1 Quick start

If you use dmrseq in published research, please cite:

Korthauer, K., Chakraborty, S., Benjamini, Y., and Irizarry, R.A. Detection and accurate False Discovery Rate control of differentially methylated regions from Whole Genome Bisulfite Sequencing Biostatistics, 2018 (in press).

This package builds upon the bsseq package (Hansen, Langmead, and Irizarry 2012), which provides efficient storage and manipulation of bisulfite sequencing data and inference for differentially methylated CpGs. The main goal of dmrseq (Korthauer et al. 2018) is to provide inference for differentially methylated regions, or groups of CpGs.

Here we show the most basic steps for a differential methylation analysis. There are a variety of steps upstream of dmrseq that result in the generation of counts of methylated reads and total reads covering each CpG for each sample, including mapping of sequencing reads to a reference genome with and without bisulfite conversion. You can use the software of your preference for this step (one option is Bismark), as long as you are able to obtain counts of methylation and coverage (as opposed to solely methylation proportions, as discussed below).

This package uses a specific data structure to store and manipulate bisulfite sequencing data introduced by the bsseq package. This data structure is a class called BSseq. Objects of the class BSseq contain all pertinent information for a bisulfite sequencing experiment, including the number of reads corresponding to methylation, and the total number of reads at each CpG site, the location of each CpG site, and experimental metadata on the samples. Note that here we focus on CpG methylation, since this is the most common form of methylation in humans and many other organisms; take care when applying this method to other types of methylation and make sure that it will be able to scale to the number of methylation sites, and that similar assumptions can be made regarding spatial correlation. Also note that the default settings for smoothing parameters and spacing/gap parameters are set to values that we found useful, but may need to be altered for datasets for other organisms.

To store your data in a BSseq object, make sure you have the following neccessary components:

  1. genomic positions, including chromosome and location, for methylation loci.

  2. a (matrix) of M (Methylation) values, describing the number of read supporting methylation covering a single loci. Each row in this matrix is a methylation loci and each column is a sample.

  3. a (matrix) of Cov (Coverage) values, describing the total number of reads covering a single loci. Each row in this matrix is a methylation loci and each column is a sample.

The following code chunk asumes that chr and pos are vectors of chromosome names and positions, respectively, for each CpG in the dataset. It also assumes that the matrices of methylation and coverage values (described above) are named M and Cov, respectively.

The sampleNames and trt objects are vectors with sample labels and condition labels for each sample. A condition label could be something like treatment or control, a tissue type, or a continous measurement. This is the covariate for which you wish to test for differences in methylation. Once the BSseq object is constructed and the sample covariate information is added, DMRs are obtained by running the dmrseq function. A continuous covariate is assmued if the data type of the testCovariate is continuous, with the exception of if there are only two unique values (then a two group comparison is carried out).

For more information on constructing and manipulating BSseq objects, see the bsseq vignettes.

  • If you used Bismark to align your bisulfite sequencing data, you can use the read.bismark function to read bismark files into BSseq objects. See below for more details.

2 How to get help for dmrseq

Please post dmrseq questions to the Bioconductor support site, which serves as a searchable knowledge base of questions and answers:

https://support.bioconductor.org

Posting a question and tagging with “dmrseq” will automatically send an alert to the package authors to respond on the support site. See the first question in the list of Frequently Asked Questions (FAQ) for information about how to construct an informative post.

3 Input data

3.1 Why counts instead of methylation proportions?

As input, the dmrseq package expects count data as obtained, e.g., from Bisulfite-sequencing. The value in the i-th row and the j-th column of the M matrix tells how many methylated reads can be assigned to CpG i in sample j. Likewise, the value in the i-th row and the j-th column of the Cov matrix tells how many total reads can be assigned to CpG i in sample j. Although we might be tempted to combine these matrices into one matrix that contains the methylation proportion (M/Cov) at each CpG site, it is critical to notice that this would be throwing away a lot of information. For example, some sites have much higher coverage than others, and naturally, we have more confidence in those with many reads mapping to them. If we only kept the proportions, a CpG with 2 out of 2 reads methylated would be treated the same as a CpG with 30 out of 30 reads methylated.

3.2 How many samples do I need?

To use dmrseq, you need to have at least 2 samples in each condition. Without this replicates, it is impossible to distinguish between biological variability due to condition/covariate of interest, and inter-individual variability within condition.

If your experiment contains additional samples, perhaps from other conditions that are not of interest in the current test, these should be filtered out prior to running dmrseq. Rather than creating a new filtered object, the filtering step can be included in the call to the main function dmrseq. For more details, see the Filtering CpGs and samples Section.

3.3 Bismark input

If you used Bismark for mapping and methylation level extraction, you can use the read.bismark function from the bsseq package to read the data directly into a BSeq object.

The following example is from the help page of the function. After running Bismark’s methylation extractor, you should have output files with names that end in .bismark.cov.gz. You can specify a vector of file names with the file argument, and a corresponding vector of sampleNames. It is recommended that you set rmZeroCov to TRUE in order to remove CpGs with no coverage in any of the samples, and set strandCollapse to TRUE in order to combine CpGs on opposite strands into one observation (since CpG methylation) is symmetric.

## [read.bismark] Reading file 'C:/Users/biocbuild/bbs-3.7-bioc/R/library/bsseq/extdata/test_data.fastq_bismark.bismark.cov.gz' ... done in 1.5 secs
## [read.bismark] Joining samples ... done in 0.2 secs
## An object of type 'BSseq' with
##   2013 methylation loci
##   1 samples
## has not been smoothed
## All assays are in-memory

See the bsseq help pages for more information on using this function.

3.4 Count matrix input

If you haven’t used Bismark but you have count data for number of methylated reads and total coverage for each CpG, along with their corresponding chromosome and position information, you can construct a BSseq object from scratch, like below. Notice that the M and Cov matrices have the same dimension, and chr and pos have the same number of elements as rows in the count matrices (which corresponds to the number of CpGs). Also note that the number of columns in the count matrices matches the number of elements in sampleNames and the condition variable ’celltype`.

## <6 x 4> DelayedMatrix object of type "double":
##      imr90.r1 imr90.r2 h1.r1 h1.r2
## [1,]       18       23    47    63
## [2,]       66       63    91    78
## [3,]       23       27    54    58
## [4,]       12       17    34    46
## [5,]       46       38    46    42
## [6,]        3        3    20    22
## <6 x 4> DelayedMatrix object of type "double":
##      imr90.r1 imr90.r2 h1.r1 h1.r2
## [1,]      115      137    93   112
## [2,]      140      137   108    91
## [3,]      168      175   138   152
## [4,]      153      165   116   108
## [5,]      174      166   136   123
## [6,]       43       42    79    69
## [1] "chr21" "chr21" "chr21" "chr21" "chr21" "chr21"
## [1] 9719962 9720054 9720224 9720323 9720909 9721175
## [1] 300684      4
## [1] 300684      4
## [1] 300684
## [1] 300684
## [1] "imr90.r1" "imr90.r2" "h1.r1"    "h1.r2"
## [1] "imr90" "imr90" "h1"    "h1"
## An object of type 'BSseq' with
##   300684 methylation loci
##   4 samples
## has not been smoothed
## All assays are in-memory

The example data contains CpGs from chromosome 21 for four samples from Lister et al. (2009). To load this data directly (already in the BSseq format), simply type data(BS.chr21). Two of the samples are replicates of the cell type ‘imr90’ and the other two are replicates of the cell type ‘h1’. Now that we have the data loaded into a BSseq object, we can use dmrseq to find regions of the genome where these two cell types have significantly different methylation levels. But first, we need to add the sample metadata that indicates which samples are from which cell type (the celltype varialbe above). This information, which we call ‘metadata’, will be used by the dmrseq function to decide which samples to compare to one another. The next section shows how to add this information to the BSseq object.

3.5 Sample metadata

To add sample metadata, including the covariate of interest, you can add it to the BSseq object by adding columns to the pData slot. You must have at least one column of pData, which contains the covariate of interest. Additional columns are optional.

## DataFrame with 4 rows and 2 columns
##             CellType   Replicate
##          <character> <character>
## imr90.r1       imr90           1
## imr90.r2       imr90           2
## h1.r1             h1           1
## h1.r2             h1           2

We will then tell the dmrseq function which metadata variable to use for testing for methylation differences by setting the testCovariate parameter equal to its column name.

3.6 Smoothing

Note that unlike in bsseq, you do not need to carry out the smoothing step with a separate function. In addition, you should not use bbseq’s bsmooth function to smooth the methylation levels, since dmrseq smooths in a very different way. Briefly, dmrseq smooths methylation differences, so it carries out the smoothing step once. This is automatically done with the main dmrseq function. bsseq on the other hand, smooths each sample independently, so smoothing needs to be carried out once per sample.

3.7 Filtering CpGs and samples

For pairwise comparisons, dmrseq analyzes all CpGs that have at least one read in at least one sample per group. Thus, if your dataset contains CpGs with zero reads in every sample within a group, you should filter them out prior to running dmrseq. Likewise, if your bsseq object contains extraneous samples that are part of the experiment but not the differential methylation testing of interest, these should be filtered out as well.

Filtering bsseq objects is straightforward:

  • Subset rows to filter CpG loci
  • Subset columns to filter samples

If we wish to remove all CpGs that have no coverage in at least one sample and only keep samples with a CellType of “imr90” or “h1”, we would do so with:

Note that this is a trivial example, since our toy example object BS.chr21 already contains only loci with coverage at least one in all samples as well as only samples from the “imr90” and “h1” conditions.

Also note that instead of creating a separate object, the filtering step can be combined with the call to dmrseq by replacing the bs input with a filtered version bs[loci.idx, sample.idx].

3.8 Adjusting for covariates

There are two ways to adjust for covariates in the dmrseq model. The first way is to specify the adjustCovariate parameter of the dmrseq function as a column of the pData() slot that contains the covariate you would like to adjust for. This will include that covariate directly in the model. This is ideal if the adjustment covariate is continuous or has more than two groups.

The second way is to specify the matchCovariate parameter of the dmrseq function as a column of the pData() slot that contains the covariate you would like to match on. This will restrict the permutations considered to only those where the matchCovariate is balanced. For example, the matchCovariate could represent the sex of each sample. In that case, a permutation that includes all males in one group and all females in another would not be considered (since there is a plausible biological difference that may induce the null distribution to resemble non-null). This matching adjustment is ideal for two-group comparisons.

4 Differentially Methylated Regions

The standard differential expression analysis steps are wrapped into a single function, dmrseq. The estimation steps performed by this function are described briefly below, as well as in more detail in the dmrseq paper. Here we run the results for a subset of 20,000 CpGs in the interest of computation time.

## Assuming the test covariate CellType is a factor.
## Condition: imr90 vs h1
## Using a single core (backend: BiocParallel:SerialParam).
## Computing on 1 chromosome(s) at a time.
## Detecting candidate regions with coefficient larger than 0.05 in magnitude.
## ...Chromosome chr21: Smoothed (0.02 min). 380 regions scored (0.46 min). 
## * 380 candidates detected
## Performing balanced permutations of condition across samples to generate a null distribution of region test statistics
## 
## Beginning permutation 1
## ...Chromosome chr21: Smoothed (0.01 min). 173 regions scored (0.17 min). 
## * 1 out of 2 permutations completed (173 null candidates)
## 
## Beginning permutation 2
## ...Chromosome chr21: Smoothed (0.01 min). 151 regions scored (0.16 min). 
## * 2 out of 2 permutations completed (151 null candidates)

Progress messages are printed to the console if verbose is TRUE. The text, condition h1 vs imr90, tells you that positive methylation differences mean h1 has higher methylation than imr90 (see below for more details).

4.1 Output of dmrseq

The results object is a GRanges object with the coordiates of each candidate region, and contains the following metadata columns (which can be extracted with the $ operator:

  1. L = the number of CpGs contained in the region,
  2. area = the sum of the smoothed beta values
  3. beta = the coefficient value for the condition difference (Note: if the test covariate is categorical with more than 2 groups, there will be more than one beta column),
  4. stat = the test statistic for the condition difference,
  5. pval = the permutation p-value for the significance of the test statistic, and
  6. qval = the q-value for the test statistic (adjustment for multiple comparisons to control false discovery rate).
  7. index = an IRanges containing the indices of the region’s first CpG to last CpG.
## GRanges object with 380 ranges and 7 metadata columns:
##         seqnames            ranges strand |         L              area
##            <Rle>         <IRanges>  <Rle> | <integer>         <numeric>
##     [1]    chr21 43605625-43606688      * |        24  12.7309412794983
##     [2]    chr21 44356429-44357250      * |        18  9.17973010000344
##     [3]    chr21 44516290-44525100      * |       154  26.0348467667111
##     [4]    chr21 44079752-44084490      * |        89  14.3214853879369
##     [5]    chr21 44477228-44484542      * |       183  22.9615117232455
##     ...      ...               ...    ... .       ...               ...
##   [376]    chr21 43951797-43952020      * |         5 0.277525955962473
##   [377]    chr21 43769879-43770694      * |         9 0.905185100223535
##   [378]    chr21 44403584-44403679      * |         6 0.340732839276484
##   [379]    chr21 43584709-43584897      * |         5 0.302315253072789
##   [380]    chr21 43933908-43934260      * |         7 0.384882621571304
##                         beta                stat                pval
##                    <numeric>           <numeric>           <numeric>
##     [1]    -1.24345510581592   -18.5650464917612 0.00307692307692308
##     [2]    -1.20134648929696   -12.5612558776382 0.00307692307692308
##     [3]   -0.438070065590934   -12.2668229354068 0.00307692307692308
##     [4]   -0.451036873372075   -11.7190967955778 0.00307692307692308
##     [5]   -0.354230719390397   -11.0595884552727 0.00307692307692308
##     ...                  ...                 ...                 ...
##   [376]   0.0713784829885713   0.348836668697137   0.923076923076923
##   [377]   0.0447749936639214    0.28773628161221   0.938461538461538
##   [378]  -0.0329621092134167  -0.234484220982969   0.944615384615385
##   [379]   0.0292136453054982    0.13227668809123   0.972307692307692
##   [380] -0.00855756994574848 -0.0662411190476108   0.978461538461538
##                      qval       index
##                 <numeric>   <IRanges>
##     [1] 0.025982905982906     845-868
##     [2] 0.025982905982906 15147-15164
##     [3] 0.025982905982906 18812-18965
##     [4] 0.025982905982906   9742-9830
##     [5] 0.025982905982906 17954-18136
##     ...               ...         ...
##   [376] 0.932896890343699   6801-6805
##   [377] 0.945929402162824   4490-4498
##   [378]  0.94961334961335 16341-16346
##   [379] 0.974873147960219     351-355
##   [380] 0.978461538461538   6360-6366
##   -------
##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

The above steps are carried out on a very small subset of data (20,000 CpGs). This package loads data into memory one chromosome at a time. For on human data, this means objects with a few million entries per sample (since there are roughly 28.2 million total CpGs in the human genome, and the largest chromosomes will have more than 2 million CpGs). This means that whole-genome BSseq objects for several samples can use up several GB of RAM. In order to improve speed, the package allows for easy parallel processing of chromosomes, but be aware that using more cores will also require the use of more RAM.

To use more cores, use the register function of BiocParallel. For example, the following chunk (not evaluated here), would register 4 cores, and then the functions above would split computation over these cores.

4.2 Steps of the dmrseq method

dmrseq is a two-stage approach that first detects candidate regions and then explicitly evaluates statistical significance at the region level while accounting for known sources of variability. Candidate DMRs are defined by segmenting the genome into groups of CpGs that show consistent evidence of differential methylation. Because the methylation levels of neighboring CpGs are highly correlated, we first smooth the signal to combat loss of power due to low coverage as done in bsseq.

In the second stage, we compute a statistic for each candidate DMR that takes into account variability between biological replicates and spatial correlation among neighboring loci. Significance of each region is assessed via a permutation procedure which uses a pooled null distribution that can be generated from as few as two biological replicates, and false discovery rate is controlled using the Benjamini-Hochberg procedure.

For more details, refer to the dmrseq paper (Korthauer et al. 2018).

4.3 Detecting large-scale methylation blocks

The default smoothing parameters (bpSpan, minInSpan, and maxGapSmooth) are designed to focus on local DMRs, generally in the range of hundreds to thousands of bases. In some applications, such as cancer, it is of interest to effectively ‘zoom out’ in order to detect larger (lower-resolution) methylation blocks on the order of hundreds of thousands to millions of bases. To do so, you can set the block argument to true, which will only include candidate regions with at least blockSize basepairs (default = 5000). This setting will also merge candidate regions that (1) are in the same direction and (2) are less than 1kb apart with no covered CpGs separating them. The region-level model used is also slightly modified - instead of a loci-specific intercept for each CpG in the region, the intercept term is modeled as a natural spline with one interior knot per each 10kb of length (up to 10 interior knots).

In addition, detecting large-scale blocks requires that the smoothing window be increased to minimize the impact of noisy local methylation measurements. To do so, increase the values of the smoothing parameters should be increased. For example, to use a smoothing window that captures at least 500 CpGs or 50,000 basepairs that are spaced apart by no more than 1e6 bases, use minInSpan=500, bpSpan=5e4, and maxGapSmooth=1e6. In addition, to avoid a block being broken up simply due to a gap with no covered CpGs, you can increase the maxGap parameter.

## Searching for large scale blocks with at least 5000 basepairs.
## Assuming the test covariate CellType is a factor.
## Condition: imr90 vs h1
## Using a single core (backend: BiocParallel:SerialParam).
## Computing on 1 chromosome(s) at a time.
## Detecting candidate regions with coefficient larger than 0.05 in magnitude.
## ...Chromosome chr21: Smoothed (0 min). 3 regions scored (0.18 min). 
## * 3 candidates detected
## Performing balanced permutations of condition across samples to generate a null distribution of region test statistics
## 
## Beginning permutation 1
## ...Chromosome chr21: Smoothed (0 min). No candidates found. 
## No regions found.
## * 1 out of 2 permutations completed ( null candidates)
## 
## Beginning permutation 2
## ...Chromosome chr21: Smoothed (0 min). No candidates found. 
## No regions found.
## * 2 out of 2 permutations completed ( null candidates)
## Warning in dmrseq(bs = bs[120001:125000, ], cutoff = 0.05, testCovariate
## = testCovariate, : No candidate regions found in permutation, so inference
## can't be carried out. Try decreasing the cutoff, or running on a larger
## dataset if you are currently using a subset.
## GRanges object with 3 ranges and 7 metadata columns:
##       seqnames            ranges strand |         L             area
##          <Rle>         <IRanges>  <Rle> | <integer>        <numeric>
##   [1]    chr21 32345307-32520539      * |      1458 345.964656698764
##   [2]    chr21 32700803-32766102      * |       775 54.9952836810173
##   [3]    chr21 32789489-32811767      * |       260 18.6190445528072
##                     beta              stat      pval      qval     index
##                <numeric>         <numeric> <logical> <logical> <IRanges>
##   [1] -0.582317249209734 -38.3717791961354      <NA>      <NA>    1-1458
##   [2]  -0.18758932110931 -8.55933928848769      <NA>      <NA> 3670-4444
##   [3] -0.272891864081724 -7.08400235242536      <NA>      <NA> 4736-4995
##   -------
##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

The top hit is 175 thousand basepairs wide. In general, it also might be advised to decrease the cutoff when detecting blocks, since a smaller methylation difference might be biologically significant if it is maintained over a large genomic region. Note that block-finding can be more computationally intensive since we are fitting region-level models to large numbers of CpGs at a time. In the toy example above we are only searching over 5,000 CpGs (which span 467 thousand basepairs), so we do not find enough null candidate regions to carry out inference and obtain significance levels.

5 Exploring and exporting results

5.1 Explore how many regions were significant

How many regions were significant at the FDR (q-value) cutoff of 0.05? We can find this by counting how many values in the qval column of the results data.frame were less than 0.05. You can also subset the regions by an FDR cutoff.

## [1] 144

5.2 Hypo- or Hyper- methylation?

You can determine the proportion of regions with hyper-methylation by counting how many had a positive direction of effect (positive statistic).

## [1] 0.25

To interpret the direction of effect, note that for a two-group comparison dmrseq uses alphabetical order of the covariate of interest. The condition with a higher alphabetical rank will become the reference category. For example, if the two conditions are “A” and “B”, the “A” group will be the reference category, so a positive direction of effect means that “B” is hyper-methylated relative to “A”. Conversely, a negative direction of effect means that “B” is hypo-methylated relative to “A”.

5.3 Plot DMRs

It can be useful to visualize individual DMRs, so we provide a plotting function that is based off of bsseq’s plotting functions. There is also functionality to add annotations using the annotatr package to see the nearby CpG categories (island, shore, shelf, open sea) and nearby coding sequences.

To retrieve annotations for genomes supported by annotatr, use the helper function getAnnot, and pass this annotation object to the plotDMRs function as the annoTrack parameter.

Here we also plot the top methylation block from the block analysis:

5.4 Plot distribution of methylation values and coverage

It can also be helpful to visualize overall distributions of methylation values and / or coverage. The function plotEmpiricalDistribution will plot the methylation values of the covariate of interest (specified with testCovariate).

By changing the type argument to Cov, it will also plot the distribution of coverage values. In addition, samples can be plotted separately by setting bySample to true.

5.5 Exporting results to CSV files

A plain-text file of the results can be exported using the base R functions write.csv or write.delim. We suggest using a descriptive file name indicating the variable and levels which were tested.

5.6 Extract raw mean methylation differences

For a two-group comparison, it might be of interest to extract the raw mean methylation differences over the DMRs. This can be done with the helper function meanDiff. For example, we can extract the raw mean difference values for the regions at FDR level 0.05 (using the sigRegions object created in the section Explore how many regions were significant).

##  num [1:144] -0.4778 0.0175 -0.0067 -0.0179 -0.3864 ...

6 Simulating DMRs

If you have multiple samples from the same condition (e.g. control samples), the function simDMRS will split these into two artificial sample groups and then add in silico DMRs. This can then be used to assess sensitivity and specificity of DMR approaches, since we hope to be able to recover the DMRs that were spiked in, but not identify too many other differences (since we don’t expect any biological difference between the two artificial sample groups).

The use of this function is demonstrated below, although note that in this toy example, we do not have enough samples from the same biological condition to split into two groups, so instead we shuffle the cell types to create a null sample comparison.

## An object of type 'BSseq' with
##   20000 methylation loci
##   4 samples
## has not been smoothed
## All assays are in-memory
## GRanges object with 100 ranges and 0 metadata columns:
##         seqnames            ranges strand
##            <Rle>         <IRanges>  <Rle>
##     [1]    chr21 10117483-10122836      *
##     [2]    chr21 15129488-15132319      *
##     [3]    chr21 15842506-15844859      *
##     [4]    chr21 10144088-10149529      *
##     [5]    chr21 14494817-14495766      *
##     ...      ...               ...    ...
##    [96]    chr21 13519836-13520592      *
##    [97]    chr21 15796842-15802274      *
##    [98]    chr21 15285161-15285501      *
##    [99]    chr21 13657704-13658715      *
##   [100]    chr21 15850611-15853036      *
##   -------
##   seqinfo: 1 sequence from an unspecified genome; no seqlengths
## [1] 0.3469045 0.2517997 0.3572765 0.3641407 0.4242691 0.1653737

The resulting object is a list with the following elements:

  • gr.dmrs: a GRanges object containing the coordinates of the true spiked in DMRs
  • dmr.mncov: a numeric vector containing the mean coverage of the simulated DMRs
  • dmr.L: a numeric vector containing the sizes (number of CpG loci) of the simulated DMRs
  • bs: the BSSeq object containing the original null data + simulated DMRs
  • delta: a numeric vector of effect sizes (proportion differences) of the simulated DMRs.

7 Session info

## R version 3.5.1 Patched (2018-07-24 r75005)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 2012 R2 x64 (build 9600)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=C                          
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats4    parallel  stats     graphics  grDevices utils     datasets 
## [8] methods   base     
## 
## other attached packages:
##  [1] rtracklayer_1.40.3                     
##  [2] org.Hs.eg.db_3.6.0                     
##  [3] TxDb.Hsapiens.UCSC.hg19.knownGene_3.2.2
##  [4] GenomicFeatures_1.32.0                 
##  [5] AnnotationDbi_1.42.1                   
##  [6] dmrseq_1.0.14                          
##  [7] bsseq_1.16.1                           
##  [8] SummarizedExperiment_1.10.1            
##  [9] DelayedArray_0.6.4                     
## [10] BiocParallel_1.14.2                    
## [11] matrixStats_0.54.0                     
## [12] Biobase_2.40.0                         
## [13] GenomicRanges_1.32.6                   
## [14] GenomeInfoDb_1.16.0                    
## [15] IRanges_2.14.10                        
## [16] S4Vectors_0.18.3                       
## [17] BiocGenerics_0.26.0                    
## [18] BiocStyle_2.8.2                        
## 
## loaded via a namespace (and not attached):
##   [1] colorspace_1.3-2              rprojroot_1.3-2              
##   [3] XVector_0.20.0                bit64_0.9-7                  
##   [5] interactiveDisplayBase_1.18.0 splines_3.5.1                
##   [7] codetools_0.2-15              R.methodsS3_1.7.1            
##   [9] knitr_1.20                    Rsamtools_1.32.2             
##  [11] R.oo_1.22.0                   shiny_1.1.0                  
##  [13] HDF5Array_1.8.1               readr_1.1.1                  
##  [15] compiler_3.5.1                httr_1.3.1                   
##  [17] backports_1.1.2               assertthat_0.2.0             
##  [19] Matrix_1.2-14                 lazyeval_0.2.1               
##  [21] limma_3.36.2                  later_0.7.3                  
##  [23] htmltools_0.3.6               prettyunits_1.0.2            
##  [25] tools_3.5.1                   bindrcpp_0.2.2               
##  [27] gtable_0.2.0                  glue_1.3.0                   
##  [29] GenomeInfoDbData_1.1.0        annotatr_1.6.0               
##  [31] reshape2_1.4.3                dplyr_0.7.6                  
##  [33] doRNG_1.7.1                   Rcpp_0.12.18                 
##  [35] bumphunter_1.22.0             Biostrings_2.48.0            
##  [37] nlme_3.1-137                  iterators_1.0.10             
##  [39] DelayedMatrixStats_1.2.0      xfun_0.3                     
##  [41] stringr_1.3.1                 mime_0.5                     
##  [43] rngtools_1.3.1                gtools_3.8.1                 
##  [45] XML_3.98-1.13                 AnnotationHub_2.12.0         
##  [47] zlibbioc_1.26.0               scales_0.5.0                 
##  [49] BSgenome_1.48.0               BiocInstaller_1.30.0         
##  [51] hms_0.4.2                     promises_1.0.1               
##  [53] rhdf5_2.24.0                  RColorBrewer_1.1-2           
##  [55] curl_3.2                      yaml_2.2.0                   
##  [57] memoise_1.1.0                 ggplot2_3.0.0                
##  [59] pkgmaker_0.27                 biomaRt_2.36.1               
##  [61] stringi_1.2.4                 RSQLite_2.1.1                
##  [63] foreach_1.4.4                 permute_0.9-4                
##  [65] bibtex_0.4.2                  rlang_0.2.1                  
##  [67] pkgconfig_2.0.1               bitops_1.0-6                 
##  [69] evaluate_0.11                 lattice_0.20-35              
##  [71] purrr_0.2.5                   Rhdf5lib_1.2.1               
##  [73] bindr_0.1.1                   labeling_0.3                 
##  [75] GenomicAlignments_1.16.0      bit_1.1-14                   
##  [77] tidyselect_0.2.4              plyr_1.8.4                   
##  [79] magrittr_1.5                  bookdown_0.7                 
##  [81] R6_2.2.2                      DBI_1.0.0                    
##  [83] withr_2.1.2                   pillar_1.3.0                 
##  [85] RCurl_1.95-4.11               tibble_1.4.2                 
##  [87] crayon_1.3.4                  rmarkdown_1.10               
##  [89] progress_1.2.0                locfit_1.5-9.1               
##  [91] grid_3.5.1                    data.table_1.11.4            
##  [93] blob_1.1.1                    digest_0.6.15                
##  [95] xtable_1.8-2                  httpuv_1.4.5                 
##  [97] regioneR_1.12.0               outliers_0.14                
##  [99] R.utils_2.6.0                 munsell_0.5.0                
## [101] registry_0.5

References

Hansen, Kasper D, Benjamin Langmead, and Rafael A Irizarry. 2012. “BSmooth: from whole genome bisulfite sequencing reads to differentially methylated regions.” Genome Biology 13 (10):R83. https://doi.org/10.1186/gb-2012-13-10-r83.

Korthauer, Keegan, Sutirtha Chakraborty, Yuval Benjamini, and Rafael A. Irizarry. 2018. “Detection and Accurate False Discovery Rate Control of Differentially Methylated Regions from Whole Genome Bisulfite Sequencing.” Biostatistics. https://doi.org/10.1101/183210.

Lister, Ryan, Mattia Pelizzola, Robert H Dowen, R David Hawkins, Gary C Hon, Julian Tonti-Filippini, Joseph R Nery, et al. 2009. “Human DNA methylomes at base resolution show widespread epigenomic differences.” Nature 462 (7271):315–22. https://doi.org/10.1038/nature08514.