161e-19 2.416625e-15
## GO:0001775 2.235552e-17 8.127722e-14
## GO:0002684 6.397192e-16 1.993548e-12
## GO:0007166 8.954155e-16 2.441574e-12
## GO:0006954 1.939973e-15 4.702062e-12
## GO:0006952 4.076932e-15 8.893419e-12From the output we can see many of the top GO categories correspond to immune system and T cell processes, which is unsurprising as the cell types being studied form part of the immune system. Typically, we consider GO categories that have associated false discovery rates of less than 5% to be statistically significant. If there aren’t any categories that achieve this significance it may be useful to scan the top 5 or 10 highly ranked GO categories to gain some insight into the biological system.
The gometh function only tests GO and KEGG pathways. For a more generalised version of gene set testing for methylation data where the user can specify the gene set to be tested, the gsameth function can be used. To display the top 20 pathways, topGSA can be called. gsameth accepts a single gene set, or a list of gene sets. The gene identifiers in the gene set must be Entrez Gene IDs. To demonstrate gsameth, we are using the curated genesets (C2) from the Broad Institute Molecular signatures database. These can be downloaded as an RData object from the WEHI Bioinformatics website.
# load Broad human curated (C2) gene sets
load(paste(dataDirectory,"human_c2_v5.rdata",sep="/"))
# perform the gene set test(s)
gsa <- gsameth(sig.cpg=sigCpGs, all.cpg=all, collection=Hs.c2)## Warning in alias2SymbolTable(flat$symbol): Multiple symbols ignored for one
## or more aliases# top 10 gene sets
topGSA(gsa, number=10)## N DE P.DE FDR
## REACTOME_IMMUNE_SYSTEM 933 127 0.000000e+00 0.000000e+00
## DACOSTA_UV_RESPONSE_VIA_ERCC3_DN 855 147 0.000000e+00 0.000000e+00
## ZHENG_BOUND_BY_FOXP3 491 138 0.000000e+00 0.000000e+00
## MARSON_BOUND_BY_FOXP3_UNSTIMULATED 1229 169 0.000000e+00 0.000000e+00
## CHEN_METABOLIC_SYNDROM_NETWORK 1210 162 0.000000e+00 0.000000e+00
## MARTENS_BOUND_BY_PML_RARA_FUSION 456 105 0.000000e+00 0.000000e+00
## PILON_KLF1_TARGETS_DN 1972 262 0.000000e+00 0.000000e+00
## JAATINEN_HEMATOPOIETIC_STEM_CELL_DN 226 59 3.995353e-18 2.359755e-15
## SMID_BREAST_CANCER_NORMAL_LIKE_UP 476 92 2.465778e-15 1.294533e-12
## LEE_EARLY_T_LYMPHOCYTE_DN 57 25 8.223310e-13 3.885514e-10While gene set testing is useful for providing some biological insight in terms of what pathways might be affected by abberant methylation, care should be taken not to over-interpret the results. Gene set testing should be used for the purpose of providing some biological insight that ideally would be tested and validated in further laboratory experiments. It is important to keep in mind that we are not observing gene level activity such as in RNA-Seq experiments, and that we have had to take an extra step to associate CpGs with genes.
4.2 Differential variability
Rather than testing for differences in mean methylation, we may be interested in testing for differences between group variances. For example, it has been hypothesised that highly variable CpGs in cancer may contribute to tumour heterogeneity (K. D. Hansen et al. 2011). Hence we may be interested in CpG sites that are consistently methylated in one group, but variably methylated in another group.
Sample size is an important consideration when testing for differentially variable CpG sites. In order to get an accurate estimate of the group variances, larger sample sizes are required than for estimating group means. A good rule of thumb is to have at least ten samples in each group (B. Phipson and Oshlack 2014). To demonstrate testing for differentially variable CpG sites, we will use a publicly available dataset on ageing GSE30870, where whole blood samples were collected from 18 centenarians and 18 newborns and profiled for methylation on the 450k array (Heyn et al. 2012). The data (age.rgSet) and sample information (age.targets) have been included as an R data object in both the workflow package or the data archive you downloaded from figshare. We can load the data using the load command, after which it needs to be normalised and filtered as previously described.
load(file.path(dataDirectory,"ageData.RData"))
# calculate detection p-values
age.detP <- detectionP(age.rgSet)
# pre-process the data after excluding poor quality samples
age.mSetSq <- preprocessQuantile(age.rgSet)## [preprocessQuantile] Mapping to genome.## [preprocessQuantile] Fixing outliers.## [preprocessQuantile] Quantile normalizing.# add sex information to targets information
age.targets$Sex <- getSex(age.mSetSq)$predictedSex
# ensure probes are in the same order in the mSetSq and detP objects
age.detP <- age.detP[match(featureNames(age.mSetSq),rownames(age.detP)),]
# remove poor quality probes
keep <- rowSums(age.detP < 0.01) == ncol(age.detP)
age.mSetSqFlt <- age.mSetSq[keep,]
# remove probes with SNPs at CpG or single base extension (SBE) site
age.mSetSqFlt <- dropLociWithSnps(age.mSetSqFlt, snps = c("CpG", "SBE"))
# remove cross-reactive probes
keep <- !(featureNames(age.mSetSqFlt) %in% xReactiveProbes$TargetID)
age.mSetSqFlt <- age.mSetSqFlt[keep,] As this dataset contains samples from both males and females, we can use it to demonstrate the effect of removing sex chromosome probes on the data. The MDS plots below show the relationship between the samples in the ageing dataset before and after sex chromosome probe removal (Figure 13). It is apparent that before the removal of sex chromosome probes, the sample cluster based on sex in the second principal component. When the sex chromosome probes are removed, age is the largest source of variation present and the male and female samples no longer form separate clusters.
# tag sex chromosome probes for removal
keep <- !(featureNames(age.mSetSqFlt) %in% ann450k$Name[ann450k$chr %in%
c("chrX","chrY")])
age.pal <- brewer.pal(8,"Set1")
par(mfrow=c(1,2))
plotMDS(getM(age.mSetSqFlt), top=1000, gene.selection="common",
col=age.pal[factor(age.targets$Sample_Group)], labels=age.targets$Sex,
main="With Sex CHR Probes")
legend("topleft", legend=levels(factor(age.targets$Sample_Group)),
text.col=age.pal)
plotMDS(getM(age.mSetSqFlt[keep,]), top=1000, gene.selection="common",
col=age.pal[factor(age.targets$Sample_Group)], labels=age.targets$Sex,
main="Without Sex CHR Probes")
legend("top", legend=levels(factor(age.targets$Sample_Group)),
text.col=age.pal)
When samples from both males and females are included in a study, sex is usually the largest source of variation in methylation data.
# remove sex chromosome probes from data
age.mSetSqFlt <- age.mSetSqFlt[keep,]Figure 13: When samples from both males and females are included in a study, sex is usually the largest source of variation in methylation data.
We can test for differentially variable CpGs using the varFit function in the missMethyl package. The syntax for specifying which groups we are interested in testing is slightly different to the standard way a model is specified in limma, particularly for designs where an intercept is fitted (see missMethyl vignette for further details). For the ageing data, the design matrix includes an intercept term, and a term for age. The coef argument in the varFit function indicates which columns of the design matrix correspond to the intercept and grouping factor. Thus, for the ageing dataset we set coef=c(1,2). Note that design matrices without intercept terms are permitted, with specific contrasts tested using the contrasts.varFit function.
# get M-values for analysis
age.mVals <- getM(age.mSetSqFlt)
design <- model.matrix(~factor(age.targets$Sample_Group))
# Fit the model for differential variability
# specifying the intercept and age as the grouping factor
fitvar <- varFit(age.mVals, design = design, coef = c(1,2))
# Summary of differential variability
summary(decideTests(fitvar))## (Intercept) factor(age.targets$Sample_Group)OLD
## -1 0 1325
## 0 11441 393451
## 1 417787 34452topDV <- topVar(fitvar, coef=2)
# Top 10 differentially variable CpGs between old vs. newborns
topDV## SampleVar LogVarRatio DiffLevene t P.Value
## cg19078576 1.1128910 3.746586 0.8539180 7.006476 6.234780e-10
## cg11661000 0.5926226 3.881306 0.8413614 6.945711 8.176807e-10
## cg07065220 1.0111380 4.181802 0.9204407 6.840327 1.306987e-09
## cg05995465 1.4478673 -5.524284 -1.3035981 -6.708321 2.346207e-09
## cg18091046 1.1121511 3.564282 1.0983340 6.679920 2.659957e-09
## cg05491001 0.9276904 3.869760 0.7118591 6.675892 2.707701e-09
## cg05542681 1.0287320 3.783637 0.9352814 6.635588 3.234735e-09
## cg02726803 0.3175570 4.063650 0.6418968 6.607508 3.660822e-09
## cg08362283 1.0028907 4.783899 0.6970960 6.564472 4.424094e-09
## cg18160402 0.5624192 3.716228 0.5907985 6.520508 5.366535e-09
## Adj.P.Value
## cg19078576 0.0001754857
## cg11661000 0.0001754857
## cg07065220 0.0001869984
## cg05995465 0.0001937035
## cg18091046 0.0001937035
## cg05491001 0.0001937035
## cg05542681 0.0001964159
## cg02726803 0.0001964159
## cg08362283 0.0002109939
## cg18160402 0.0002303467Similarly to the differential methylation analysis, is it useful to plot sample-wise beta values for the differentially variable CpGs to ensure the significant results are not driven by artifacts or outliers (Figure 14).
# get beta values for ageing data
age.bVals <- getBeta(age.mSetSqFlt)par(mfrow=c(2,2))
sapply(rownames(topDV)[1:4], function(cpg){
plotCpg(age.bVals, cpg=cpg, pheno=age.targets$Sample_Group,
ylab = "Beta values")
})
As for DMPs, it is useful to plot the top few differentially variable CpGs to check that the results make sense.
Figure 14: As for DMPs, it is useful to plot the top few differentially variable CpGs to check that the results make sense.
An example of testing for differential variability when the design matrix does not have an intercept term is detailed in the missMethyl vignette.
4.3 Cell type composition
As methylation is cell type specific and methylation arrays provide CpG methylation values for a population of cells, biological findings from samples that are comprised of a mixture of cell types, such as blood, can be confounded with cell type composition (Jaffe and Irizarry 2014). The minfi function estimateCellCounts facilitates the estimation of the level of confounding between phenotype and cell type composition in a set of samples. The function uses a modified version of the method published by Houseman et al. (2012) and the package FlowSorted.Blood.450k, which contains 450k methylation data from sorted blood cells, to estimate the cell type composition of blood samples.
# load sorted blood cell data package
library(FlowSorted.Blood.450k)
# ensure that the "Slide" column of the rgSet pheno data is numeric
# to avoid "estimateCellCounts" error
pData(age.rgSet)$Slide <- as.numeric(pData(age.rgSet)$Slide)
# estimate cell counts
cellCounts <- estimateCellCounts(age.rgSet)# plot cell type proportions by age
par(mfrow=c(1,1))
a = cellCounts[age.targets$Sample_Group == "NewBorns",]
b = cellCounts[age.targets$Sample_Group == "OLD",]
boxplot(a, at=0:5*3 + 1, xlim=c(0, 18), ylim=range(a, b), xaxt="n",
col=age.pal[1], main="", ylab="Cell type proportion")
boxplot(b, at=0:5*3 + 2, xaxt="n", add=TRUE, col=age.pal[2])
axis(1, at=0:5*3 + 1.5, labels=colnames(a), tick=TRUE)
legend("topleft", legend=c("NewBorns","OLD"), fill=age.pal)
Figure 15: If samples come from a population of mixed cells e.g. blood, it is advisable to check for potential confounding between differences in cell type proportions and the factor of interest.
As reported by Jaffe and Irizarry (2014), the preceding plot demonstrates that differences in blood cell type proportions are strongly confounded with age in this dataset (Figure 15). Performing cell composition estimation can alert you to potential issues with confounding when analysing a mixed cell type dataset. Based on the results, some type of adjustment for cell type composition may be considered, although a naive cell type adjustment is not recommended. Jaffe and Irizarry (2014) outline several strategies for dealing with cell type composition issues.
5 Discussion
Here we present a commonly used workflow for methylation array analysis based on a series of Bioconductor packages. While we have not included all the possible functions or analysis options that are available for detecting differential methylation, we have demonstrated a common and well used workflow that we regularly use in our own analysis. Specifically, we have not demonstrated more complex types of analyses such as removing unwanted variation in a differential methylation study (Maksimovic et al. 2015; Leek et al. 2012; Teschendorff, Zhuang, and Widschwendter 2011), block finding (K. D. Hansen et al. 2011; Aryee et al. 2014) or A/B compartment prediction (Fortin and Hansen 2015). Our differential methylation workflow presented here demonstrates how to read in data, perform quality control and filtering, normalisation and differential methylation testing. In addition we demonstrate analysis for differential variability, gene set testing and estimating cell type composition. One important aspect of exploring results of an analysis is visualisation and we also provide an example of generating region-level views of the data.
6 Software versions
sessionInfo()## R version 3.4.1 (2017-06-30)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Debian GNU/Linux 9 (stretch)
##
## Matrix products: default
## BLAS/LAPACK: /usr/lib/libopenblasp-r0.2.19.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=C
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] splines grid stats4 parallel methods stats graphics
## [8] grDevices utils datasets base
##
## other attached packages:
## [1] stringr_1.2.0
## [2] DMRcate_1.12.1
## [3] DMRcatedata_1.12.0
## [4] DSS_2.16.0
## [5] bsseq_1.12.2
## [6] Gviz_1.20.0
## [7] minfiData_0.22.0
## [8] missMethyl_1.10.0
## [9] RColorBrewer_1.1-2
## [10] IlluminaHumanMethylation450kmanifest_0.4.0
## [11] IlluminaHumanMethylation450kanno.ilmn12.hg19_0.6.0
## [12] minfi_1.22.1
## [13] bumphunter_1.16.0
## [14] locfit_1.5-9.1
## [15] iterators_1.0.8
## [16] foreach_1.4.3
## [17] Biostrings_2.44.2
## [18] XVector_0.16.0
## [19] SummarizedExperiment_1.6.3
## [20] DelayedArray_0.2.7
## [21] matrixStats_0.52.2
## [22] Biobase_2.36.2
## [23] GenomicRanges_1.28.4
## [24] GenomeInfoDb_1.12.2
## [25] IRanges_2.10.2
## [26] S4Vectors_0.14.3
## [27] BiocGenerics_0.22.0
## [28] limma_3.32.3
## [29] shiny_1.0.3
## [30] rmarkdown_1.6
## [31] knitr_1.16
##
## loaded via a namespace (and not attached):
## [1] backports_1.1.0
## [2] Hmisc_4.0-3
## [3] AnnotationHub_2.8.2
## [4] plyr_1.8.4
## [5] lazyeval_0.2.0
## [6] BiocParallel_1.10.1
## [7] ggplot2_2.2.1
## [8] digest_0.6.12
## [9] BiocInstaller_1.26.0
## [10] ensembldb_2.0.3
## [11] htmltools_0.3.6
## [12] GO.db_3.4.1
## [13] magrittr_1.5
## [14] checkmate_1.8.3
## [15] memoise_1.1.0
## [16] BSgenome_1.44.0
## [17] cluster_2.0.6
## [18] annotate_1.54.0
## [19] R.utils_2.5.0
## [20] siggenes_1.50.0
## [21] rmdformats_0.3.3
## [22] colorspace_1.3-2
## [23] blob_1.1.0
## [24] BiasedUrn_1.07
## [25] RCurl_1.95-4.8
## [26] genefilter_1.58.1
## [27] GEOquery_2.42.0
## [28] survival_2.41-3
## [29] VariantAnnotation_1.22.3
## [30] ruv_0.9.6
## [31] registry_0.3
## [32] gtable_0.2.0
## [33] zlibbioc_1.22.0
## [34] questionr_0.6.1
## [35] scales_0.4.1
## [36] DBI_0.7
## [37] rngtools_1.2.4
## [38] miniUI_0.1.1
## [39] Rcpp_0.12.11
## [40] xtable_1.8-2
## [41] htmlTable_1.9
## [42] foreign_0.8-69
## [43] bit_1.1-12
## [44] mclust_5.3
## [45] preprocessCore_1.38.1
## [46] Formula_1.2-2
## [47] htmlwidgets_0.9
## [48] httr_1.2.1
## [49] acepack_1.4.1
## [50] R.methodsS3_1.7.1
## [51] pkgconfig_2.0.1
## [52] reshape_0.8.6
## [53] XML_3.98-1.9
## [54] nnet_7.3-12
## [55] rlang_0.1.1
## [56] AnnotationDbi_1.38.1
## [57] munsell_0.4.3
## [58] tools_3.4.1
## [59] RSQLite_2.0
## [60] evaluate_0.10.1
## [61] yaml_2.1.14
## [62] org.Hs.eg.db_3.4.1
## [63] bit64_0.9-7
## [64] beanplot_1.2
## [65] methylumi_2.22.0
## [66] AnnotationFilter_1.0.0
## [67] nlme_3.1-131
## [68] doRNG_1.6.6
## [69] mime_0.5
## [70] nor1mix_1.2-2
## [71] R.oo_1.21.0
## [72] biomaRt_2.32.1
## [73] compiler_3.4.1
## [74] rstudioapi_0.6
## [75] curl_2.7
## [76] interactiveDisplayBase_1.14.0
## [77] tibble_1.3.3
## [78] statmod_1.4.30
## [79] stringi_1.1.5
## [80] highr_0.6
## [81] GenomicFeatures_1.28.4
## [82] lattice_0.20-35
## [83] IlluminaHumanMethylationEPICanno.ilm10b2.hg19_0.6.0
## [84] ProtGenerics_1.8.0
## [85] Matrix_1.2-10
## [86] permute_0.9-4
## [87] multtest_2.32.0
## [88] data.table_1.10.4
## [89] bitops_1.0-6
## [90] httpuv_1.3.5
## [91] rtracklayer_1.36.4
## [92] R6_2.2.2
## [93] latticeExtra_0.6-28
## [94] bookdown_0.4
## [95] gridExtra_2.2.1
## [96] codetools_0.2-15
## [97] dichromat_2.0-0
## [98] gtools_3.5.0
## [99] MASS_7.3-47
## [100] openssl_0.9.6
## [101] pkgmaker_0.22
## [102] rprojroot_1.2
## [103] GenomicAlignments_1.12.1
## [104] Rsamtools_1.28.0
## [105] GenomeInfoDbData_0.99.0
## [106] quadprog_1.5-5
## [107] rpart_4.1-11
## [108] base64_2.0
## [109] illuminaio_0.18.0
## [110] biovizBase_1.24.0
## [111] base64enc_0.1-38 Competing interests
No competing interests were disclosed.
9 Grant information
AO was supported by an NHMRC Career Development Fellowship APP1051481.
References
Aryee, Martin J, Andrew E Jaffe, Hector Corrada-Bravo, Christine Ladd-Acosta, Andrew P Feinberg, Kasper D Hansen, and Rafael a Irizarry. 2014. “Minfi: a flexible and comprehensive Bioconductor package for the analysis of Infinium DNA methylation microarrays.” Bioinformatics (Oxford, England) 30 (10): 1363–9. doi:10.1093/bioinformatics/btu049.
Aryee, Martin J, Zhijin Wu, Christine Ladd-Acosta, Brian Herb, Andrew P Feinberg, Srinivasan Yegnasubramanian, and Rafael a Irizarry. 2011. “Accurate genome-scale percentage DNA methylation estimates from microarray data.” Biostatistics (Oxford, England) 12 (2): 197–210. doi:10.1093/biostatistics/kxq055.
Benjamini, Y, and Y Hochberg. 1995. “Controlling the false discovery rate: a practical and powerful approach to multiple testing.” Journal of the Royal Statistical Society: Series B 57: 289–300.
Bibikova, Marina, Bret Barnes, Chan Tsan, Vincent Ho, Brandy Klotzle, Jennie M Le, David Delano, et al. 2011. “High density DNA methylation array with single CpG site resolution.” Genomics 98 (4). Elsevier Inc.: 288–95. doi:10.1016/j.ygeno.2011.07.007.
Bibikova, Marina, Jennie Le, Bret Barnes, Shadi Saedinia-Melnyk, Lixin Zhou, Richard Shen, and Kevin L Gunderson. 2009. “Genome-wide DNA methylation profiling using Infinium assay.” Epigenomics 1 (1). Future Medicine Ltd London, UK: 177–200. doi:10.2217/epi.09.14.
Bird, Adrian. 2002. “DNA methylation patterns and epigenetic memory.” Genes & Development 16 (1): 6–21. doi:10.1101/gad.947102.
Chen, Yi-an, Mathieu Lemire, Sanaa Choufani, Darci T Butcher, Daria Grafodatskaya, Brent W Zanke, Steven Gallinger, Thomas J Hudson, and Rosanna Weksberg. 2013. “Discovery of cross-reactive probes and polymorphic CpGs in the Illumina Infinium HumanMethylation450 microarray.” Epigenetics : Official Journal of the DNA Methylation Society 8 (2). Landes Bioscience: 203–9. doi:10.4161/epi.23470.
Cruickshank, Mark N, Alicia Oshlack, Christiane Theda, Peter G Davis, David Martino, Penelope Sheehan, Yun Dai, Richard Saffery, Lex W Doyle, and Jeffrey M Craig. 2013. “Analysis of epigenetic changes in survivors of preterm birth reveals the effect of gestational age and evidence for a long term legacy.” Genome Medicine 5 (10): 96. doi:10.1186/gm500.
Davis, Sean, Pan Du, Sven Bilke, Tim Triche, Jr., and Moiz Bootwalla. 2015. Methylumi: Handle Illumina Methylation Data.
Du, Pan, Xiao Zhang, Chiang-Ching Huang, Nadereh Jafari, Warren a Kibbe, Lifang Hou, and Simon M Lin. 2010. “Comparison of Beta-value and M-value methods for quantifying methylation levels by microarray analysis.” BMC Bioinformatics 11 (1). BioMed Central Ltd: 587. doi:10.1186/1471-2105-11-587.
Fortin, JP, and KD Hansen. 2015. “Reconstructing A/B compartments as revealed by Hi-C using long-range correlations in epigenetic data.” Genome Biology 16 (1). BioMed Central: 180. doi:10.1186/s13059-015-0741-y.
Fortin, JP, Aurélie Labbe, Mathieu Lemire, and BW Zanke. 2014. “Functional normalization of 450k methylation array data improves replication in large cancer studies.” Genome Biology 15 (503): 1–17.
Hansen, Kasper Daniel, Winston Timp, Héctor Corrada Bravo, Sarven Sabunciyan, Benjamin Langmead, Oliver G McDonald, Bo Wen, et al. 2011. “Increased methylation variation in epigenetic domains across cancer types.” Nature Genetics 43 (8): 768–75. doi:10.1038/ng.865.
Heyn, Holger, Ning Li, HJ Humberto J Ferreira, Sebastian Moran, David G Pisano, Antonio Gomez, and Javier Diez. 2012. “Distinct DNA methylomes of newborns and centenarians.” Proceedings of the National Academy of Sciences of the United States of America 109 (26): 10522–7. doi:10.1073/pnas.1120658109/-/DCSupplemental.www.pnas.org/cgi/doi/10.1073/pnas.1120658109.
Hicks, Stephanie C, and Rafael A Irizarry. 2015. “Quantro: A Data-Driven Approach to Guide the Choice of an Appropriate Normalization Method.” Genome Biology 16 (1). BioMed Central: 1.
Houseman, Eugene Andres, William P Accomando, Devin C Koestler, Brock C Christensen, Carmen J Marsit, Heather H Nelson, John K Wiencke, and Karl T Kelsey. 2012. “DNA methylation arrays as surrogate measures of cell mixture distribution.” BMC Bioinformatics 13 (1): 86. doi:10.1186/1471-2105-13-86.
Huber, W., Carey, V. J., Gentleman, R., Anders, et al. 2015. “Orchestrating High-Throughput Genomic Analysis with Bioconductor.” Nature Methods 12 (2): 115–21. http://www.nature.com/nmeth/journal/v12/n2/full/nmeth.3252.html.
Jaffe, Andrew E, and Rafael a Irizarry. 2014. “Accounting for cellular heterogeneity is critical in epigenome-wide association studies.” Genome Biology 15 (2): R31. doi:10.1186/gb-2014-15-2-r31.
Jaffe, Andrew E, Peter Murakami, Hwajin Lee, Jeffrey T Leek, M Daniele Fallin, Andrew P Feinberg, and Rafael a Irizarry. 2012. “Bump hunting to identify differentially methylated regions in epigenetic epidemiology studies.” International Journal of Epidemiology 41 (1): 200–209. doi:10.1093/ije/dyr238.
Laird, Peter W. 2003. “The power and the promise of DNA methylation markers.” Nature Reviews. Cancer 3 (4): 253–66. doi:10.1038/nrc1045.
Leek, Jeffrey T, W Evan Johnson, Hilary S Parker, Andrew E Jaffe, and John D Storey. 2012. “The sva package for removing batch effects and other unwanted variation in high-throughput experiments.” Bioinformatics (Oxford, England) 28 (6): 882–3. doi:10.1093/bioinformatics/bts034.
Lonnstedt, I, and T Speed. 2002. “Replicated Microarray Data.” Statistica Sinica 12: 31–46.
Maksimovic, Jovana, Johann A Gagnon-Bartsch, Terence P Speed, and Alicia Oshlack. 2015. “Removing unwanted variation in a differential methylation analysis of Illumina HumanMethylation450 array data.” Nucleic Acids Research, May, gkv526. doi:10.1093/nar/gkv526.
Maksimovic, Jovana, Lavinia Gordon, and Alicia Oshlack. 2012. “SWAN: Subset-quantile within array normalization for illumina infinium HumanMethylation450 BeadChips.” Genome Biology 13 (6). BioMed Central Ltd: R44. doi:10.1186/gb-2012-13-6-r44.
Mancuso, Francesco M, Magda Montfort, Anna Carreras, Andreu Alibés, and Guglielmo Roma. 2011. “HumMeth27QCReport: an R package for quality control and primary analysis of Illumina Infinium methylation data.” BMC Research Notes 4 (January): 546. doi:10.1186/1756-0500-4-546.
Morris, Tiffany J, Lee M Butcher, Andrew Feber, Andrew E Teschendorff, Ankur R Chakravarthy, Tomasz K Wojdacz, and Stephan Beck. 2014. “ChAMP: 450k Chip Analysis Methylation Pipeline.” Bioinformatics (Oxford, England) 30 (3): 428–30. doi:10.1093/bioinformatics/btt684.
Peters, Timothy J, Michael J Buckley, Aaron L Statham, Ruth Pidsley, Katherine Samaras, Reginald V Lord, Susan J Clark, and Peter L Molloy. 2015. “De novo identification of differentially methylated regions in the human genome.” Epigenetics & Chromatin 8 (1). BioMed Central: 6. doi:10.1186/1756-8935-8-6.
Phipson, Belinda, and Alicia Oshlack. 2014. “DiffVar: a new method for detecting differential variability with application to methylation in cancer and aging.” Genome Biology 15 (9). BioMed Central: 465. doi:10.1186/s13059-014-0465-4.
Phipson, Belinda, Jovana Maksimovic, and Alicia Oshlack. 2016. “missMethyl: an R package for analyzing data from Illumina’s HumanMethylation450 platform.” Bioinformatics (Oxford, England) 32 (2): 286–88. doi:10.1093/bioinformatics/btv560.
Pidsley, Ruth, Chloe C Y Wong, Manuela Volta, Katie Lunnon, Jonathan Mill, and Leonard C Schalkwyk. 2013. “A data-driven approach to preprocessing Illumina 450K methylation array data.” BMC Genomics 14 (1). BioMed Central: 293. doi:10.1186/1471-2164-14-293.
R Core Team. 2014. “R: A language and environment for statistical computing.” Vienna, Austria: R Foundation for Statistical Computing. http://www.r-project.org/.
Ritchie, M. E., B. Phipson, D. Wu, Y. Hu, C. W. Law, W. Shi, and G. K. Smyth. 2015. “limma powers differential expression analyses for RNA-sequencing and microarray studies.” Nucleic Acids Research, January, gkv007. doi:10.1093/nar/gkv007.
Smith, Mike L, Keith A. Baggerly, Henrik Bengtsson, Matthew E. Ritchie, Kasper D. Hansen, Mike L Smith, Keith A. Baggerly, Henrik Bengtsson, Matthew E. Ritchie, and Kasper D. Hansen. 2013. “illuminaio: An open source IDAT parsing tool for Illumina microarrays.” F1000Research 2 (December). doi:10.12688/f1000research.2-264.v1.
Smyth, G K. 2004. “Linear models and empirical Bayes methods for assessing differential expression in microarray experiments.” Statistical Applications in Genetics and Molecular Biology 3 (1). bepress: Article~3.
Sun, Zhifu, High Seng Chai, Yanhong Wu, Wendy M White, Krishna V Donkena, Christopher J Klein, Vesna D Garovic, Terry M Therneau, and Jean-Pierre a Kocher. 2011. “Batch effect correction for genome-wide methylation data with Illumina Infinium platform.” BMC Medical Genomics 4 (January): 84. doi:10.1186/1755-8794-4-84.
Teschendorff, Andrew E, Francesco Marabita, Matthias Lechner, Thomas Bartlett, Jesper Tegner, David Gomez-Cabrero, and Stephan Beck. 2013. “A beta-mixture quantile normalization method for correcting probe design bias in Illumina Infinium 450 k DNA methylation data.” Bioinformatics (Oxford, England) 29 (2): 189–96. doi:10.1093/bioinformatics/bts680.
Teschendorff, Andrew E, Joanna Zhuang, and Martin Widschwendter. 2011. “Independent surrogate variable analysis to deconvolve confounding factors in large-scale microarray profiling studies.” Bioinformatics (Oxford, England) 27 (11): 1496–1505. doi:10.1093/bioinformatics/btr171.
Touleimat, Nizar, and Jörg Tost. 2012. “Complete pipeline for Infinium Human Methylation 450K BeadChip data processing using subset quantile normalization for accurate DNA methylation estimation.” Epigenomics 4 (3): 325–41. doi:10.2217/epi.12.21.
Triche, Timothy J, Daniel J Weisenberger, David Van Den Berg, Peter W Laird, and Kimberly D Siegmund. 2013. “Low-level processing of Illumina Infinium DNA Methylation BeadArrays.” Nucleic Acids Research 41 (7): e90. doi:10.1093/nar/gkt090.
Wang, Dong, Yuannv Zhang, Yan Huang, Pengfei Li, Mingyue Wang, Ruihong Wu, Lixin Cheng, et al. 2012. “Comparison of different normalization assumptions for analyses of DNA methylation data from the cancer genome.” Gene 506 (1). Elsevier B.V.: 36–42. doi:10.1016/j.gene.2012.06.075.
Wu, Hao, Brian Caffo, Harris A Jaffee, Rafael A Irizarry, and Andrew P Feinberg. 2010. “Redefining CpG islands using hidden Markov models.” Biostatistics (Oxford, England) 11 (3): 499–514. doi:10.1093/biostatistics/kxq005.
Wu, Michael C, Bonnie R Joubert, Pei-fen Kuan, Siri E Håberg, Wenche Nystad, Shyamal D Peddada, and Stephanie J London. 2014. “A systematic assessment of normalization approaches for the Infinium 450K methylation platform.” Epigenetics : Official Journal of the DNA Methylation Society 9 (2): 318–29. doi:10.4161/epi.27119.
Zhang, Yuxia, Jovana Maksimovic, Gaetano Naselli, Junyan Qian, Michael Chopin, Marnie E Blewitt, Alicia Oshlack, and Leonard C Harrison. 2013. “Genome-wide DNA methylation analysis identifies hypomethylated genes regulated by FOXP3 in human regulatory T cells.” Blood 122 (16): 2823–36. doi:10.1182/blood-2013-02-481788.