# missMethyl: Analysing Illumina HumanMethylation BeadChip Data

# Introduction

The missMethyl package contains functions to analyse methylation data from Illumina’s HumanMethylation450 and MethylationEPIC beadchip. These arrays are a cost-effective alternative to whole genome bisulphite sequencing, and as such are widely used to profile DNA methylation. Specifically, missMethyl contains functions to perform SWAN normalisation (Maksimovic, Gordon, and Oshlack 2012),perform differential methylation analysis using RUVm (Maksimovic et al. 2015), differential variability analysis (Phipson and Oshlack 2014) and gene set enrichment analysis (Phipson, Maksimovic, and Oshlack 2016). As our lab’s research into specialised analyses of these arrays continues we anticipate that the package will be updated with new functions.

Raw data files are in IDAT format, which can be read into R using the minfi package (Aryee et al. 2014). Statistical analyses are usually performed on M-values, and \(\beta\) values are used for visualisation, both of which can be extracted from `MethylSet` data objects, which is a class of object created by minfi. For detecting differentially variable CpGs we recommend that the analysis is performed on M-values. All analyses described here are performed at the CpG site level.

## Analysis of Illumina MethylationEPIC v2.0 beadchip datasets

The missMethyl package has been updated to support Illumina’s MethylationEPIC v2.0 beadchip. This array contains replicate probes which map to the same CpG dinucleotides. We recommend filtering these replicates prior to analysis with the missMethyl package using the DMRcate package. An example of this is shown in this vignette.

# Reading data into R

We will use the data in the minfiData package to demonstrate the functions in missMethyl. The example dataset has 6 samples across two slides. There are 3 cancer samples and 3 normal sample. The sample information is in the targets file. An essential column in the targets file is the `Basename` column which tells us where the idat files to be read in are located. The R commands to read in the data are taken from the minfi User’s Guide. For additional details on how to read the IDAT files into R, as well as information regarding quality control please refer to the minfi User’s Guide.

    library(missMethyl)
    library(limma)
    library(minfi)
    library(minfiData)

    baseDir <- system.file("extdata", package = "minfiData")
    targets <- read.metharray.sheet(baseDir)

    ## [1] "/github/workspace/pkglib/minfiData/extdata/SampleSheet.csv"

    targets[,1:9]

    ##   Sample_Name Sample_Well Sample_Plate Sample_Group Pool_ID person age sex
    ## 1    GroupA_3          H5         <NA>       GroupA    <NA>    id3  83   M
    ## 2    GroupA_2          D5         <NA>       GroupA    <NA>    id2  58   F
    ## 3    GroupB_3          C6         <NA>       GroupB    <NA>    id3  83   M
    ## 4    GroupB_1          F7         <NA>       GroupB    <NA>    id1  75   F
    ## 5    GroupA_1          G7         <NA>       GroupA    <NA>    id1  75   F
    ## 6    GroupB_2          H7         <NA>       GroupB    <NA>    id2  58   F
    ##   status
    ## 1 normal
    ## 2 normal
    ## 3 cancer
    ## 4 cancer
    ## 5 normal
    ## 6 cancer

    targets[,10:12]

    ##    Array      Slide
    ## 1 R02C02 5723646052
    ## 2 R04C01 5723646052
    ## 3 R05C02 5723646052
    ## 4 R04C02 5723646053
    ## 5 R05C02 5723646053
    ## 6 R06C02 5723646053
    ##                                                                  Basename
    ## 1 /github/workspace/pkglib/minfiData/extdata/5723646052/5723646052_R02C02
    ## 2 /github/workspace/pkglib/minfiData/extdata/5723646052/5723646052_R04C01
    ## 3 /github/workspace/pkglib/minfiData/extdata/5723646052/5723646052_R05C02
    ## 4 /github/workspace/pkglib/minfiData/extdata/5723646053/5723646053_R04C02
    ## 5 /github/workspace/pkglib/minfiData/extdata/5723646053/5723646053_R05C02
    ## 6 /github/workspace/pkglib/minfiData/extdata/5723646053/5723646053_R06C02

    rgSet <- read.metharray.exp(targets = targets)

The data is now an `RGChannelSet` object and needs to be normalised and converted to a `MethylSet` object.

## Annotation for Illumina MethylationEPIC v2.0 beadchip datasets

When using MethylationEPIC v2.0 datasets, the array and annotation details in the `RGChannelSet` object must be set manually.

    ### This code is not run within this vignette

    # If using EPIC_V2, please run these lines:
    annotation(rgSet)["array"] = "IlluminaHumanMethylationEPICv2"
    annotation(rgSet)["annotation"] = "20a1.hg38"

    ### End of not run

# Subset-quantile within array normalization (SWAN)

SWAN (subset-quantile within array normalization) is a within-array normalization method for Illumina 450k & EPIC BeadChips. Technical differencs have been demonstrated to exist between the Infinium I and Infinium II assays on a single Illumina HumanMethylation array Dedeurwaerder, Defrance, and Calonne (2011). Using the SWAN method substantially reduces the technical variability between the assay designs whilst maintaining important biological differences. The SWAN method makes the assumption that the number of CpGs within the 50bp probe sequence reflects the underlying biology of the region being interrogated. Hence, the overall distribution of intensities of probes with the same number of CpGs in the probe body should be the same regardless of assay type. The method then uses a subset quantile normalization approach to adjust the intensities of each array (Maksimovic, Gordon, and Oshlack 2012).

`SWAN` can take a `MethylSet`, `RGChannelSet` or `MethyLumiSet` as input. It should be noted that, in order to create the normalization subset, `SWAN` randomly selects Infinium I and II probes that have one, two and three underlying CpGs; as such, we recommend using `set.seed` before to ensure that the normalized intensities will be identical, if the normalization is repeated.

The technical differences between Infinium I and II assay designs can result in aberrant \(\beta\) value distributions (Figure @ref(fig:betasByType), panel “Raw”). Using SWAN corrects for the technical differences between the Infinium I and II assay designs and produces a smoother overall \(\beta\) value distribution (Figure @ref(fig:betasByType), panel “SWAN”).

    mSet <- preprocessRaw(rgSet)

    mSetSw <- SWAN(mSet,verbose=TRUE)

    ## [SWAN] Preparing normalization subset
    ## 450k
    ## [SWAN] Normalizing methylated channel
    ## [SWAN] Normalizing array 1 of 6
    ## [SWAN] Normalizing array 2 of 6
    ## [SWAN] Normalizing array 3 of 6
    ## [SWAN] Normalizing array 4 of 6
    ## [SWAN] Normalizing array 5 of 6
    ## [SWAN] Normalizing array 6 of 6
    ## [SWAN] Normalizing unmethylated channel
    ## [SWAN] Normalizing array 1 of 6
    ## [SWAN] Normalizing array 2 of 6
    ## [SWAN] Normalizing array 3 of 6
    ## [SWAN] Normalizing array 4 of 6
    ## [SWAN] Normalizing array 5 of 6
    ## [SWAN] Normalizing array 6 of 6

    par(mfrow=c(1,2), cex=1.25)
    densityByProbeType(mSet[,1], main = "Raw")
    densityByProbeType(mSetSw[,1], main = "SWAN")

Beta value dustributions. Density distributions of beta values before and after using SWAN.

# Filter out poor quality probes

Poor quality probes can be filtered out based on the detection p-value. For this example, to retain a CpG for further analysis, we require that the detection p-value is less than 0.01 in all samples.

    detP <- detectionP(rgSet)
    keep <- rowSums(detP < 0.01) == ncol(rgSet)
    mSetSw <- mSetSw[keep,]

# Extracting \(\beta\) and M-values

Now that the data has been `SWAN` normalised we can extract \(\beta\) and M-values from the object. We prefer to add an offset to the methylated and unmethylated intensities when calculating M-values, hence we extract the methylated and unmethylated channels separately and perform our own calculation. For all subsequent analyses we use a random selection of 20000 CpGs to reduce computation time.

    set.seed(10)
    mset_reduced <- mSetSw[sample(1:nrow(mSetSw), 20000),]
    meth <- getMeth(mset_reduced)
    unmeth <- getUnmeth(mset_reduced)
    Mval <- log2((meth + 100)/(unmeth + 100))
    beta <- getBeta(mset_reduced)
    dim(Mval)

    ## [1] 20000     6

    par(mfrow=c(1,1))
    plotMDS(Mval, labels=targets$Sample_Name, col=as.integer(factor(targets$status)))
    legend("topleft",legend=c("Cancer","Normal"),pch=16,cex=1.2,col=1:2)

MDS plot. A multi-dimensional scaling (MDS) plot of cancer and normal samples.

An MDS plot (Figure @ref(fig:mdsplot)) is a good sanity check to make sure samples cluster together according to the main factor of interest, in this case, cancer and normal.

## Filtering replicate probes in Illumina MethylationEPIC v2.0 beadchip datasets

The MethylationEPIC v2.0 array contains replicate probes which map to the same CpG dinucleotides. We recommend filtering these replicate probes prior to continuing analysis. The DMRcate package contains information describing possible approaches for filtering replicate probes. We also suggest filtering out non-cg probes, as shown below.

    ### This code is not run within this vignette

    # For EPIC_V2, please run these lines to remove replicate and non-cg probes:
    # Remove non-cg probes
    Mval <- Mval[grepl("^cg", rownames(Mval)),]

    # Please also filter replicate probes using an appropriate strategy. See the
    # DMRcate EPIC v2 vignette for details.

    ### End of not run

# Testing for differential methylation using limma

To test for differential methylation we use the limma package (Smyth 2005), which employs an empirical Bayes framework based on Guassian model theory. First we need to set up the design matrix. There are a number of ways to do this, the most straightforward is directly from the targets file. There are a number of variables, with the `status` column indicating cancer/normal samples. From the `person` column of the targets file, we see that the cancer/normal samples are matched, with 3 individuals each contributing both a cancer and normal sample. Since the limma model framework can handle any experimental design which can be summarised by a design matrix, we can take into account the paired nature of the data in the analysis. For more complicated experimental designs, please refer to the limma User’s Guide.

    group <- factor(targets$status,levels=c("normal","cancer"))
    id <- factor(targets$person)
    design <- model.matrix(~id + group)
    design

    ##   (Intercept) idid2 idid3 groupcancer
    ## 1           1     0     1           0
    ## 2           1     1     0           0
    ## 3           1     0     1           1
    ## 4           1     0     0           1
    ## 5           1     0     0           0
    ## 6           1     1     0           1
    ## attr(,"assign")
    ## [1] 0 1 1 2
    ## attr(,"contrasts")
    ## attr(,"contrasts")$id
    ## [1] "contr.treatment"
    ##
    ## attr(,"contrasts")$group
    ## [1] "contr.treatment"

Now we can test for differential methylation using the `lmFit` and `eBayes` functions from limma. As input data we use the matrix of M-values.

    fit.reduced <- lmFit(Mval,design)
    fit.reduced <- eBayes(fit.reduced, robust=TRUE)

The numbers of hyper-methylated (1) and hypo-methylated (-1) can be displayed using the `decideTests` function in limma and the top 10 differentially methylated CpGs for cancer versus normal extracted using `topTable`.

    summary(decideTests(fit.reduced))

    ##        (Intercept) idid2 idid3 groupcancer
    ## Down          6972     0   116         574
    ## NotSig        3394 20000 19879       18956
    ## Up            9634     0     5         470

    top<-topTable(fit.reduced,coef=4)
    top

    ##               logFC    AveExpr        t      P.Value  adj.P.Val        B
    ## cg16969623 4.712871 -1.3412958 18.15356 5.324174e-06 0.02986746 4.412185
    ## cg24115221 4.224058 -0.4730293 16.23879 9.560115e-06 0.02986746 4.025762
    ## cg13692446 4.354979  0.3166287 15.66942 1.152573e-05 0.02986746 3.894548
    ## cg11334818 4.028658  0.9142632 15.31860 1.297572e-05 0.02986746 3.809482
    ## cg10341556 5.001803 -1.5675421 15.52877 1.316453e-05 0.02986746 3.785898
    ## cg17815252 3.709207 -2.3500134 14.75556 1.578128e-05 0.02986746 3.665764
    ## cg24331301 3.837538 -1.4211781 14.41130 1.785123e-05 0.02986746 3.573259
    ## cg26976732 3.844495 -0.9242894 14.40007 1.792395e-05 0.02986746 3.570181
    ## cg26328335 3.726982  0.3679190 14.16625 1.952175e-05 0.02986746 3.505154
    ## cg05621343 4.269455 -0.5533659 14.08940 2.078686e-05 0.02986746 3.453347

Note that since we performed our analysis on M-values, the `logFC` and `AveExpr` columns are computed on the M-value scale. For interpretability and visualisation we can look at the \(\beta\) values. The \(\beta\) values for the top 4 differentially methylated CpGs shown in Figure @ref(fig:top4).

    cpgs <- rownames(top)
    par(mfrow=c(2,2))
    for(i in 1:4){
    stripchart(beta[rownames(beta)==cpgs[i],]~design[,4],method="jitter",
    group.names=c("Normal","Cancer"),pch=16,cex=1.5,col=c(4,2),ylab="Beta values",
    vertical=TRUE,cex.axis=1.5,cex.lab=1.5)
    title(cpgs[i],cex.main=1.5)
    }

Top DM CpGs. The beta values for the top 4 differentially methylated CpGs.

# Removing unwanted variation when testing for differential methylation

Like other platforms, 450k array studies are subject to unwanted technical variation such as batch effects and other, often unknown, sources of variation. The adverse effects of unwanted variation have been extensively documented in gene expression array studies and have been shown to be able to both reduce power to detect true differences and to increase the number of false discoveries. As such, when it is apparent that data is significantly affected by unwanted variation, it is advisable to perform an adjustment to mitigate its effects.

missMethyl provides a limma inspired interface to functions from the CRAN package ruv, which enable the removal of unwanted variation when performing a differential methylation analysis (Maksimovic et al. 2015).

`RUVfit` uses the RUV-inverse method by default, as this does not require the user to specify a \(k\) parameter. The ridged version of RUV-inverse is also available by setting `method = rinv`. The RUV-2 and RUV-4 functions can also be used by setting `method = ruv2` or `method = ruv4`, respectively, and specifying an appropriate value for k (number of components of unwanted variation to remove) where \(0 \leq k < no. samples\).

All of the methods rely on negative control features to accurately estimate the components of unwanted variation. Negative control features are probes/genes/etc. that are known a priori to not truly be associated with the biological factor of interest, but are affected by unwanted variation. For example, in a microarray gene expression study, these could be house-keeping genes or a set of spike-in controls. Negative control features are extensively discussed in Gagnon-Bartsch and Speed (2012) and Gagnon-Bartsch et al. (2013). Once the unwanted factors are accurately estimated from the data, they are adjusted for in the linear model that describes the differential analysis.

If the negative control features are not known a priori, they can be identified empirically. This can be achieved via a 2-stage approach, RUVm. Stage 1 involves performing a differential methylation analysis using RUV-inverse (by default) and the 613 Illumina negative controls (INCs) as negative control features. This will produce a list of CpGs ranked by p-value according to their level of association with the factor of interest. This list can then be used to identify a set of empirical control probes (ECPs), which will capture more of the unwanted variation than using the INCs alone. ECPs are selected by designating a proportion of the CpGs least associated with the factor of interest as negative control features; this can be done based on either an FDR cut-off or by taking a fixed percentage of probes from the bottom of the ranked list. Stage 2 involves performing a second differential methylation analysis on the original data using RUV-inverse (by default) and the ECPs. For simplicity, we are ignoring the paired nature of the cancer and normal samples in this example.

    # get M-values for ALL probes
    meth <- getMeth(mSet)
    unmeth <- getUnmeth(mSet)
    M <- log2((meth + 100)/(unmeth + 100))

    ### This code is not run within this vignette

    # For EPIC_V2, please run these lines to remove replicate and non-cg probes:
    # remove non-cg probes
    M <- M[grepl("^cg", rownames(M)),]

    # Please also filter replicate probes using an appropriate strategy. See the
    # DMRcate EPIC v2 vignette for details.

    ### End of not run

    # setup the factor of interest
    grp <- factor(targets$status, labels=c(0,1))
    # extract Illumina negative control data
    INCs <- getINCs(rgSet)
    head(INCs)

    ##          5723646052_R02C02 5723646052_R04C01 5723646052_R05C02
    ## 13792480        -0.3299654        -1.0955482        -0.5266103
    ## 69649505        -1.0354488        -1.4943396        -1.0067050
    ## 34772371        -1.1286422        -0.2995603        -0.8192636
    ## 28715352        -0.5553373        -0.7599489        -0.7186973
    ## 74737439        -1.1169178        -0.8656399        -0.6429681
    ## 33730459        -0.7714684        -0.5622424        -0.7724825
    ##          5723646053_R04C02 5723646053_R05C02 5723646053_R06C02
    ## 13792480        -0.6374299         -1.116598        -0.4332793
    ## 69649505        -0.8854881         -1.586679        -0.9217329
    ## 34772371        -0.6895514         -1.161155        -0.6186795
    ## 28715352        -1.7903619         -1.348105        -1.0067259
    ## 74737439        -0.8872082         -1.064986        -0.9841833
    ## 33730459        -1.5623138         -2.079184        -1.0445246

    # add negative control data to M-values
    Mc <- rbind(M,INCs)
    # create vector marking negative controls in data matrix
    ctl1 <- rownames(Mc) %in% rownames(INCs)
    table(ctl1)

    ## ctl1
    ##  FALSE   TRUE
    ## 485512    613

    rfit1 <- RUVfit(Y = Mc, X = grp, ctl = ctl1) # Stage 1 analysis
    rfit2 <- RUVadj(Y = Mc, fit = rfit1)

Now that we have performed an initial differential methylation analysis to rank the CpGs with respect to their association with the factor of interest, we can designate the CpGs that are least associated with the factor of interest based on FDR-adjusted p-value as ECPs.

    top1 <- topRUV(rfit2, num=Inf, p.BH = 1)
    head(top1)

    ##                     F.p     F.p.BH       p_X1.1  p.BH_X1.1    b_X1.1     sigma2
    ## cg04743961 3.516091e-07 0.01017357 3.516091e-07 0.01017357 -4.838190 0.10749571
    ## cg07155336 3.583107e-07 0.01017357 3.583107e-07 0.01017357 -5.887409 0.16002329
    ## cg20925841 3.730375e-07 0.01017357 3.730375e-07 0.01017357 -4.790211 0.10714494
    ## cg03607359 4.721205e-07 0.01017357 4.721205e-07 0.01017357 -4.394397 0.09636129
    ## cg10566121 5.238865e-07 0.01017357 5.238865e-07 0.01017357 -4.787914 0.11780108
    ## cg07655636 6.080091e-07 0.01017357 6.080091e-07 0.01017357 -4.571758 0.11201883
    ##            var.b_X1.1 fit.ctl        mean
    ## cg04743961 0.07729156   FALSE -2.31731496
    ## cg07155336 0.11505994   FALSE -1.27676413
    ## cg20925841 0.07703935   FALSE -0.87168892
    ## cg03607359 0.06928569   FALSE -2.19187147
    ## cg10566121 0.08470133   FALSE  0.03138961
    ## cg07655636 0.08054378   FALSE -1.29294851

    ctl2 <- rownames(M) %in% rownames(top1[top1$p.BH_X1.1 > 0.5,])
    table(ctl2)

    ## ctl2
    ##  FALSE   TRUE
    ## 172540 312972

We can then use the ECPs to perform a second differential methylation with RUV-inverse, which is adjusted for the unwanted variation estimated from the data.

    # Perform RUV adjustment and fit
    rfit3 <- RUVfit(Y = M, X = grp, ctl = ctl2) # Stage 2 analysis
    rfit4 <- RUVadj(Y = M, fit = rfit3)
    # Look at table of top results
    topRUV(rfit4)

    ##              F.p F.p.BH p_X1.1 p.BH_X1.1    b_X1.1    sigma2 var.b_X1.1 fit.ctl
    ## cg07155336 1e-24  1e-24  1e-24     1e-24 -5.769286 0.1668414  0.1349771   FALSE
    ## cg06463958 1e-24  1e-24  1e-24     1e-24 -5.733093 0.1668414  0.1349771   FALSE
    ## cg00024472 1e-24  1e-24  1e-24     1e-24 -5.662959 0.1668414  0.1349771   FALSE
    ## cg02040433 1e-24  1e-24  1e-24     1e-24 -5.651399 0.1668414  0.1349771   FALSE
    ## cg13355248 1e-24  1e-24  1e-24     1e-24 -5.595396 0.1668414  0.1349771   FALSE
    ## cg02467990 1e-24  1e-24  1e-24     1e-24 -5.592707 0.1668414  0.1349771   FALSE
    ## cg00817367 1e-24  1e-24  1e-24     1e-24 -5.527501 0.1668414  0.1349771   FALSE
    ## cg11396157 1e-24  1e-24  1e-24     1e-24 -5.487992 0.1668414  0.1349771   FALSE
    ## cg16306898 1e-24  1e-24  1e-24     1e-24 -5.466780 0.1668414  0.1349771   FALSE
    ## cg03735888 1e-24  1e-24  1e-24     1e-24 -5.396242 0.1668414  0.1349771   FALSE
    ##                  mean
    ## cg07155336 -1.2767641
    ## cg06463958  0.2776252
    ## cg00024472 -2.4445762
    ## cg02040433 -1.2918259
    ## cg13355248 -0.8483387
    ## cg02467990 -0.4154370
    ## cg00817367 -0.2911294
    ## cg11396157 -1.3800170
    ## cg16306898 -2.1469768
    ## cg03735888 -1.1527557

## Alternative approach for RUVm stage 1

If the number of samples in your experiment is greater than the number of Illumina negative controls on the array platform used - 613 for 450k, 411 for EPIC - stage 1 of RUVm will not work. In such cases, we recommend performing a standard limma analysis in stage 1.

    # setup design matrix
    des <- model.matrix(~grp)
    des

    ##   (Intercept) grp1
    ## 1           1    1
    ## 2           1    1
    ## 3           1    0
    ## 4           1    0
    ## 5           1    1
    ## 6           1    0
    ## attr(,"assign")
    ## [1] 0 1
    ## attr(,"contrasts")
    ## attr(,"contrasts")$grp
    ## [1] "contr.treatment"

    # limma differential methylation analysis
    lfit1 <- lmFit(M, design=des)
    lfit2 <- eBayes(lfit1) # Stage 1 analysis
    # Look at table of top results
    topTable(lfit2)

    ## Removing intercept from test coefficients

    ##                logFC   AveExpr         t      P.Value   adj.P.Val        B
    ## cg07155336 -6.037439 -1.276764 -19.22210 1.175108e-07 0.005755968 7.635736
    ## cg04743961 -4.887986 -2.317315 -19.21709 1.177367e-07 0.005755968 7.634494
    ## cg03607359 -4.393946 -2.191871 -18.07007 1.852304e-07 0.005755968 7.334032
    ## cg13272280 -4.559707 -2.099665 -17.25531 2.599766e-07 0.005755968 7.099628
    ## cg22263007 -4.438420 -1.010994 -17.12384 2.749857e-07 0.005755968 7.060036
    ## cg03556069 -5.456754 -1.811718 -17.00720 2.891269e-07 0.005755968 7.024476
    ## cg08443814 -4.597347 -2.062275 -16.80835 3.151706e-07 0.005755968 6.962907
    ## cg18672939 -5.159383 -0.705992 -16.65643 3.368597e-07 0.005755968 6.915046
    ## cg24385334 -4.157473 -1.943370 -16.59313 3.463909e-07 0.005755968 6.894890
    ## cg18044663 -4.426118 -1.197724 -16.57851 3.486357e-07 0.005755968 6.890216

The results of this can then be used to define ECPs for stage 2, as in the previous example.

    topl1 <- topTable(lfit2, num=Inf)

    ## Removing intercept from test coefficients

    head(topl1)

    ##                logFC   AveExpr         t      P.Value   adj.P.Val        B
    ## cg07155336 -6.037439 -1.276764 -19.22210 1.175108e-07 0.005755968 7.635736
    ## cg04743961 -4.887986 -2.317315 -19.21709 1.177367e-07 0.005755968 7.634494
    ## cg03607359 -4.393946 -2.191871 -18.07007 1.852304e-07 0.005755968 7.334032
    ## cg13272280 -4.559707 -2.099665 -17.25531 2.599766e-07 0.005755968 7.099628
    ## cg22263007 -4.438420 -1.010994 -17.12384 2.749857e-07 0.005755968 7.060036
    ## cg03556069 -5.456754 -1.811718 -17.00720 2.891269e-07 0.005755968 7.024476

    ctl3 <- rownames(M) %in% rownames(topl1[topl1$adj.P.Val > 0.5,])
    table(ctl3)

    ## ctl3
    ##  FALSE   TRUE
    ## 199150 286362

We can then use the ECPs to perform a second differential methylation with `RUV-inverse` as before.

    # Perform RUV adjustment and fit
    rfit5 <- RUVfit(Y = M, X = grp, ctl = ctl3) # Stage 2 analysis
    rfit6 <- RUVadj(Y = M, fit = rfit5)
    # Look at table of top results
    topRUV(rfit6)

    ##              F.p F.p.BH p_X1.1 p.BH_X1.1    b_X1.1    sigma2 var.b_X1.1 fit.ctl
    ## cg06463958 1e-24  1e-24  1e-24     1e-24 -5.910598 0.1667397  0.1170589   FALSE
    ## cg07155336 1e-24  1e-24  1e-24     1e-24 -5.909549 0.1667397  0.1170589   FALSE
    ## cg02467990 1e-24  1e-24  1e-24     1e-24 -5.841079 0.1667397  0.1170589   FALSE
    ## cg00024472 1e-24  1e-24  1e-24     1e-24 -5.823529 0.1667397  0.1170589   FALSE
    ## cg01893212 1e-24  1e-24  1e-24     1e-24 -5.699627 0.1667397  0.1170589   FALSE
    ## cg11396157 1e-24  1e-24  1e-24     1e-24 -5.699331 0.1667397  0.1170589   FALSE
    ## cg13355248 1e-24  1e-24  1e-24     1e-24 -5.658606 0.1667397  0.1170589   FALSE
    ## cg00817367 1e-24  1e-24  1e-24     1e-24 -5.649284 0.1667397  0.1170589   FALSE
    ## cg16306898 1e-24  1e-24  1e-24     1e-24 -5.610118 0.1667397  0.1170589   FALSE
    ## cg16556906 1e-24  1e-24  1e-24     1e-24 -5.567659 0.1667397  0.1170589   FALSE
    ##                   mean
    ## cg06463958  0.27762518
    ## cg07155336 -1.27676413
    ## cg02467990 -0.41543703
    ## cg00024472 -2.44457624
    ## cg01893212 -0.08273355
    ## cg11396157 -1.38001701
    ## cg13355248 -0.84833866
    ## cg00817367 -0.29112939
    ## cg16306898 -2.14697683
    ## cg16556906 -0.96821744

## Visualising the effect of RUVm adjustment

To visualise the effect that the RUVm adjustment is having on the data, using an MDS plot for example, the `getAdj` function can be used to extract the adjusted values from the RUVm fit object produced by `RUVfit`. NOTE: The adjusted values should only be used for visualisations - it is NOT recommended that they are used in any downstream analysis.

    Madj <- getAdj(M, rfit5) # get adjusted values

The MDS plots below show how the relationship between the samples changes with and without RUVm adjustment. RUVm reduces the distance between the samples in each group by removing unwanted variation. It can be useful to examine this type of plot when trying to decide on the best set of ECPs or to help select the optimal value of \(k\), if using RUV-4 or RUV-2.

    par(mfrow=c(1,2))
    plotMDS(M, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Unadjusted", gene.selection = "common")
    legend("right",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)
    plotMDS(Madj, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Adjusted: RUV-inverse", gene.selection = "common")

    ## Warning in plotMDS.default(Madj, labels = targets$Sample_Name, col =
    ## as.integer(factor(targets$status)), : dimension 2 is degenerate or all zero

    legend("topright",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)

RUVm adjusted data. An MDS plot of cancer and normal data, before and after RUVm adjustment.

To illustrate how the `getAdj` function can be used to help select an appropriate value for \(k\), we will run the second stage of the RUVm analysis using RUV-4 with two different \(k\) values.

    # Use RUV-4 in stage 2 of RUVm with k=1 and k=2
    rfit7 <- RUVfit(Y = M, X = grp, ctl = ctl3,
                    method = "ruv4", k=1) # Stage 2 with RUV-4, k=1
    rfit9 <- RUVfit(Y = M, X = grp, ctl = ctl3,
                    method = "ruv4", k=2) # Stage 2 with RUV-4, k=2
    # get adjusted values
    Madj1 <- getAdj(M, rfit7)
    Madj2 <- getAdj(M, rfit9)

The following MDS plots show how the relationship between the samples changes from the unadjusted data to data adjusted with RUV-inverse and RUV-4 with two different \(k\) values. For this small dataset, RUV-inverse appears to be removing far too much variation as we can see the samples in each group are completely overlapping. Using RUV-4 and choosing a smaller value for \(k\) produces more sensible results.

    par(mfrow=c(2,2))
    plotMDS(M, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Unadjusted", gene.selection = "common")
    legend("top",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)
    plotMDS(Madj, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Adjusted: RUV-inverse", gene.selection = "common")

    ## Warning in plotMDS.default(Madj, labels = targets$Sample_Name, col =
    ## as.integer(factor(targets$status)), : dimension 2 is degenerate or all zero

    legend("topright",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)
    plotMDS(Madj1, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Adjusted: RUV-4, k=1", gene.selection = "common")
    legend("bottom",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)
    plotMDS(Madj2, labels=targets$Sample_Name, col=as.integer(factor(targets$status)),
            main="Adjusted: RUV-4, k=2", gene.selection = "common")
    legend("bottomright",legend=c("Cancer","Normal"),pch=16,cex=1,col=1:2)

Effect of different adjustment methods and parameters. MDS plots of cancer and normal data before an after adjustment with RUV-inverse and RUV-4 with different k values.

More information about the various RUV methods can be found at http://www-personal.umich.edu/~johanngb/ruv/, including links to all relevant publications. Further examples of RUV analyses, with code, can be found at https://github.com/johanngb/ruv-useR2018. The tutorials demonstrate how the various plotting functions available in the ruv package (which are not covered in this vignette) can be used to select sensible parameters and assess if the adjustment is “helping” your analysis.

# Testing for differential variability (DiffVar)

## Methylation data

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 are important for tumour progression (Hansen et al. 2011). Hence we may be interested in CpG sites that are consistently methylated in the normal samples, but variably methylated in the cancer samples.

In general we recommend at least 10 samples in each group for accurate variance estimation, however for the purpose of this vignette we perform the analysis on 3 vs 3. In this example, we are interested in testing for differential variability in the cancer versus normal group.

An important note on the `coef` parameter: please always explicitly state which columns of design matrix correspond to the groups that you are interested in testing for differential variability. The default setting for `coef` is to include all columns of the design matrix when calculating the Levene residuals, which is not suitable for when there are additional variables that need to be taken into account in the linear model. To avoid misspecification of the model, it is best to explicitly state the `coef` parameter. The additional nuisance or confounding variables will still be taken into account in the linear modelling step, however we find that including them when calculating Levene residuals often removes all the (possibly interesting) variation in the data.

When the design matrix includes an intercept term, the `coef` parameter must include both the intercept and groups of interest. Consider the design matrix that was used when performing the limma analysis:

    design

    ##   (Intercept) idid2 idid3 groupcancer
    ## 1           1     0     1           0
    ## 2           1     1     0           0
    ## 3           1     0     1           1
    ## 4           1     0     0           1
    ## 5           1     0     0           0
    ## 6           1     1     0           1
    ## attr(,"assign")
    ## [1] 0 1 1 2
    ## attr(,"contrasts")
    ## attr(,"contrasts")$id
    ## [1] "contr.treatment"
    ##
    ## attr(,"contrasts")$group
    ## [1] "contr.treatment"

The first column of the design matrix is the intercept term, and the fourth column tells us which samples are cancer and normal samples. The 2nd and 3rd columns correspond to the ID parameter, which is not interesting in terms of finding differentially variable CpGs, but may be important to include in the linear model. Hence for this example we would specify `coef = c(1,4)` in the call to `varFit`.

For methylation data, the `varFit` function will take either a matrix of M-values, \(\beta\) values or a `MethylSet` object as input. If \(\beta\) values are supplied, a logit transformation is performed. Note that as a default, `varFit` uses the robust setting in the limma framework, which requires the use of the statmod package.

    fitvar <- varFit(Mval, design = design, coef = c(1,4))

The numbers of hyper-variable (1) and hypo-variable (-1) genes in cancer vs normal can be obtained using `decideTests`. In the cancer vs normal context, we would expect to see more variability in methylation in cancer compared to normal (i.e. hyper-variable).

    summary(decideTests(fitvar))

    ##        (Intercept) idid2 idid3 groupcancer
    ## Down             0     3     1           0
    ## NotSig       19717 19996 19992       19991
    ## Up             283     1     7           9

    topDV <- topVar(fitvar, coef=4)
    topDV

    ##            SampleVar LogVarRatio DiffLevene        t      P.Value Adj.P.Value
    ## cg13516820  5.690088    3.421191   2.883860 5.428080 5.729402e-08 0.001145880
    ## cg14267725  8.315587    4.370011   2.888360 4.882415 1.051981e-06 0.009120332
    ## cg22091297  6.122715    4.032293   2.807074 4.830338 1.368050e-06 0.009120332
    ## cg26744375  6.108719    2.689231   2.476809 4.754890 1.992451e-06 0.009962254
    ## cg23071808  5.529235    3.375761   2.644465 4.671673 2.997277e-06 0.010887078
    ## cg24879782  4.763810    3.864397   2.723026 4.653992 3.266124e-06 0.010887078
    ## cg15174834  4.859486    3.821722   2.622976 4.406933 1.051171e-05 0.028147863
    ## cg09912667  4.218882    5.045329   2.780052 4.392018 1.125915e-05 0.028147863
    ## cg09028204  5.208016    2.968815   2.412770 4.334459 1.464753e-05 0.032550073
    ## cg17969902  4.845231    3.699393   2.492553 4.079785 4.516471e-05 0.090329420

An alternate parameterisation of the design matrix that does not include an intercept term can also be used (i.e. a cell means model), and specific contrasts tested with `contrasts.varFit`. Here we specify the design matrix such that the first two columns correspond to the normal and cancer groups, respectively. Note that we now specify `coef=c(1,2)`.

    design2 <- model.matrix(~0+group+id)
    fitvar.contr <- varFit(Mval, design=design2, coef=c(1,2))
    contr <- makeContrasts(groupcancer-groupnormal,levels=colnames(design2))
    fitvar.contr <- contrasts.varFit(fitvar.contr,contrasts=contr)

The results are identical to before.

    summary(decideTests(fitvar.contr))

    ##        groupcancer - groupnormal
    ## Down                           0
    ## NotSig                     19991
    ## Up                             9

    topVar(fitvar.contr,coef=1)

    ##            SampleVar LogVarRatio DiffLevene        t      P.Value Adj.P.Value
    ## cg13516820  5.690088    3.421191   2.883860 5.428080 5.729402e-08 0.001145880
    ## cg14267725  8.315587    4.370011   2.888360 4.882415 1.051981e-06 0.009120332
    ## cg22091297  6.122715    4.032293   2.807074 4.830338 1.368050e-06 0.009120332
    ## cg26744375  6.108719    2.689231   2.476809 4.754890 1.992451e-06 0.009962254
    ## cg23071808  5.529235    3.375761   2.644465 4.671673 2.997277e-06 0.010887078
    ## cg24879782  4.763810    3.864397   2.723026 4.653992 3.266124e-06 0.010887078
    ## cg15174834  4.859486    3.821722   2.622976 4.406933 1.051171e-05 0.028147863
    ## cg09912667  4.218882    5.045329   2.780052 4.392018 1.125915e-05 0.028147863
    ## cg09028204  5.208016    2.968815   2.412770 4.334459 1.464753e-05 0.032550073
    ## cg17969902  4.845231    3.699393   2.492553 4.079785 4.516471e-05 0.090329420

The \(\beta\) values for the top 4 differentially variable CpGs can be seen in Figure @ref(fig:top4DV).

    cpgsDV <- rownames(topDV)
    par(mfrow=c(2,2))
    for(i in 1:4){
    stripchart(beta[rownames(beta)==cpgsDV[i],]~design[,4],method="jitter",
    group.names=c("Normal","Cancer"),pch=16,cex=1.5,col=c(4,2),ylab="Beta values",
    vertical=TRUE,cex.axis=1.5,cex.lab=1.5)
    title(cpgsDV[i],cex.main=1.5)
    }

Top DV CpGs. The beta values for the top 4 differentially variable CpGs.

## RNA-Seq expression data

Testing for differential variability in expression data is straightforward if the technology is gene expression microarrays. The matrix of expression values can be supplied directly to the `varFit` function. For RNA-Seq data, the mean-variance relationship that occurs in count data needs to be taken into account. In order to deal with this issue, we apply a `voom` transformation (Law et al. 2014) to obtain observation weights, which are then used in the linear modelling step. For RNA-Seq data, the `varFit` function will take a `DGElist` object as input.

To demonstrate this, we use data from the tweeDEseqCountData package. This data is part of the International HapMap project, consisting of RNA-Seq profiles from 69 unrelated Nigerian individuals (Pickrell et al. 2010). The only covariate is gender, so we can look at differentially variable expression between males and females. We follow the code from the limma vignette to read in and process the data before testing for differential variability.

First we load up the data and extract the relevant information.

    library(tweeDEseqCountData)
    data(pickrell1)
    counts<-exprs(pickrell1.eset)
    dim(counts)

    ## [1] 38415    69

    gender <- pickrell1.eset$gender
    table(gender)

    ## gender
    ## female   male
    ##     40     29

    rm(pickrell1.eset)
    data(genderGenes)
    data(annotEnsembl63)
    annot <- annotEnsembl63[,c("Symbol","Chr")]
    rm(annotEnsembl63)

We now have the counts, gender of each sample and annotation (gene symbol and chromosome) for each Ensemble gene. We can form a `DGElist` object using the edgeR package.

    library(edgeR)
    y <- DGEList(counts=counts, genes=annot[rownames(counts),])

We filter out lowly expressed genes by keeping genes with at least 1 count per million reads in at least 20 samples, as well as genes that have defined annotation. Finally we perform scaling normalisation.

    isexpr <- rowSums(cpm(y)>1) >= 20
    hasannot <- rowSums(is.na(y$genes))==0
    y <- y[isexpr & hasannot,,keep.lib.sizes=FALSE]
    dim(y)

    ## [1] 17310    69

    y <- calcNormFactors(y)

We set up the design matrix and test for differential variability.

    design.hapmap <- model.matrix(~gender)
    fitvar.hapmap <- varFit(y, design = design.hapmap, coef=c(1,2))

    ## Converting counts to log counts-per-million using voom.

    fitvar.hapmap$genes <- y$genes

We can display the results of the test:

    summary(decideTests(fitvar.hapmap))

    ##        (Intercept) gendermale
    ## Down             0          2
    ## NotSig           0      17308
    ## Up           17310          0

    topDV.hapmap <- topVar(fitvar.hapmap,coef=ncol(design.hapmap))
    topDV.hapmap

    ##                       Symbol Chr  SampleVar LogVarRatio DiffLevene         t
    ## ENSG00000213318 RP11-331F4.1  16 5.69839463   -2.562939 -0.9873072 -8.043479
    ## ENSG00000129824       RPS4Y1   Y 2.32497726   -2.087025 -0.4581834 -4.942033
    ## ENSG00000233864       TTTY15   Y 6.79004140   -2.245369 -0.6084678 -4.529415
    ## ENSG00000176171        BNIP3  10 0.41317384    1.199292  0.3635909  4.221153
    ## ENSG00000197358      BNIP3P1  14 0.39969125    1.149754  0.3357314  4.061035
    ## ENSG00000025039        RRAGD   6 0.91837213    1.091229  0.4928779  3.976688
    ## ENSG00000103671        TRIP4  15 0.07456448   -1.457139 -0.1520311 -3.915810
    ## ENSG00000171100         MTM1   X 0.44049558   -1.133295 -0.3336303 -3.910918
    ## ENSG00000149476          DAK  11 0.13289523   -1.470460 -0.1920176 -3.787801
    ## ENSG00000157828       RPS4Y2   Y 2.95789619   -1.417305 -0.2793904 -3.782506
    ##                      P.Value  Adj.P.Value
    ## ENSG00000213318 6.980147e-12 1.208263e-07
    ## ENSG00000129824 4.219220e-06 3.651735e-02
    ## ENSG00000233864 2.058016e-05 1.187475e-01
    ## ENSG00000176171 6.417937e-05 2.777362e-01
    ## ENSG00000197358 1.138836e-04 3.942650e-01
    ## ENSG00000025039 1.532798e-04 4.170847e-01
    ## ENSG00000103671 1.895160e-04 4.170847e-01
    ## ENSG00000171100 1.927601e-04 4.170847e-01
    ## ENSG00000149476 2.942622e-04 4.609062e-01
    ## ENSG00000157828 2.996120e-04 4.609062e-01

The log counts per million for the top 4 differentially variable genes can be seen in Figure @ref(fig:top4DVhapmap).

    genesDV <- rownames(topDV.hapmap)
    par(mfrow=c(2,2))
    for(i in 1:4){
    stripchart(cpm(y,log=TRUE)[rownames(y)==genesDV[i],]~design.hapmap[,ncol(design.hapmap)],method="jitter",
    group.names=c("Female","Male"),pch=16,cex=1.5,col=c(4,2),ylab="Log counts per million",
    vertical=TRUE,cex.axis=1.5,cex.lab=1.5)
    title(genesDV[i],cex.main=1.5)
    }

Top DV CpGs. The log counts per million for the top 4 differentially variably expressed genes.

# Gene ontology analysis

Once a differential methylation or differential variability analysis has been performed, it may be of interest to know which gene pathways are targeted by the significant CpG sites. Geeleher et al. (Geeleher et al. 2013) showed there is a severe bias when performing gene ontology analysis with methylation data. This is due to the fact that there are differing numbers of probes per gene on several different array technologies. For the Illumina Infinium HumanMethylation450 array the number of probes per gene ranges from 1 to 1299, with a median of 15 probes per gene. For the EPIC array, the range is 1 to 1487, with a median of 20 probes per gene. This means that when annotating CpG sites to genes, a gene is more likely to be identified as differentially methylated if there are many CpG sites associated with the gene. We refer to this source of bias as “probe number bias”.

One way to take into account this selection bias is to model the relationship between the number of probes per gene and the probability of being differentially methylated. This can be performed by adapting the goseq method of Young et al. (Young et al. 2010). Each gene then has a prior probability associated with it, and a modified version of a hypergeometric test can be performed, testing for over-representation of the selected genes in each gene set. The BiasedUrn package can be used to obtain p-values from the Wallenius’ noncentral hypergeometric distribution, taking into account the odds of differential methylation for each gene set. Note that the BiasedUrn package can occassionally return p-values of 0. For the gene sets where a p-value of exactly zero is outputted we perform a hypergeometric test, which ensures non-zero p-values and hence false discovery rates.

We have recently uncovered a new source of bias in gene set testing for methylation array data (Maksimovic, Oshlack, and Phipson 2020) that we refer to as “multi-gene bias”. This second source of bias arises due to the fact that around 10% of gene-annotated CpGs are annotated to more than one gene, violating assumptions of independently measured genes. This can lead to some GO categories being identified as significantly enriched as they contain genes with methylation measurements from shared CpGs. This can occur for large gene families such as the protocadherin gamma gene cluster which happen to be over-represented in the GO category “GO:0007156: homophilic cell adhesion via plasma membrane adhesion molecules”. This is now taken into account in the gene set testing functions in missMethyl.

We have developed methods for both CpG and region level analyses. The `gometh` function performs gene set testing on GO categories or KEGG pathways for significant CpG sites. The `gsameth` function is a more generalised gene set testing function which can take as input a list of user specified gene sets. Note that for `gsameth`, the format for the gene ids for each gene in the gene set needs to be Entrez Gene IDs. For example, the entire curated gene set list (C2) from the Broad’s Molecular Signatures Database can be specified as input. The R version of these lists can be downloaded from http://bioinf.wehi.edu.au/software/MSigDB/index.html. Both functions take a vector of significant CpG probe names as input. For a region level analysis, using the DMRcate package, for example, `goregion` and `gsaregion` can perform gene set enrichment analysis using the ranged object as input.

NOTE ON UPDATES IN SEPTEMBER 2020: We have added new functionality to the gene set testing functions to allow the user to limit the input CpGs to specific genomic features of interest using the `genomic.features` argument. This is based on the annotation information in the manifest files for the 450K and EPIC arrays. Possible values are ““ALL”, “TSS200”, “TSS1500”, “Body”, “1stExon”, “3’UTR”, “5’UTR” and “ExonBnd” (only for EPIC), and any combination can be specified. In order to include the significant genes that overlap with the gene set of interest, the `sig.genes` parameter can be set to `TRUE`. This adds an additional column to the results dataframe.

## CpG level analysis

To illustrate how to use `gometh`, consider the results from the differential methylation analysis with RUVm.

    top <- topRUV(rfit4, number = Inf, p.BH = 1)
    table(top$p.BH_X1.1 < 0.01)

    ##
    ##  FALSE   TRUE
    ## 424168  61344

At a 1% false discovery rate cut-off, there are more than 60,000 CpG sites differentially methylated. These CpGs are annotated to almost 10,000 genes, which means that a gene ontology analysis is unlikely to be relevant or reveal anything biologically interesting. One option for selecting CpGs in this context is to apply not only a false discovery rate cut-off, but also a \(\Delta\beta\) cut-off. However, for this dataset, taking a relatively large \(\Delta\beta\) cut-off of 0.25 still leaves more than 30000 CpGs differentially methylated, which can be annotated to more than 6000 genes.

    beta <- getBeta(mSet)
    # make sure that order of beta values matches orer after analysis
    beta <- beta[match(rownames(top),rownames(beta)),]
    beta_norm <- rowMeans(beta[,grp==0])
    beta_can <- rowMeans(beta[,grp==1])
    Delta_beta <- beta_can - beta_norm
    sigDM <- top$p.BH_X1.1 < 0.01 & abs(Delta_beta) > 0.25
    table(sigDM)

    ## sigDM
    ##  FALSE   TRUE
    ## 451760  33748

Instead, we take the top 10000 CpG sites as input to `gometh` which can be annotated to around 2500 genes.

    topCpGs<-topRUV(rfit4,number=10000)
    sigCpGs <- rownames(topCpGs)
    sigCpGs[1:10]

    ##  [1] "cg07155336" "cg06463958" "cg00024472" "cg02040433" "cg13355248"
    ##  [6] "cg02467990" "cg00817367" "cg11396157" "cg16306898" "cg03735888"

    # Check number of genes that significant CpGs are annotated to
    check <- getMappedEntrezIDs(sig.cpg = sigCpGs)

    ## All input CpGs are used for testing.

    length(check$sig.eg)

    ## [1] 2490

The`gometh` function takes as input a character vector of CpG names, and optionally, a character vector of all CpG sites tested. This is important to include if filtering of the CpGs has been performed prior to differential methylation analysis. If the `all.cpg` argument is omitted, all the CpGs on the array are used as background. To change the array type, the `array.type` argument can be specified as either “450K”, “EPIC” or “EPIC_V2”. The default is “450K”.

If the `plot.bias` argument is `TRUE`, a figure showing the relationship between the probability of differential methylation and the number of probes per gene will be displayed.

For testing of GO terms, the `collection` argument takes the value “GO”, which is the default setting. For KEGG pathway analysis, set `collection` to “KEGG”. The function `topGSA` shows the top enriched GO categories. The `gsameth` function is called for GO and KEGG pathway analysis with the appropriate inputs.

For GO testing on our example dataset:

    library(IlluminaHumanMethylation450kanno.ilmn12.hg19)
    gst <- gometh(sig.cpg=sigCpGs, all.cpg=rownames(top), collection="GO",
                  plot.bias=TRUE)

    ## All input CpGs are used for testing.

Probe number bias in the cancer dataset.

    topGSA(gst, n=10)

    ##            ONTOLOGY                               TERM    N   DE         P.DE
    ## GO:0048731       BP                 system development 4182  933 8.174793e-40
    ## GO:0007399       BP         nervous system development 2650  667 2.338500e-35
    ## GO:0007275       BP multicellular organism development 4849 1002 3.570781e-32
    ## GO:0048699       BP              generation of neurons 1556  439 5.108098e-30
    ## GO:0048856       BP   anatomical structure development 6121 1162 9.220206e-30
    ## GO:0030182       BP             neuron differentiation 1477  419 6.305756e-29
    ## GO:0022008       BP                       neurogenesis 1818  484 1.005211e-27
    ## GO:0032502       BP              developmental process 6695 1220 5.290359e-27
    ## GO:0032501       BP   multicellular organismal process 7529 1292 1.759721e-25
    ## GO:0071944       CC                     cell periphery 5984 1057 5.704921e-24
    ##                     FDR
    ## GO:0048731 1.805403e-35
    ## GO:0007399 2.582289e-31
    ## GO:0007275 2.628690e-28
    ## GO:0048699 2.820309e-26
    ## GO:0048856 4.072565e-26
    ## GO:0030182 2.321044e-25
    ## GO:0022008 3.171440e-24
    ## GO:0032502 1.460470e-23
    ## GO:0032501 4.318161e-22
    ## GO:0071944 1.259932e-20

Testing all GO categories (>20,000) can be a little slow. To demonstrate the `genomic.features` parameter, let us rather focus on KEGG pathways (~330 pathways).

    gst.kegg <- gometh(sig.cpg=sigCpGs, all.cpg=rownames(top), collection="KEGG")

    ## All input CpGs are used for testing.

    topGSA(gst.kegg, n=10)

    ##                                       Description   N DE         P.DE
    ## hsa04080  Neuroactive ligand-receptor interaction 364 81 2.177236e-08
    ## hsa04020                Calcium signaling pathway 250 76 5.884977e-08
    ## hsa04082             Neuroactive ligand signaling 199 58 2.291602e-06
    ## hsa04514 Cell adhesion molecule (CAM) interaction 153 48 8.833186e-06
    ## hsa04081                        Hormone signaling 217 52 2.657449e-05
    ## hsa04970                       Salivary secretion  92 27 1.100661e-04
    ## hsa04024                   cAMP signaling pathway 225 57 1.309032e-04
    ## hsa04950     Maturity onset diabetes of the young  26 12 2.855415e-04
    ## hsa04151               PI3K-Akt signaling pathway 347 79 7.369812e-04
    ## hsa04517                       IgSF CAM signaling 294 75 8.911533e-04
    ##                   FDR
    ## hsa04080 8.034002e-06
    ## hsa04020 1.085778e-05
    ## hsa04082 2.818670e-04
    ## hsa04514 8.148614e-04
    ## hsa04081 1.961197e-03
    ## hsa04970 6.769068e-03
    ## hsa04024 6.900467e-03
    ## hsa04950 1.317060e-02
    ## hsa04151 3.021623e-02
    ## hsa04517 3.288356e-02

We can limit the input CpGs to those in the promoter regions of genes:

    gst.kegg.prom <- gometh(sig.cpg=sigCpGs, all.cpg=rownames(top),
                            collection="KEGG", genomic.features = c("TSS200",
                                                                    "TSS1500",
                                                                    "1stExon"))
    topGSA(gst.kegg.prom, n=10)

    ##                                       Description   N DE         P.DE
    ## hsa04080  Neuroactive ligand-receptor interaction 364 58 2.740941e-09
    ## hsa04081                        Hormone signaling 217 38 1.758637e-06
    ## hsa04082             Neuroactive ligand signaling 199 39 2.903301e-06
    ## hsa04020                Calcium signaling pathway 250 46 8.316483e-06
    ## hsa04024                   cAMP signaling pathway 225 37 1.695552e-04
    ## hsa04514 Cell adhesion molecule (CAM) interaction 153 29 2.072059e-04
    ## hsa04911                        Insulin secretion  86 19 5.015236e-04
    ## hsa04517                       IgSF CAM signaling 294 47 8.656899e-04
    ## hsa05032                       Morphine addiction  91 20 9.657744e-04
    ## hsa05217                     Basal cell carcinoma  63 15 1.529262e-03
    ##                   FDR
    ## hsa04080 1.011407e-06
    ## hsa04081 3.244686e-04
    ## hsa04082 3.571061e-04
    ## hsa04020 7.671955e-04
    ## hsa04024 1.251317e-02
    ## hsa04514 1.274316e-02
    ## hsa04911 2.643746e-02
    ## hsa04517 3.959675e-02
    ## hsa05032 3.959675e-02
    ## hsa05217 5.366417e-02

We can see if the results are different if we only include CpGs in gene bodies:

    gst.kegg.body <- gometh(sig.cpg=sigCpGs, all.cpg=rownames(top),
                            collection="KEGG", genomic.features = c("Body"))
    topGSA(gst.kegg.body, n=10)

    ##                                                       Description   N DE
    ## hsa04514                 Cell adhesion molecule (CAM) interaction 153 29
    ## hsa04820                             Cytoskeleton in muscle cells 233 38
    ## hsa04974                         Protein digestion and absorption 102 19
    ## hsa04020                                Calcium signaling pathway 250 40
    ## hsa04512                                 ECM-receptor interaction  89 19
    ## hsa04640                               Hematopoietic cell lineage  93 15
    ## hsa04518                                       Integrin signaling 153 28
    ## hsa04950                     Maturity onset diabetes of the young  26  7
    ## hsa04151                               PI3K-Akt signaling pathway 347 45
    ## hsa04550 Signaling pathways regulating pluripotency of stem cells 141 24
    ##                  P.DE        FDR
    ## hsa04514 0.0002590916 0.05181538
    ## hsa04820 0.0003508476 0.05181538
    ## hsa04974 0.0004212632 0.05181538
    ## hsa04020 0.0007278618 0.05399123
    ## hsa04512 0.0008302229 0.05399123
    ## hsa04640 0.0008779062 0.05399123
    ## hsa04518 0.0018544673 0.09775692
    ## hsa04950 0.0056792228 0.26195415
    ## hsa04151 0.0066321183 0.27191685
    ## hsa04550 0.0077294688 0.28521740

The KEGG pathways are quite different when limiting CpGs to those in gene bodies versus CpGs in promoters. To include the significant genes that overlap with each gene set, set the `sig.genes` parameter to TRUE.

    gst.kegg.body <- gometh(sig.cpg=sigCpGs, all.cpg=rownames(top),
                            collection="KEGG", genomic.features = c("Body"),
                            sig.genes = TRUE)
    topGSA(gst.kegg.body, n=5)

    ##                                       Description   N DE         P.DE
    ## hsa04514 Cell adhesion molecule (CAM) interaction 153 29 0.0002590916
    ## hsa04820             Cytoskeleton in muscle cells 233 38 0.0003508476
    ## hsa04974         Protein digestion and absorption 102 19 0.0004212632
    ## hsa04020                Calcium signaling pathway 250 40 0.0007278618
    ## hsa04512                 ECM-receptor interaction  89 19 0.0008302229
    ##                 FDR
    ## hsa04514 0.05181538
    ## hsa04820 0.05181538
    ## hsa04974 0.05181538
    ## hsa04020 0.05399123
    ## hsa04512 0.05399123
    ##                                                                                                                                                                                                                                                          SigGenesInSet
    ## hsa04514                                                                             CDH2,CDH4,CNTNAP2,ICOS,HLA-DQA2,HLA-DQB1,HLA-DQB2,HLA-F,HLA-G,ITGA4,ITGAM,MAG,NCAM1,CLDN11,CLDN18,PDCD1,PTPRM,PTPRS,JAM2,SDC2,JAM3,NTNG2,ITGA8,CLDN12,CLDN1,CD8A,NRXN1,NRXN2,CD34
    ## hsa04820                COL1A2,COL4A1,COL4A2,COL4A3,COL5A1,COL5A2,COL6A3,COL11A2,COMP,SGCZ,SYNE3,ELN,FBLN1,FBLN2,MYH15,SUN1,COL24A1,PDLIM3,LAMA1,ITGA4,ITGB4,ITGB5,AGRN,LAMA2,MYBPC3,MYH11,NID1,ATP1B2,FMN2,SPTBN4,ACTA1,SDC2,TNNI2,TNNT3,VIM,OBSCN,ITGA8,COL27A1,SGCE
    ## hsa04974                                                                                                                 COL1A2,COL4A1,COL4A2,COL4A3,COL5A1,COL5A2,COL6A3,COL11A2,COL15A1,CPA2,COL26A1,COL22A1,ELN,COL24A1,KCNQ1,ATP1B2,SLC8A2,COL18A1,COL27A1,COL23A1
    ## hsa04020 ADCY1,GRIN3A,ADRA1B,ADCY4,ERBB4,FGF3,FGFR2,P2RX2,FLT1,FLT4,GDNF,GRIN2A,GRIN2D,GRM5,HTR2A,ITPKB,ITPR2,NFATC1,ATP2A1,ATP2B2,NTRK1,NTRK2,NTRK3,PDE1A,PDGFB,PLCG2,PRKCB,RYR1,RYR2,RYR3,SLC8A2,CACNA1B,CACNA1D,PDGFD,CAMK4,CAMK2B,CACNA1I,CACNA1H,PLCZ1,CD38,FGF19
    ## hsa04512                                                                                                                                         COL1A2,COL4A1,COL4A2,COL4A3,COL6A3,COMP,LAMA1,FREM2,ITGA4,ITGB4,ITGB5,AGRN,LAMA2,LAMA4,GP6,RELN,TNXB,FRAS1,ITGA8,CD36

For a more generalised version of gene set testing in methylation data where the user can specify the gene set to be tested, the function `gsameth` can be used. To display the top 20 pathways, `topGSA` can be called. `gsameth` can take 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 download and use the Hallmark gene set.

    hallmark <- readRDS(url("http://bioinf.wehi.edu.au/MSigDB/v7.1/Hs.h.all.v7.1.entrez.rds"))
    gsa <- gsameth(sig.cpg=sigCpGs, all.cpg=rownames(top), collection=hallmark)

    ## All input CpGs are used for testing.

    topGSA(gsa, n=10)

    ##                                              N DE         P.DE          FDR
    ## HALLMARK_EPITHELIAL_MESENCHYMAL_TRANSITION 199 62 1.502509e-07 7.512545e-06
    ## HALLMARK_KRAS_SIGNALING_DN                 200 47 1.599089e-04 3.997724e-03
    ## HALLMARK_PANCREAS_BETA_CELLS                40 14 7.598882e-04 1.266480e-02
    ## HALLMARK_MYOGENESIS                        200 46 1.784710e-02 2.230888e-01
    ## HALLMARK_APICAL_JUNCTION                   199 43 3.214686e-02 3.171141e-01
    ## HALLMARK_SPERMATOGENESIS                   135 25 3.805369e-02 3.171141e-01
    ## HALLMARK_UV_RESPONSE_DN                    144 36 9.675631e-02 6.186248e-01
    ## HALLMARK_HEDGEHOG_SIGNALING                 36 11 9.897998e-02 6.186248e-01
    ## HALLMARK_KRAS_SIGNALING_UP                 198 34 1.260699e-01 7.003883e-01
    ## HALLMARK_NOTCH_SIGNALING                    32  9 1.415457e-01 7.077283e-01

Note that if it is of interest to obtain the Entrez Gene IDs that the significant CpGs are mapped to, the `getMappedEntrezIDs` function can be called.

## Region level analysis

We have extended `gometh` and `gsameth` to perform gene set testing following a region analysis. The region gene set testing function analogues are `goregion` and `gsaregion`. Instead of inputting significant CpGs, a ranged object as typically outputted from region finding software is used. The CpGs overlapping the significant differentially methylated regions (DMRs) are extracted and the same statistical framework in `gometh` and `gsameth` is applied to test for enrichment of gene sets. We find that genes that have more CpGs measuring methylation are more likely to be called as differentially methylated regions, and hence it is important to take into account this bias when performing gene set testing.

To demonstrate `goregion` and `gsaregion` we will perform a region analysis on the cancer dataset using the DMRcate package.

    library(DMRcate)

First, the matrix of M-values is annotated with the relevant annotation information about the probes such as their genomic position, gene annotation, etc. By default, this is done using the ilmn12.hg19 annotation. The limma pipeline is then used for differential methylation analysis to calculate moderated t-statistics.

    myAnnotation <- cpg.annotate(object = M, datatype = "array", what = "M",
                                 arraytype = c("450K"),
                                 analysis.type = "differential", design = design,
                                 coef = 4)

    ## Your contrast returned 23435 individually significant probes. We recommend the default setting of pcutoff in dmrcate().

Next we can use the `dmrcate` function to combine the CpGs to identify differentially methylated regions. We can use the `extractRanges` function to extract a `GRanges` object with the genomic location and the relevant statistics associated with each DMR. This object can then be used as input to `goregion` and `gsaregion`.

    DMRs <- dmrcate(myAnnotation, lambda=1000, C=2)

    ## Fitting chr1...

    ## Fitting chr2...

    ## Fitting chr3...

    ## Fitting chr4...

    ## Fitting chr5...

    ## Fitting chr6...

    ## Fitting chr7...

    ## Fitting chr8...

    ## Fitting chr9...

    ## Fitting chr10...

    ## Fitting chr11...

    ## Fitting chr12...

    ## Fitting chr13...

    ## Fitting chr14...

    ## Fitting chr15...

    ## Fitting chr16...

    ## Fitting chr17...

    ## Fitting chr18...

    ## Fitting chr19...

    ## Fitting chr20...

    ## Fitting chr21...

    ## Fitting chr22...

    ## Fitting chrX...

    ## Fitting chrY...

    ## Demarcating regions...

    ## Done!

    results.ranges <- extractRanges(DMRs)

    ## DMRcatedata not installed.
    ##   Full functionality, documentation, and loading of data might not be possible without installing

    ## downloading 1 resources

    ## retrieving 1 resource

    ## loading from cache

    results.ranges

    ## GRanges object with 2578 ranges and 8 metadata columns:
    ##          seqnames              ranges strand |   no.cpgs min_smoothed_fdr
    ##             <Rle>           <IRanges>  <Rle> | <integer>        <numeric>
    ##      [1]     chr4 154709441-154714069      * |        54                0
    ##      [2]     chr6 133561224-133564066      * |        50                0
    ##      [3]    chr13   78491982-78494462      * |        50                0
    ##      [4]    chr11   32454216-32461240      * |        43                0
    ##      [5]    chr10 118030292-118034357      * |        31                0
    ##      ...      ...                 ...    ... .       ...              ...
    ##   [2574]     chr6   91005117-91005162      * |         2      3.59972e-25
    ##   [2575]     chr2 241085024-241085043      * |         2      3.64478e-25
    ##   [2576]    chr17   48071685-48071706      * |         2      3.86812e-25
    ##   [2577]     chr6 166720997-166721155      * |         2      4.22386e-25
    ##   [2578]    chr19   58446898-58446988      * |         3      4.47316e-25
    ##             Stouffer      HMFDR      Fisher   maxdiff   meandiff
    ##            <numeric>  <numeric>   <numeric> <numeric>  <numeric>
    ##      [1] 1.14510e-52 0.00102944 3.61330e-54  0.586292   0.224951
    ##      [2] 3.29083e-86 0.00103909 4.98468e-81  0.653903   0.362511
    ##      [3] 5.17970e-75 0.00119367 4.78794e-69  0.548184   0.323927
    ##      [4] 1.59959e-71 0.00102449 1.02503e-64  0.648133   0.298009
    ##      [5] 5.43504e-75 0.00102449 1.44576e-66  0.688941   0.411306
    ##      ...         ...        ...         ...       ...        ...
    ##   [2574] 2.15797e-05 0.00197580 4.71393e-05  0.284672  0.2309882
    ##   [2575] 1.94558e-06 0.00113219 4.68351e-06 -0.344832 -0.3291230
    ##   [2576] 3.47644e-05 0.00256174 7.50944e-05  0.331912  0.3141771
    ##   [2577] 1.33409e-04 0.00251525 2.35477e-04  0.252990  0.2377386
    ##   [2578] 1.89862e-04 0.00923636 4.63475e-04 -0.200463  0.0256059
    ##          overlapping.genes
    ##                <character>
    ##      [1]             SFRP2
    ##      [2]              EYA4
    ##      [3] RNF219-AS1, EDNRB
    ##      [4]       WT1-AS, WT1
    ##      [5]             GFRA1
    ##      ...               ...
    ##   [2574]             BACH2
    ##   [2575]              <NA>
    ##   [2576]              DLX3
    ##   [2577]             PRR18
    ##   [2578]              <NA>
    ##   -------
    ##   seqinfo: 23 sequences from an unspecified genome; no seqlengths

We can visualise the top DMR using the `DMR.plot` function:

    cols <- c(2,4)[group]
    names(cols) <-group
    beta <- getBeta(mSet)
    par(mfrow=c(1,1))
    DMR.plot(ranges=results.ranges, dmr=2, CpGs=beta, phen.col=cols,
             what="Beta", arraytype="450K", genome="hg19")

Top DMR from DMRcate.

Now that we have performed our region analysis, we can use `goregion` and `gsaregion` to perform gene set testing. Setting `plot.bias` to TRUE, we can see strong probe number bias in the data. This can be interpretted that a gene is more likely to have a DMR called if it has more CpGs measuring methylation.

    gst.region <- goregion(results.ranges, all.cpg=rownames(M),
                           collection="GO", array.type="450K", plot.bias=TRUE)

    ## All input CpGs are used for testing.

Probe number bias for DMRs in the cancer dataset.

    topGSA(gst.region, n=10)

    ##            ONTOLOGY
    ## GO:0007399       BP
    ## GO:0048731       BP
    ## GO:0007275       BP
    ## GO:0003700       MF
    ## GO:0048856       BP
    ## GO:0030182       BP
    ## GO:0000981       MF
    ## GO:0048699       BP
    ## GO:0022008       BP
    ## GO:0032502       BP
    ##                                                                             TERM
    ## GO:0007399                                            nervous system development
    ## GO:0048731                                                    system development
    ## GO:0007275                                    multicellular organism development
    ## GO:0003700                             DNA-binding transcription factor activity
    ## GO:0048856                                      anatomical structure development
    ## GO:0030182                                                neuron differentiation
    ## GO:0000981 DNA-binding transcription factor activity, RNA polymerase II-specific
    ## GO:0048699                                                 generation of neurons
    ## GO:0022008                                                          neurogenesis
    ## GO:0032502                                                 developmental process
    ##               N  DE         P.DE          FDR
    ## GO:0007399 2650 564 2.298210e-41 2.645961e-37
    ## GO:0048731 4182 758 2.396162e-41 2.645961e-37
    ## GO:0007275 4849 815 1.131927e-35 8.332871e-32
    ## GO:0003700 1352 303 1.289322e-32 7.118669e-29
    ## GO:0048856 6121 931 3.507615e-32 1.549314e-28
    ## GO:0030182 1477 355 1.231484e-31 4.532887e-28
    ## GO:0000981 1272 288 5.405217e-31 1.705346e-27
    ## GO:0048699 1556 366 7.165032e-31 1.977997e-27
    ## GO:0022008 1818 403 2.993678e-29 7.346154e-26
    ## GO:0032502 6695 972 4.523409e-29 9.989948e-26

We can also test for enrichment of KEGG pathways:

    gst.region.kegg <- goregion(results.ranges, all.cpg=rownames(M),
                           collection="KEGG", array.type="450K")

    ## All input CpGs are used for testing.

    topGSA(gst.region.kegg, n=10)

    ##                                       Description   N DE         P.DE
    ## hsa04080  Neuroactive ligand-receptor interaction 364 82 6.716191e-15
    ## hsa04082             Neuroactive ligand signaling 199 60 1.427663e-11
    ## hsa04081                        Hormone signaling 217 53 1.222949e-09
    ## hsa04514 Cell adhesion molecule (CAM) interaction 153 44 2.428730e-07
    ## hsa04020                Calcium signaling pathway 250 61 5.226155e-07
    ## hsa04950     Maturity onset diabetes of the young  26 12 2.111128e-05
    ## hsa04024                   cAMP signaling pathway 225 48 6.025039e-05
    ## hsa04713                    Circadian entrainment  97 27 4.660464e-04
    ## hsa04970                       Salivary secretion  92 21 5.536101e-04
    ## hsa04517                       IgSF CAM signaling 294 62 5.910268e-04
    ##                   FDR
    ## hsa04080 2.478275e-12
    ## hsa04082 2.634038e-09
    ## hsa04081 1.504227e-07
    ## hsa04514 2.240504e-05
    ## hsa04020 3.856903e-05
    ## hsa04950 1.298344e-03
    ## hsa04024 3.176056e-03
    ## hsa04713 2.149639e-02
    ## hsa04970 2.180889e-02
    ## hsa04517 2.180889e-02

What is interesting is that although very similar pathways are highly ranked compared to the CpG level analysis, gene set testing on the regions is more powerful i.e. the p-values are more significant. In experiments where there are tens of thousands of significant CpGs from a CpG level analysis, we recommend that a good quality region analysis can be a more powerful approach for gene set enrichment analysis.

We can also perform gene set testing on the Hallmark gene sets using `gsaregion`:

    gsa.region <- gsaregion(results.ranges, all.cpg=rownames(M),
                            collection=hallmark)

    ## All input CpGs are used for testing.

    topGSA(gsa.region, n=10)

    ##                                              N DE        P.DE        FDR
    ## HALLMARK_EPITHELIAL_MESENCHYMAL_TRANSITION 199 41 0.001362907 0.06814533
    ## HALLMARK_PANCREAS_BETA_CELLS                40 11 0.002825619 0.07064047
    ## HALLMARK_KRAS_SIGNALING_DN                 200 33 0.005913953 0.09856588
    ## HALLMARK_SPERMATOGENESIS                   135 22 0.012088866 0.15111083
    ## HALLMARK_APICAL_JUNCTION                   199 34 0.043486809 0.43486809
    ## HALLMARK_MYOGENESIS                        200 34 0.067238289 0.55648384
    ## HALLMARK_KRAS_SIGNALING_UP                 198 28 0.077907738 0.55648384
    ## HALLMARK_ANGIOGENESIS                       36  7 0.107806996 0.67379373
    ## HALLMARK_APICAL_SURFACE                     44  7 0.287580480 1.00000000
    ## HALLMARK_INFLAMMATORY_RESPONSE             200 20 0.313507366 1.00000000

Note that the DMR analysis can be further refined by imposing a \(\Delta\beta\) value cut-off and changing various parameters. Please refer to the DMRcate package vignette for more details on how to do this.

# Session information

    sessionInfo()

R version 4.5.2 (2025-10-31) Platform: x86_64-pc-linux-gnu Running under: Ubuntu 24.04.3 LTS

Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0

locale: [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[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

time zone: Etc/UTC tzcode source: system (glibc)

attached base packages: [1] parallel stats4 stats graphics grDevices utils datasets [8] methods base

other attached packages: [1] DMRcate_3.7.0
[2] edgeR_4.9.2
[3] tweeDEseqCountData_1.49.0
[4] minfiData_0.57.0
[5] IlluminaHumanMethylation450kmanifest_0.4.0
[6] limma_3.67.0
[7] missMethyl_1.45.0
[8] IlluminaHumanMethylationEPICv2anno.20a1.hg38_1.0.1 [9] IlluminaHumanMethylationEPICanno.ilm10b4.hg19_0.6.0 [10] IlluminaHumanMethylation450kanno.ilmn12.hg19_0.6.1 [11] minfi_1.57.0
[12] bumphunter_1.53.0
[13] locfit_1.5-9.12
[14] iterators_1.0.14
[15] foreach_1.5.2
[16] Biostrings_2.79.4
[17] XVector_0.51.0
[18] SummarizedExperiment_1.41.1
[19] Biobase_2.71.0
[20] MatrixGenerics_1.23.0
[21] matrixStats_1.5.0
[22] GenomicRanges_1.63.1
[23] Seqinfo_1.1.0
[24] IRanges_2.45.0
[25] S4Vectors_0.49.0
[26] BiocGenerics_0.57.0
[27] generics_0.1.4
[28] BiocStyle_2.39.0

loaded via a namespace (and not attached): [1] ProtGenerics_1.43.0 bitops_1.0-9
[3] httr_1.4.8 RColorBrewer_1.1-3
[5] tools_4.5.2 doRNG_1.8.6.3
[7] backports_1.5.0 R6_2.6.1
[9] HDF5Array_1.39.0 lazyeval_0.2.2
[11] Gviz_1.55.0 rhdf5filters_1.23.3
[13] permute_0.9-10 withr_3.0.2
[15] prettyunits_1.2.0 gridExtra_2.3
[17] base64_2.0.2 preprocessCore_1.73.0
[19] cli_3.6.5 sass_0.4.10
[21] S7_0.2.1 readr_2.2.0
[23] genefilter_1.93.0 askpass_1.2.1
[25] Rsamtools_2.27.0 foreign_0.8-91
[27] siggenes_1.85.0 illuminaio_0.53.0
[29] R.utils_2.13.0 rentrez_1.2.4
[31] dichromat_2.0-0.1 scrime_1.3.7
[33] BSgenome_1.79.1 rstudioapi_0.18.0
[35] RSQLite_2.4.6 BiocIO_1.21.0
[37] gtools_3.9.5 dplyr_1.2.0
[39] GO.db_3.22.0 Matrix_1.7-4
[41] interp_1.1-6 abind_1.4-8
[43] R.methodsS3_1.8.2 lifecycle_1.0.5
[45] yaml_2.3.12 rhdf5_2.55.13
[47] SparseArray_1.11.10 BiocFileCache_3.1.0
[49] grid_4.5.2 blob_1.3.0
[51] ExperimentHub_3.1.0 crayon_1.5.3
[53] lattice_0.22-9 beachmat_2.27.2
[55] GenomicFeatures_1.63.1 cigarillo_1.1.0
[57] annotate_1.89.0 KEGGREST_1.51.1
[59] sys_3.4.3 maketools_1.3.2
[61] pillar_1.11.1 knitr_1.51
[63] beanplot_1.3.1 rjson_0.2.23
[65] codetools_0.2-20 glue_1.8.0
[67] data.table_1.18.2.1 vctrs_0.7.1
[69] png_0.1-8 gtable_0.3.6
[71] cachem_1.1.0 xfun_0.56
[73] S4Arrays_1.11.1 survival_3.8-6
[75] statmod_1.5.1 nlme_3.1-168
[77] bit64_4.6.0-1 bsseq_1.47.1
[79] progress_1.2.3 filelock_1.0.3
[81] GenomeInfoDb_1.47.2 bslib_0.10.0
[83] nor1mix_1.3-3 rpart_4.1.24
[85] colorspace_2.1-2 DBI_1.2.3
[87] Hmisc_5.2-5 nnet_7.3-20
[89] tidyselect_1.2.1 bit_4.6.0
[91] compiler_4.5.2 curl_7.0.0
[93] httr2_1.2.2 htmlTable_2.4.3
[95] h5mread_1.3.1 BiasedUrn_2.0.12
[97] xml2_1.5.2 DelayedArray_0.37.0
[99] rtracklayer_1.71.3 checkmate_2.3.4
[101] scales_1.4.0 quadprog_1.5-8
[103] rappdirs_0.3.4 stringr_1.6.0
[105] digest_0.6.39 rmarkdown_2.30
[107] GEOquery_2.79.0 htmltools_0.5.9
[109] pkgconfig_2.0.3 jpeg_0.1-11
[111] base64enc_0.1-6 sparseMatrixStats_1.23.0 [113] dbplyr_2.5.2 ruv_0.9.7.1
[115] fastmap_1.2.0 ensembldb_2.35.0
[117] rlang_1.1.7 htmlwidgets_1.6.4
[119] UCSC.utils_1.7.1 DelayedMatrixStats_1.33.0 [121] farver_2.1.2 jquerylib_0.1.4
[123] jsonlite_2.0.0 BiocParallel_1.45.0
[125] mclust_6.1.2 R.oo_1.27.1
[127] VariantAnnotation_1.57.1 RCurl_1.98-1.17
[129] magrittr_2.0.4 Formula_1.2-5
[131] Rhdf5lib_1.33.0 Rcpp_1.1.1
[133] stringi_1.8.7 MASS_7.3-65
[135] AnnotationHub_4.1.0 plyr_1.8.9
[137] org.Hs.eg.db_3.22.0 deldir_2.0-4
[139] splines_4.5.2 multtest_2.67.0
[141] hms_1.1.4 rngtools_1.5.2
[143] buildtools_1.0.0 biomaRt_2.67.3
[145] BiocVersion_3.23.1 XML_3.99-0.22
[147] evaluate_1.0.5 latticeExtra_0.6-31
[149] biovizBase_1.59.0 BiocManager_1.30.27
[151] tzdb_0.5.0 tidyr_1.3.2
[153] openssl_2.3.4 purrr_1.2.1
[155] reshape_0.8.10 ggplot2_4.0.2
[157] xtable_1.8-4 restfulr_0.0.16
[159] AnnotationFilter_1.35.0 tibble_3.3.1
[161] memoise_2.0.1 AnnotationDbi_1.73.0
[163] GenomicAlignments_1.47.0 cluster_2.1.8.2

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