MultiAssayExperiment: The Integrative Bioconductor Container

MultiAssay Special Interest Group

Contents

1 Installation

if (!require("BiocManager"))
    install.packages("BiocManager")
BiocManager::install("MultiAssayExperiment")

Loading the packages:

library(MultiAssayExperiment)
library(GenomicRanges)
library(SummarizedExperiment)
library(RaggedExperiment)

2 A Brief Description

MultiAssayExperiment offers a data structure for representing and analyzing multi-omics experiments: a biological analysis approach utilizing multiple types of observations, such as DNA mutations and abundance of RNA and proteins, in the same biological specimens.

2.1 Choosing the appropriate data structure

For assays with different numbers of rows and even columns, MultiAssayExperiment is recommended. For sets of assays with the same information across all rows (e.g., genes or genomic ranges), SummarizedExperiment is the recommended data structure.

3 Overview of the MultiAssayExperiment class

Here is an overview of the class and its constructors and extractors:

empty <- MultiAssayExperiment()
empty

## A MultiAssayExperiment object of 0 listed
##  experiments with no user-defined names and respective classes.
##  Containing an ExperimentList class object of length 0:
##  Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

slotNames(empty)

## [1] "ExperimentList" "colData"        "sampleMap"      "drops"         
## [5] "metadata"

A visual representation of the MultiAssayExperiment class and its accessor functions can be seen below. There are three main components:

1. ExperimentList
2. colData
3. sampleMap

Figure 1: MultiAssayExperiment object schematic shows the design of the infrastructure class
The colData provides data about the patients, cell lines, or other biological units, with one row per unit and one column per variable. The experiments are a list of assay datasets of arbitrary class, with one column per observation. The sampleMap links a single table of patient data (colData) to a list of experiments via a simple but powerful table of experiment:patient edges (relationships), that can be created automatically in simple cases or in a spreadsheet if assay-specific sample identifiers are used. sampleMap relates each column (observation) in the assays (experiments) to exactly one row (biological unit) in colData; however, one row of colData may map to zero, one, or more columns per assay, allowing for missing and replicate assays. Green stripes indicate a mapping of one subject to multiple observations across experiments.

3.1 Components of the MultiAssayExperiment

3.1.1 ExperimentList: experimental data

The ExperimentList slot and class is the container workhorse for the MultiAssayExperiment class. It contains all the experimental data. It inherits from class S4Vectors::SimpleList with one element/component per data type.

class(experiments(empty)) # ExperimentList

## [1] "ExperimentList"
## attr(,"package")
## [1] "MultiAssayExperiment"

The elements of the ExperimentList can contain ID-based and range-based data. Requirements for all classes in the ExperimentList are listed in the API.

The following base and Bioconductor classes are known to work as elements of the ExperimentList:

• base::matrix: the base class, can be used for ID-based datasets such as gene expression summarized per-gene, microRNA, metabolomics, or microbiome data.

• SummarizedExperiment::SummarizedExperiment: A richer representation compared to a ordinary matrix of ID-based datasets capable of storing additional assay- level metadata.

• Biobase::ExpressionSet: A legacy representation of ID-based datasets, supported for convenience and supplanted by SummarizedExperiment.

• SummarizedExperiment::RangedSummarizedExperiment: For rectangular range-based datasets, one set of genomic ranges are assayed for multiple samples. It can be used for gene expression, methylation, or other data types that refer to genomic positions.

• RaggedExperiment::RaggedExperiment: For range-based datasets, such as copy number and mutation data, the RaggedExperiment class can be used to represent measurements by genomic positions.

3.1.1.1 Class requirements within ExperimentList container

See the API section for details on requirements for using other data classes. In general, data classes meeting minimum requirements, including support for square bracket [ subsetting and dimnames() will work by default.

The datasets contained in elements of the ExperimentList can have:

• column names (required)
• row names (optional)

The column names correspond to samples, and are used to match assay data to specimen metadata stored in colData.

The row names can correspond to a variety of features in the data including but not limited to gene names, probe IDs, proteins, and named ranges. Note that the existence of “row” names does not mean the data must be rectangular or matrix-like.

Classes contained in the ExperimentList must support the following list of methods:

• [: single square bracket subsetting, with a single comma. It is assumed that values before the comma subset rows, and values after the comma subset columns.
• dimnames() : corresponding to features (such as genes, proteins, etc.) and experimental samples
• dim(): returns a vector of the number of rows and number of columns

3.1.2 colData: primary data

The MultiAssayExperiment keeps one set of “primary” metadata that describes the ‘biological unit’ which can refer to specimens, experimental subjects, patients, etc. In this vignette, we will refer to each experimental subject as a patient.

3.1.2.1 colData slot requirements

The colData dataset should be of class DataFrame but can accept a data.frame class object that will be coerced.

In order to relate metadata of the biological unit, the row names of the colData dataset must contain patient identifiers.

patient.data <- data.frame(sex=c("M", "F", "M", "F"),
    age=38:41,
    row.names=c("Jack", "Jill", "Bob", "Barbara"))
patient.data

##         sex age
## Jack      M  38
## Jill      F  39
## Bob       M  40
## Barbara   F  41

Key points:

• one row of colData can map to zero, one, or more columns in any ExperimentList element
• each row of colData must map to at least one column in at least one ExperimentList element.
• each column of each ExperimentList element must map to exactly one row of colData.

These relationships are defined by the sampleMap.

3.1.2.2 Note on the flexibility of the DataFrame

For many typical purposes the DataFrame and data.frame behave equivalently; but the Dataframe is more flexible as it allows any vector-like data type to be stored in its columns. The flexibility of the DataFrame permits, for example, storing multiple dose-response values for a single cell line, even if the number of doses and responses is not consistent across all cell lines. Doses could be stored in one column of colData as a SimpleList, and responses in another column, also as a SimpleList. Or, dose-response values could be stored in a single column of colData as a two-column matrix for each cell line.

3.1.3 sampleMap: relating colData to multiple assays

The sampleMap is a DataFrame that relates the “primary” data (colData) to the experimental assays:

is(sampleMap(empty), "DataFrame") # TRUE

## [1] TRUE

The sampleMap provides an unambiguous map from every experimental observation to one and only one row in colData. It is, however, permissible for a row of colData to be associated with multiple experimental observations or no observations at all. In other words, there is a “many-to-one” mapping from experimental observations to rows of colData, and a “one-to-any-number” mapping from rows of colData to experimental observations.

3.1.3.1 sampleMap structure

The sampleMap has three columns, with the following column names:

1. assay provides the names of the different experiments / assays performed. These are user-defined, with the only requirement that the names of the ExperimentList, where the experimental assays are stored, must be contained in this column.

2. primary provides the “primary” sample names. All values in this column must also be present in the rownames of colData(MultiAssayExperiment). In this example, allowable values in this column are “Jack”, “Jill”, “Barbara”, and “Bob”.

3. colname provides the sample names used by experimental datasets, which in practice are often different than the primary sample names. For each assay, all column names must be found in this column. Otherwise, those assays would be orphaned: it would be impossible to match them up to samples in the overall experiment. As mentioned above, duplicate values are allowed, to represent replicates with the same overall experiment-level annotation.

This design is motivated by the following situations:

1. It allows flexibility for any amount of technical replication and biological replication (such as tumor and matched normal for a single patient) of individual assays.
2. It allows missing observations (such as RNA-seq performed only for some of the patients).
3. It allows the use of different identifiers to be used for patients / specimens and for each assay. These different identifiers are matched unambiguously, and consistency between them is maintained during subsetting and re-ordering.

3.1.3.1.1 Instances where sampleMap isn’t provided

If each assay uses the same colnames (i.e., if the same sample identifiers are used for each experiment), a simple list of these datasets is sufficient for the MultiAssayExperiment constructor function. It is not necessary for them to have the same rownames or colnames:

exprss1 <- matrix(rnorm(16), ncol = 4,
        dimnames = list(sprintf("ENST00000%i", sample(288754:290000, 4)),
                c("Jack", "Jill", "Bob", "Bobby")))
exprss2 <- matrix(rnorm(12), ncol = 3,
        dimnames = list(sprintf("ENST00000%i", sample(288754:290000, 4)),
                c("Jack", "Jane", "Bob")))
doubleExp <- list("methyl 2k"  = exprss1, "methyl 3k" = exprss2)
simpleMultiAssay <- MultiAssayExperiment(experiments=doubleExp)
simpleMultiAssay

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] methyl 2k: matrix with 4 rows and 4 columns
##  [2] methyl 3k: matrix with 4 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

In the above example, the user did not provide the colData argument so the constructor function filled it with an empty DataFrame:

colData(simpleMultiAssay)

## DataFrame with 5 rows and 0 columns

But the colData can be provided. Here, note that any assay sample (column) that cannot be mapped to a corresponding row in the provided colData gets dropped. This is part of ensuring internal validity of the MultiAssayExperiment.

simpleMultiAssay2 <- MultiAssayExperiment(experiments=doubleExp,
                                          colData=patient.data)

## Warning: Data dropped from ExperimentList (element - column):
##  methyl 2k - Bobby
##  methyl 3k - Jane
## Unable to map to rows of colData

## harmonizing input:
##   removing 1 colData rownames not in sampleMap 'primary'

simpleMultiAssay2

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] methyl 2k: matrix with 4 rows and 3 columns
##  [2] methyl 3k: matrix with 4 rows and 2 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

colData(simpleMultiAssay2)

## DataFrame with 3 rows and 2 columns
##              sex       age
##      <character> <integer>
## Jack           M        38
## Jill           F        39
## Bob            M        40

3.1.4 metadata

Metadata can be added at different levels of the MultiAssayExperiment.

Can be of ANY class, for storing study-wide metadata, such as citation information. For an empty MultiAssayExperiment object, it is NULL.

class(metadata(empty)) # NULL (class "ANY")

## [1] "list"

At the ExperimentList level, the metadata function would allow the user to enter metadata as a list.

metadata(experiments(empty))

## list()

At the individual assay level, certain classes may support metadata, for example, metadata and mcols for a SummarizedExperiment. It is recommended to use metadata at the ExperimentList level.

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4 Creating a MultiAssayExperiment object: a rich example

In this section we demonstrate all core supported data classes, using different sample ID conventions for each assay, with primary colData. The some supported classes such as, matrix, SummarizedExperiment, and RangedSummarizedExperiment.

4.1 Create toy datasets demonstrating all supported data types

We have three matrix-like datasets. First, let’s represent expression data as a SummarizedExperiment:

(arraydat <- matrix(seq(101, 108), ncol=4,
    dimnames=list(c("ENST00000294241", "ENST00000355076"),
    c("array1", "array2", "array3", "array4"))))

##                 array1 array2 array3 array4
## ENST00000294241    101    103    105    107
## ENST00000355076    102    104    106    108

coldat <- data.frame(slope53=rnorm(4),
    row.names=c("array1", "array2", "array3", "array4"))

exprdat <- SummarizedExperiment(arraydat, colData=coldat)
exprdat

## class: SummarizedExperiment 
## dim: 2 4 
## metadata(0):
## assays(1): ''
## rownames(2): ENST00000294241 ENST00000355076
## rowData names(0):
## colnames(4): array1 array2 array3 array4
## colData names(1): slope53

The following map matches colData sample names to exprdata sample names. Note that row orders aren’t initially matched up, and this is OK.

(exprmap <- data.frame(primary=rownames(patient.data)[c(1, 2, 4, 3)],
                       colname=c("array1", "array2", "array3", "array4"),
                       stringsAsFactors = FALSE))

##   primary colname
## 1    Jack  array1
## 2    Jill  array2
## 3 Barbara  array3
## 4     Bob  array4

Now methylation data, which we will represent as a matrix. It uses gene identifiers also, but measures a partially overlapping set of genes. Now, let’s store this as a simple matrix which can contains a replicate for one of the patients.

(methyldat <-
   matrix(1:10, ncol=5,
          dimnames=list(c("ENST00000355076", "ENST00000383706"),
                        c("methyl1", "methyl2", "methyl3",
                          "methyl4", "methyl5"))))

##                 methyl1 methyl2 methyl3 methyl4 methyl5
## ENST00000355076       1       3       5       7       9
## ENST00000383706       2       4       6       8      10

The following map matches colData sample names to methyldat sample names.

(methylmap <- data.frame(primary = c("Jack", "Jack", "Jill", "Barbara", "Bob"),
    colname = c("methyl1", "methyl2", "methyl3", "methyl4", "methyl5"),
    stringsAsFactors = FALSE))

##   primary colname
## 1    Jack methyl1
## 2    Jack methyl2
## 3    Jill methyl3
## 4 Barbara methyl4
## 5     Bob methyl5

Now we have a microRNA platform, which has no common identifiers with the other datasets, and which we also represent as a matrix. It is also missing data for “Jill”. We will use the same sample naming convention as we did for arrays.

(microdat <- matrix(201:212, ncol=3,
                    dimnames=list(c("hsa-miR-21", "hsa-miR-191",
                                    "hsa-miR-148a", "hsa-miR148b"),
                                  c("micro1", "micro2", "micro3"))))

##              micro1 micro2 micro3
## hsa-miR-21      201    205    209
## hsa-miR-191     202    206    210
## hsa-miR-148a    203    207    211
## hsa-miR148b     204    208    212

And the following map matches colData sample names to microdat sample names.

(micromap <- data.frame(primary = c("Jack", "Barbara", "Bob"),
    colname = c("micro1", "micro2", "micro3"), stringsAsFactors = FALSE))

##   primary colname
## 1    Jack  micro1
## 2 Barbara  micro2
## 3     Bob  micro3

Finally, we create a dataset of class RangedSummarizedExperiment:

nrows <- 5; ncols <- 4
counts <- matrix(runif(nrows * ncols, 1, 1e4), nrows)
rowRanges <- GRanges(rep(c("chr1", "chr2"), c(2, nrows - 2)),
    IRanges(floor(runif(nrows, 1e5, 1e6)), width=100),
    strand=sample(c("+", "-"), nrows, TRUE),
    feature_id=sprintf("ID\\%03d", 1:nrows))
names(rowRanges) <- letters[1:5]
colData <- DataFrame(Treatment=rep(c("ChIP", "Input"), 2),
    row.names= c("mysnparray1", "mysnparray2", "mysnparray3", "mysnparray4"))
rse <- SummarizedExperiment(assays=SimpleList(counts=counts),
    rowRanges=rowRanges, colData=colData)

And we map the colData samples to the RangedSummarizedExperiment:

(rangemap <-
    data.frame(primary = c("Jack", "Jill", "Bob", "Barbara"),
    colname = c("mysnparray1", "mysnparray2", "mysnparray3", "mysnparray4"),
        stringsAsFactors = FALSE))

##   primary     colname
## 1    Jack mysnparray1
## 2    Jill mysnparray2
## 3     Bob mysnparray3
## 4 Barbara mysnparray4

4.2 sampleMap creation

The MultiAssayExperiment constructor function can create the sampleMap automatically if a single naming convention is used, but in this example it cannot because we used platform-specific sample identifiers (e.g. mysnparray1, etc). So we must provide an ID map that matches the samples of each experiment back to the colData, as a three-column data.frame or DataFrame with three columns named “assay”, primary“, and”colname". Here we start with a list:

listmap <- list(exprmap, methylmap, micromap, rangemap)
names(listmap) <- c("Affy", "Methyl 450k", "Mirna", "CNV gistic")
listmap

## $Affy
##   primary colname
## 1    Jack  array1
## 2    Jill  array2
## 3 Barbara  array3
## 4     Bob  array4
## 
## $`Methyl 450k`
##   primary colname
## 1    Jack methyl1
## 2    Jack methyl2
## 3    Jill methyl3
## 4 Barbara methyl4
## 5     Bob methyl5
## 
## $Mirna
##   primary colname
## 1    Jack  micro1
## 2 Barbara  micro2
## 3     Bob  micro3
## 
## $`CNV gistic`
##   primary     colname
## 1    Jack mysnparray1
## 2    Jill mysnparray2
## 3     Bob mysnparray3
## 4 Barbara mysnparray4

and use the convenience function listToMap to convert the list of data.frame objects to a valid object for the sampleMap:

dfmap <- listToMap(listmap)
dfmap

## DataFrame with 16 rows and 3 columns
##           assay     primary     colname
##        <factor> <character> <character>
## 1   Affy               Jack      array1
## 2   Affy               Jill      array2
## 3   Affy            Barbara      array3
## 4   Affy                Bob      array4
## 5   Methyl 450k        Jack     methyl1
## ...         ...         ...         ...
## 12   Mirna              Bob      micro3
## 13   CNV gistic        Jack mysnparray1
## 14   CNV gistic        Jill mysnparray2
## 15   CNV gistic         Bob mysnparray3
## 16   CNV gistic     Barbara mysnparray4

Note, dfmap can be reverted to a list with another provided function:

mapToList(dfmap, "assay")

4.3 Experimental data as a list()

Create an named list of experiments for the MultiAssayExperiment function. All of these names must be found within in the third column of dfmap:

objlist <- list("Affy" = exprdat, "Methyl 450k" = methyldat,
    "Mirna" = microdat, "CNV gistic" = rse)

4.4 Creation of the MultiAssayExperiment class object

We recommend using the MultiAssayExperiment constructor function:

myMultiAssay <- MultiAssayExperiment(objlist, patient.data, dfmap)
myMultiAssay

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

The following extractor functions can be used to get extract data from the object:

experiments(myMultiAssay)

## ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns

colData(myMultiAssay)

## DataFrame with 4 rows and 2 columns
##                 sex       age
##         <character> <integer>
## Jack              M        38
## Jill              F        39
## Bob               M        40
## Barbara           F        41

sampleMap(myMultiAssay)

## DataFrame with 16 rows and 3 columns
##           assay     primary     colname
##        <factor> <character> <character>
## 1   Affy               Jack      array1
## 2   Affy               Jill      array2
## 3   Affy            Barbara      array3
## 4   Affy                Bob      array4
## 5   Methyl 450k        Jack     methyl1
## ...         ...         ...         ...
## 12   Mirna              Bob      micro3
## 13   CNV gistic        Jack mysnparray1
## 14   CNV gistic        Jill mysnparray2
## 15   CNV gistic         Bob mysnparray3
## 16   CNV gistic     Barbara mysnparray4

metadata(myMultiAssay)

## list()

Note that the ExperimentList class extends the SimpleList class to add some validity checks specific to MultiAssayExperiment. It can be used like a list.

4.5 Helper function to create a MultiAssayExperiment object

The prepMultiAssay function helps diagnose common problems when creating a MultiAssayExperiment object. It provides error messages and/or warnings in instances where names (either colnames or ExperimentList element names) are inconsistent with those found in the sampleMap. Input arguments are the same as those in the MultiAssayExperiment (i.e., ExperimentList, colData, sampleMap). The resulting output of the prepMultiAssay function is a list of inputs including a “metadata$drops” element for names that were not able to be matched.

Instances where ExperimentList is created without names will prompt an error from prepMultiAssay. Named ExperimentList elements are essential for checks in MultiAssayExperiment.

objlist3 <- objlist
(names(objlist3) <- NULL)

## NULL

try(prepMultiAssay(objlist3, patient.data, dfmap)$experiments,
    outFile = stdout())

## Error in prepMultiAssay(objlist3, patient.data, dfmap) : 
##   ExperimentList does not have names, assign names

Non-matching names may also be present in the ExperimentList elements and the “assay” column of the sampleMap. If names only differ by case and are identical and unique, names will be standardized to lower case and replaced.

names(objlist3) <- toupper(names(objlist))
names(objlist3)

## [1] "AFFY"        "METHYL 450K" "MIRNA"       "CNV GISTIC"

unique(dfmap[, "assay"])

## [1] Affy        Methyl 450k Mirna       CNV gistic 
## Levels: Affy Methyl 450k Mirna CNV gistic

prepMultiAssay(objlist3, patient.data, dfmap)$experiments

## 
## Names in the ExperimentList do not match sampleMap assay
## standardizing will be attempted...

##  - names set to lowercase

## ExperimentList class object of length 4:
##  [1] affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] methyl 450k: matrix with 2 rows and 5 columns
##  [3] mirna: matrix with 4 rows and 3 columns
##  [4] cnv gistic: RangedSummarizedExperiment with 5 rows and 4 columns

When colnames in the ExperimentList cannot be matched back to the primary data (colData), these will be dropped and added to the drops element.

exampleMap <- sampleMap(simpleMultiAssay2)
sapply(doubleExp, colnames)

## $`methyl 2k`
## [1] "Jack"  "Jill"  "Bob"   "Bobby"
## 
## $`methyl 3k`
## [1] "Jack" "Jane" "Bob"

exampleMap

## DataFrame with 5 rows and 3 columns
##       assay     primary     colname
##    <factor> <character> <character>
## 1 methyl 2k        Jack        Jack
## 2 methyl 2k        Jill        Jill
## 3 methyl 2k         Bob         Bob
## 4 methyl 3k        Jack        Jack
## 5 methyl 3k         Bob         Bob

prepMultiAssay(doubleExp, patient.data, exampleMap)$metadata$drops

## 
## Not all colnames in the ExperimentList are found in the 
## sampleMap, dropping samples from ExperimentList...

## $`methyl 2k`
## [1] "Bobby"
## 
## $`methyl 3k`
## [1] "Jane"

## $`columns.methyl 2k`
## [1] "Bobby"
## 
## $`columns.methyl 3k`
## [1] "Jane"

A similar operation is performed for checking “primary” sampleMap names and colData rownames. In this example, we add a row corresponding to “Joe” that does not have a match in the experimental data.

exMap <- rbind(dfmap,
    DataFrame(assay = "New methyl", primary = "Joe",
        colname = "Joe"))
invisible(prepMultiAssay(objlist, patient.data, exMap))

## Warning in prepMultiAssay(objlist, patient.data, exMap): 
## Lengths of names in the ExperimentList and sampleMap
##  are not equal

## 
## Not all names in the primary column of the sampleMap
##  could be matched to the colData rownames; see $drops

## DataFrame with 1 row and 3 columns
##        assay     primary     colname
##     <factor> <character> <character>
## 1 New methyl         Joe         Joe

To create a MultiAssayExperiment from the results of the prepMultiAssay function, take each corresponding element from the resulting list and enter them as arguments to the MultiAssayExperiment constructor function.

prepped <- prepMultiAssay(objlist, patient.data, exMap)

## Warning in prepMultiAssay(objlist, patient.data, exMap): 
## Lengths of names in the ExperimentList and sampleMap
##  are not equal

## 
## Not all names in the primary column of the sampleMap
##  could be matched to the colData rownames; see $drops

## DataFrame with 1 row and 3 columns
##        assay     primary     colname
##     <factor> <character> <character>
## 1 New methyl         Joe         Joe

preppedMulti <- MultiAssayExperiment(prepped$experiments, prepped$colData,
    prepped$sampleMap, prepped$metadata)
preppedMulti

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

Alternatively, use the do.call function to easily create a MultiAssayExperiment from the output of prepMultiAssay function:

do.call(MultiAssayExperiment, prepped)

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

4.6 Helper functions to create Bioconductor classes from raw data

Recent updates to the GenomicRanges and SummarizedExperiment packages allow the user to create standard Bioconductor classes from raw data. Raw data read in as either data.frame or DataFrame can be converted to GRangesList or SummarizedExperiment classes depending on the type of data.

The function to create a GRangesList from a data.frame, called makeGRangesListFromDataFrame can be found in the GenomicRanges package. makeSummarizedExperimentFromDataFrame is available in the SummarizedExperiment package. It is also possible to create a RangedSummarizedExperiment class object from raw data when ranged data is available.

A simple example can be obtained from the function documentation in GenomicRanges:

grlls <- list(chr = rep("chr1", nrows), start = seq(11, 15),
    end = seq(12, 16), strand = c("+", "-", "+", "*", "*"),
    score = seq(1, 5), specimen = c("a", "a", "b", "b", "c"),
    gene_symbols = paste0("GENE", letters[seq_len(nrows)]))

grldf <- as.data.frame(grlls, stringsAsFactors = FALSE)

GRL <- makeGRangesListFromDataFrame(grldf, split.field = "specimen",
    names.field = "gene_symbols")

This can then be converted to a RaggedExperiment object for a rectangular representation that will conform more easily to the MultiAssayExperiment API requirements.

RaggedExperiment(GRL)

## class: RaggedExperiment 
## dim: 5 3 
## assays(0):
## rownames(5): GENEa GENEb GENEc GENEd GENEe
## colnames(3): a b c
## colData names(0):

Note. See the RaggedExperiment vignette for more details.

In the SummarizedExperiment package:

sels <- list(chr = rep("chr2", nrows), start = seq(11, 15),
    end = seq(12, 16), strand = c("+", "-", "+", "*", "*"),
    expr0 = seq(3, 7), expr1 = seq(8, 12), expr2 = seq(12, 16))
sedf <- as.data.frame(sels,
    row.names = paste0("GENE", letters[rev(seq_len(nrows))]),
    stringsAsFactors = FALSE)
sedf

##        chr start end strand expr0 expr1 expr2
## GENEe chr2    11  12      +     3     8    12
## GENEd chr2    12  13      -     4     9    13
## GENEc chr2    13  14      +     5    10    14
## GENEb chr2    14  15      *     6    11    15
## GENEa chr2    15  16      *     7    12    16

makeSummarizedExperimentFromDataFrame(sedf)

## class: RangedSummarizedExperiment 
## dim: 5 3 
## metadata(0):
## assays(1): ''
## rownames(5): GENEe GENEd GENEc GENEb GENEa
## rowData names(0):
## colnames(3): expr0 expr1 expr2
## colData names(0):

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5 Integrated subsetting across experiments

MultiAssayExperiment allows subsetting by rows, columns, and assays, rownames, and colnames, across all experiments simultaneously while guaranteeing continued matching of samples.

Subsetting can be done most compactly by the square bracket method, or more verbosely and potentially more flexibly by the subsetBy*() methods.

5.1 Subsetting by square bracket [

The three positions within the bracket operator indicate rows, columns, and assays, respectively (pseudocode):

myMultiAssay[rows, columns, assays]

For example, to select the gene “ENST00000355076”:

myMultiAssay["ENST00000355076", , ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 1 rows and 4 columns
##  [2] Methyl 450k: matrix with 1 rows and 5 columns
##  [3] Mirna: matrix with 0 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 0 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

The above operation works across all types of assays, whether ID-based (e.g. matrix, ExpressionSet, SummarizedExperiment) or range-based (e.g. RangedSummarizedExperiment). Note that when using the bracket method [, the drop argument is TRUE by default.

You can subset by rows, columns, and assays in a single bracket operation, and they will be performed in that order (rows, then columns, then assays). The following selects the ENST00000355076 gene across all samples, then the first two samples of each assay, and finally the Affy and Methyl 450k assays:

myMultiAssay["ENST00000355076", 1:2, c("Affy", "Methyl 450k")]

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 3 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] Affy: SummarizedExperiment with 1 rows and 2 columns
##  [2] Methyl 450k: matrix with 1 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

5.2 Subsetting by character, integer, and logical

By columns - character, integer, and logical are all allowed, for example:

myMultiAssay[, "Jack", ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 1 columns
##  [2] Methyl 450k: matrix with 2 rows and 2 columns
##  [3] Mirna: matrix with 4 rows and 1 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 1 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

myMultiAssay[, 1, ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 1 columns
##  [2] Methyl 450k: matrix with 2 rows and 2 columns
##  [3] Mirna: matrix with 4 rows and 1 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 1 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

myMultiAssay[, c(TRUE, FALSE, FALSE, FALSE), ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 1 columns
##  [2] Methyl 450k: matrix with 2 rows and 2 columns
##  [3] Mirna: matrix with 4 rows and 1 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 1 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

By assay - character, integer, and logical are allowed:

myMultiAssay[, , "Mirna"]

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 13 sampleMap rows not in names(experiments)
##   removing 1 colData rownames not in sampleMap 'primary'

## A MultiAssayExperiment object of 1 listed
##  experiment with a user-defined name and respective class.
##  Containing an ExperimentList class object of length 1:
##  [1] Mirna: matrix with 4 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

myMultiAssay[, , 3]

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 13 sampleMap rows not in names(experiments)
##   removing 1 colData rownames not in sampleMap 'primary'

## A MultiAssayExperiment object of 1 listed
##  experiment with a user-defined name and respective class.
##  Containing an ExperimentList class object of length 1:
##  [1] Mirna: matrix with 4 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

myMultiAssay[, , c(FALSE, FALSE, TRUE, FALSE, FALSE)]

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 13 sampleMap rows not in names(experiments)
##   removing 1 colData rownames not in sampleMap 'primary'

## A MultiAssayExperiment object of 1 listed
##  experiment with a user-defined name and respective class.
##  Containing an ExperimentList class object of length 1:
##  [1] Mirna: matrix with 4 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

5.3 the “drop” argument

Specify drop=FALSE to keep assays with zero rows or zero columns, e.g.:

myMultiAssay["ENST00000355076", , , drop=FALSE]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 1 rows and 4 columns
##  [2] Methyl 450k: matrix with 1 rows and 5 columns
##  [3] Mirna: matrix with 0 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 0 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

Using the default drop=TRUE, assays with no rows or no columns are removed:

myMultiAssay["ENST00000355076", , , drop=TRUE]

## Warning: 'experiments' dropped; see 'metadata'

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 7 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] Affy: SummarizedExperiment with 1 rows and 4 columns
##  [2] Methyl 450k: matrix with 1 rows and 5 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

5.4 More on subsetting by columns

Experimental samples are stored in the rows of colData but the columns of elements of ExperimentList, so when we refer to subsetting by columns, we are referring to columns of the experimental assays. Subsetting by samples / columns will be more obvious after recalling the colData:

colData(myMultiAssay)

## DataFrame with 4 rows and 2 columns
##                 sex       age
##         <character> <integer>
## Jack              M        38
## Jill              F        39
## Bob               M        40
## Barbara           F        41

Subsetting by samples identifies the selected samples in rows of the colData DataFrame, then selects all columns of the ExperimentList corresponding to these rows. Here we use an integer to keep the first two rows of colData, and all experimental assays associated to those two primary samples:

myMultiAssay[, 1:2]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 2 columns
##  [2] Methyl 450k: matrix with 2 rows and 3 columns
##  [3] Mirna: matrix with 4 rows and 1 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 2 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

Note that the above operation keeps different numbers of columns / samples from each assay, reflecting the reality that some samples may not have been assayed in all experiments, and may have replicates in some.

Columns can be subset using a logical vector. Here the dollar sign operator ($) accesses one of the columns in colData.

malesMultiAssay <- myMultiAssay[, myMultiAssay$sex == "M"]
colData(malesMultiAssay)

## DataFrame with 2 rows and 2 columns
##              sex       age
##      <character> <integer>
## Jack           M        38
## Bob            M        40

Finally, for special use cases you can exert detailed control of row or column subsetting, by using a list or CharacterList to subset. The following creates a CharacterList of the column names of each assay:

allsamples <- colnames(myMultiAssay)
allsamples

## CharacterList of length 4
## [["Affy"]] array1 array2 array3 array4
## [["Methyl 450k"]] methyl1 methyl2 methyl3 methyl4 methyl5
## [["Mirna"]] micro1 micro2 micro3
## [["CNV gistic"]] mysnparray1 mysnparray2 mysnparray3 mysnparray4

Now let’s get rid of three Methyl 450k arrays, those in positions 3, 4, and 5:

allsamples[["Methyl 450k"]] <- allsamples[["Methyl 450k"]][-3:-5]
myMultiAssay[, as.list(allsamples), ]

## harmonizing input:
##   removing 3 sampleMap rows with 'colname' not in colnames of experiments

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 2 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

subsetByColumn(myMultiAssay,  as.list(allsamples))  #equivalent

## harmonizing input:
##   removing 3 sampleMap rows with 'colname' not in colnames of experiments

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 2 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

5.5 Subsetting assays

You can select certain assays / experiments using subset, by providing a character, logical, or integer vector. An example using character:

myMultiAssay[, , c("Affy", "CNV gistic")]

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 8 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

You can subset assays also using logical or integer vectors:

is.cnv <- grepl("CNV", names(experiments(myMultiAssay)))
is.cnv

## [1] FALSE FALSE FALSE  TRUE

myMultiAssay[, , is.cnv]  #logical subsetting

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 12 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 1 listed
##  experiment with a user-defined name and respective class.
##  Containing an ExperimentList class object of length 1:
##  [1] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

myMultiAssay[, , which(is.cnv)] #integer subsetting

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 12 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 1 listed
##  experiment with a user-defined name and respective class.
##  Containing an ExperimentList class object of length 1:
##  [1] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

5.6 Subsetting rows (features) by IDs, integers, or logicals

Rows of the assays correspond to assay features or measurements, such as genes. Regardless of whether the assay is ID-based (e.g., matrix, ExpressionSet) or range-based (e.g., RangedSummarizedExperiment), they can be subset using any of the following:

• a character vector of IDs that will be matched to rownames in each assay

• an integer vector that will select rows of this position from each assay. This probably doesn’t make sense unless every ExperimentList element represents the same measurements in the same order and will generate an error if any of the integer elements exceeds the number of rows in any ExperimentList element. The most likely use of integer subsetting would be as a head function, for example to look at the first 6 rows of each assay.

• a logical vector that will be passed directly to the row subsetting operation for each assay.

• a list or List with element names matching those in the ExperimentList. Each element of the subsetting list will be passed on exactly to subset rows of the corresponding element of the ExperimentList.

Any list or List input allows for selective subsetting. The subsetting is applied only to the matching element names in the ExperimentList. For example, to only take the first two rows of the microRNA dataset, we use a named list to indicate what element we want to subset along with the drop = FALSE argument.

myMultiAssay[list(Mirna = 1:2), , ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 2 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

## equivalently
subsetByRow(myMultiAssay, list(Mirna = 1:2))

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 2 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

Again, these operations always return a MultiAssayExperiment class, unless drop=TRUE is passed to the [ backet subset, with any ExperimentList element not containing the feature having zero rows.

For example, return a MultiAssayExperiment where Affy and Methyl 450k contain only “ENST0000035076”" row, and “Mirna” and “CNV gistic” have zero rows (drop argument is set to FALSE by default in subsetBy*):

featSub0 <- subsetByRow(myMultiAssay, "ENST00000355076")
featSub1 <- myMultiAssay["ENST00000355076", , drop = FALSE] #equivalent
all.equal(featSub0, featSub1)

## [1] TRUE

class(featSub1)

## [1] "MultiAssayExperiment"
## attr(,"package")
## [1] "MultiAssayExperiment"

class(experiments(featSub1))

## [1] "ExperimentList"
## attr(,"package")
## [1] "MultiAssayExperiment"

experiments(featSub1)

## ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 1 rows and 4 columns
##  [2] Methyl 450k: matrix with 1 rows and 5 columns
##  [3] Mirna: matrix with 0 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 0 rows and 4 columns

In the following, Affy SummarizedExperiment keeps both rows but with their order reversed, and Methyl 450k keeps only its second row.

featSubsetted <-
  subsetByRow(myMultiAssay, c("ENST00000355076", "ENST00000294241"))
assay(myMultiAssay, 1L)

##                 array1 array2 array3 array4
## ENST00000294241    101    103    105    107
## ENST00000355076    102    104    106    108

assay(featSubsetted, 1L)

##                 array1 array2 array3 array4
## ENST00000355076    102    104    106    108
## ENST00000294241    101    103    105    107

5.7 Subsetting rows (features) by GenomicRanges

For MultiAssayExperiment objects containing range-based objects (currently RangedSummarizedExperiment), these can be subset using a GRanges object, for example:

gr <- GRanges(seqnames = c("chr1", "chr1", "chr2"), strand = c("-", "+", "+"),
              ranges = IRanges(start = c(230602, 443625, 934533),
                               end = c(330701, 443724, 934632)))

Now do the subsetting. The function doing the work here is IRanges::subsetByOverlaps - see its arguments for flexible types of subsetting by range. The first three arguments here are for subset, the rest passed on to IRanges::subsetByOverlaps through “…”:

subsetted <- subsetByRow(myMultiAssay, gr, maxgap = 2L, type = "within")
experiments(subsetted)

## ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 0 rows and 4 columns
##  [2] Methyl 450k: matrix with 0 rows and 5 columns
##  [3] Mirna: matrix with 0 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 0 rows and 4 columns

rowRanges(subsetted[[4]])

## GRanges object with 0 ranges and 1 metadata column:
##    seqnames    ranges strand |  feature_id
##       <Rle> <IRanges>  <Rle> | <character>
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Square bracket subsetting can still be used here, but passing on arguments to IRanges::subsetByOverlaps through “…” is simpler using subsetByRow().

5.8 Subsetting is endomorphic

subsetByRow, subsetByColumn, subsetByAssay, and square bracket subsetting are all “endomorphic” operations, in that they always return another MultiAssayExperiment object.

5.9 Double-bracket subsetting to select experiments

A double-bracket subset operation refers to an experiment, and will return the object contained within an ExperimentList element. It is not endomorphic. For example, the first ExperimentList element is called “Affy” and contains a SummarizedExperiment:

names(myMultiAssay)

## [1] "Affy"        "Methyl 450k" "Mirna"       "CNV gistic"

myMultiAssay[[1]]

## class: SummarizedExperiment 
## dim: 2 4 
## metadata(0):
## assays(1): ''
## rownames(2): ENST00000294241 ENST00000355076
## rowData names(0):
## colnames(4): array1 array2 array3 array4
## colData names(1): slope53

myMultiAssay[["Affy"]]

## class: SummarizedExperiment 
## dim: 2 4 
## metadata(0):
## assays(1): ''
## rownames(2): ENST00000294241 ENST00000355076
## rowData names(0):
## colnames(4): array1 array2 array3 array4
## colData names(1): slope53

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6 Helpers for data clean-up and management

6.1 complete.cases

The complete.cases function returns a logical vector of colData rows identifying which primary units have data for all experiments. Recall that myMultiAssay provides data for four individuals:

colData(myMultiAssay)

## DataFrame with 4 rows and 2 columns
##                 sex       age
##         <character> <integer>
## Jack              M        38
## Jill              F        39
## Bob               M        40
## Barbara           F        41

Of these, only Jack has data for all 5 experiments:

complete.cases(myMultiAssay)

## [1]  TRUE FALSE  TRUE  TRUE

But all four have complete cases for Affy and Methyl 450k:

complete.cases(myMultiAssay[, , 1:2])

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 7 sampleMap rows not in names(experiments)

## [1] TRUE TRUE TRUE TRUE

This output can be used to select individuals with complete data:

myMultiAssay[, complete.cases(myMultiAssay), ]

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 3 columns
##  [2] Methyl 450k: matrix with 2 rows and 4 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

6.2 replicated

The replicated function identifies primary column values or biological units that have multiple observations per assay. It returns a list of LogicalLists that indicate what biological units have one or more replicate measurements. This output is used for merging replicates by default.

replicated(myMultiAssay)

## $Affy
## LogicalList of length 4
## [["Jack"]] FALSE FALSE FALSE FALSE
## [["Jill"]] FALSE FALSE FALSE FALSE
## [["Barbara"]] FALSE FALSE FALSE FALSE
## [["Bob"]] FALSE FALSE FALSE FALSE
## 
## $`Methyl 450k`
## LogicalList of length 4
## [["Jack"]] TRUE TRUE FALSE FALSE FALSE
## [["Jill"]] FALSE FALSE FALSE FALSE FALSE
## [["Barbara"]] FALSE FALSE FALSE FALSE FALSE
## [["Bob"]] FALSE FALSE FALSE FALSE FALSE
## 
## $Mirna
## LogicalList of length 3
## [["Jack"]] FALSE FALSE FALSE
## [["Barbara"]] FALSE FALSE FALSE
## [["Bob"]] FALSE FALSE FALSE
## 
## $`CNV gistic`
## LogicalList of length 4
## [["Jack"]] FALSE FALSE FALSE FALSE
## [["Jill"]] FALSE FALSE FALSE FALSE
## [["Bob"]] FALSE FALSE FALSE FALSE
## [["Barbara"]] FALSE FALSE FALSE FALSE

6.3 intersectRows

The intersectRows function takes all common rownames across all experiments and returns a MultiAssayExperiment with those rows.

(ensmblMatches <- intersectRows(myMultiAssay[, , 1:2]))

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 7 sampleMap rows not in names(experiments)

## A MultiAssayExperiment object of 2 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 2:
##  [1] Affy: SummarizedExperiment with 1 rows and 4 columns
##  [2] Methyl 450k: matrix with 1 rows and 5 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

rownames(ensmblMatches)

## CharacterList of length 2
## [["Affy"]] ENST00000355076
## [["Methyl 450k"]] ENST00000355076

6.4 intersectColumns

A call to intersectColumns returns another MultiAssayExperiment where the columns of each element of the ExperimentList correspond exactly to the rows of colData. In many cases, this operation returns a 1-to-1 correspondence of samples to patients for each experiment assay unless replicates are present in the data.

intersectColumns(myMultiAssay)

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 3 columns
##  [2] Methyl 450k: matrix with 2 rows and 4 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

6.5 mergeReplicates

The mergeReplicates function allows the user to specify a function (default: mean) for combining replicate columns in each assay element. This can be combined with intersectColumns to create a MultiAssayExperiment object with one measurement in each experiment per biological unit.

mergeReplicates(intersectColumns(myMultiAssay))

## harmonizing input:
##   removing 1 sampleMap rows with 'colname' not in colnames of experiments

## A MultiAssayExperiment object of 4 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 4:
##  [1] Affy: SummarizedExperiment with 2 rows and 3 columns
##  [2] Methyl 450k: matrix with 2 rows and 3 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 3 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

6.6 combine c

The combine c function allows the user to append an experiment to the list of experiments already present in MultiAssayExperiment. In the case that additional observations on the same set of samples were performed, the c function can conveniently be referenced to an existing assay that contains the same ordering of sample measurements.

The mapFrom argument indicates what experiment has the exact same organization of samples that will be introduced by the new experiment dataset. If the number of columns in the new experiment do not match those in the reference experiment, an error will be thrown.

Here we introduce a toy dataset created on the fly:

c(myMultiAssay, ExpScores = matrix(1:8, ncol = 4,
dim = list(c("ENSMBL0001", "ENSMBL0002"), paste0("pt", 1:4))),
mapFrom = 1L)

## Warning: Assuming column order in the data provided 
##  matches the order in 'mapFrom' experiment(s) colnames

## A MultiAssayExperiment object of 5 listed
##  experiments with user-defined names and respective classes.
##  Containing an ExperimentList class object of length 5:
##  [1] Affy: SummarizedExperiment with 2 rows and 4 columns
##  [2] Methyl 450k: matrix with 2 rows and 5 columns
##  [3] Mirna: matrix with 4 rows and 3 columns
##  [4] CNV gistic: RangedSummarizedExperiment with 5 rows and 4 columns
##  [5] ExpScores: matrix with 2 rows and 4 columns
## Functionality:
##  experiments() - obtain the ExperimentList instance
##  colData() - the primary/phenotype DataFrame
##  sampleMap() - the sample coordination DataFrame
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment
##  *Format() - convert into a long or wide DataFrame
##  assays() - convert ExperimentList to a SimpleList of matrices
##  exportClass() - save data to flat files

Note: Alternatively, a sampleMap for the additional dataset can be provided.

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7 Extractor functions

Extractor functions convert a MultiAssayExperiment into other forms that are convenient for analyzing. These would normally be called after any desired subsetting has been performed.

7.1 getWithColData

Provides a single assay along with any associated ‘colData’ columns while keeping the assay class constant.

(affex <- getWithColData(myMultiAssay, 1L))

## Warning: 'experiments' dropped; see 'metadata'

## class: SummarizedExperiment 
## dim: 2 4 
## metadata(0):
## assays(1): ''
## rownames(2): ENST00000294241 ENST00000355076
## rowData names(0):
## colnames(4): array1 array2 array3 array4
## colData names(3): slope53 sex age

colData(affex)

## DataFrame with 4 rows and 3 columns
##           slope53         sex       age
##         <numeric> <character> <integer>
## array1  1.7799557           M        38
## array2  1.4240575           F        39
## array3  0.0179191           F        41
## array4 -0.9829740           M        40

class(affex)

## [1] "SummarizedExperiment"
## attr(,"package")
## [1] "SummarizedExperiment"

It will error when the target data class does not support a colData replacement method, meaning that it typically works with SummarizedExperiment and RaggedExperiment assays and their extensions.

7.2 longFormat & wideFormat

Produces long (default) or wide DataFrame objects. The following produces a long DataFrame (the default) for the first two assays:

longFormat(myMultiAssay[, , 1:2])

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 7 sampleMap rows not in names(experiments)

## DataFrame with 18 rows and 5 columns
##           assay     primary         rowname     colname     value
##     <character> <character>     <character> <character> <integer>
## 1          Affy        Jack ENST00000294241      array1       101
## 2          Affy        Jack ENST00000355076      array1       102
## 3          Affy        Jill ENST00000294241      array2       103
## 4          Affy        Jill ENST00000355076      array2       104
## 5          Affy     Barbara ENST00000294241      array3       105
## ...         ...         ...             ...         ...       ...
## 14  Methyl 450k        Jill ENST00000383706     methyl3         6
## 15  Methyl 450k     Barbara ENST00000355076     methyl4         7
## 16  Methyl 450k     Barbara ENST00000383706     methyl4         8
## 17  Methyl 450k         Bob ENST00000355076     methyl5         9
## 18  Methyl 450k         Bob ENST00000383706     methyl5        10

This is especially useful for performing regression against patient or sample data from colData using the pDataCols argument:

longFormat(myMultiAssay[, , 1:2], colDataCols="age")

## Warning: 'experiments' dropped; see 'metadata'

## harmonizing input:
##   removing 7 sampleMap rows not in names(experiments)

## DataFrame with 18 rows and 6 columns
##           assay     primary         rowname     colname     value       age
##     <character> <character>     <character> <character> <integer> <integer>
## 1          Affy        Jack ENST00000294241      array1       101        38
## 2          Affy        Jack ENST00000355076      array1       102        38
## 3          Affy        Jill ENST00000294241      array2       103        39
## 4          Affy        Jill ENST00000355076      array2       104        39
## 5          Affy     Barbara ENST00000294241      array3       105        41
## ...         ...         ...             ...         ...       ...       ...
## 14  Methyl 450k        Jill ENST00000383706     methyl3         6        39
## 15  Methyl 450k     Barbara ENST00000355076     methyl4         7        41
## 16  Methyl 450k     Barbara ENST00000383706     methyl4         8        41
## 17  Methyl 450k         Bob ENST00000355076     methyl5         9        40
## 18  Methyl 450k         Bob ENST00000383706     methyl5        10        40

The “wide” format is useful for calculating correlations or performing regression against different genomic features. Wide format is in general not possible with replicate measurements, so we demonstrate on the cleaned MultiAssayExperiment for the first 5 columns:

maemerge <- mergeReplicates(intersectColumns(myMultiAssay))

## harmonizing input:
##   removing 1 sampleMap rows with 'colname' not in colnames of experiments

wideFormat(maemerge, colDataCols="sex")[, 1:5]

## DataFrame with 3 rows and 5 columns
##       primary         sex Affy_ENST00000294241 Affy_ENST00000355076
##   <character> <character>            <integer>            <integer>
## 1        Jack           M                  101                  102
## 2         Bob           M                  107                  108
## 3     Barbara           F                  105                  106
##   Methyl.450k_ENST00000355076
##                     <numeric>
## 1                           2
## 2                           9
## 3                           7

7.3 assay / assays

The assay (singular) function takes a particular experiment and returns a matrix. By default, it will return the first experiment as a matrix.

assay(myMultiAssay)

##                 array1 array2 array3 array4
## ENST00000294241    101    103    105    107
## ENST00000355076    102    104    106    108

The assays (plural) function returns a SimpleList of data matrices from the ExperimentList:

assays(myMultiAssay)

## List of length 4
## names(4): Affy Methyl 450k Mirna CNV gistic

8 The Cancer Genome Atlas and MultiAssayExperiment

Our most recent efforts include the release of the experiment data package, curatedTCGAData. This package will allow users to selectively download cancer datasets from The Cancer Genome Atlas (TCGA) and represent the data as MultiAssayExperiment objects. Please see the package vignette for more details.

BiocManager::install("curatedTCGAData")

9 Dimension names: rownames and colnames

rownames and colnames return a CharacterList of row names and column names across all the assays. A CharacterList is an efficient alternative to list used when each element contains a character vector. It also provides a nice show method:

rownames(myMultiAssay)

## CharacterList of length 4
## [["Affy"]] ENST00000294241 ENST00000355076
## [["Methyl 450k"]] ENST00000355076 ENST00000383706
## [["Mirna"]] hsa-miR-21 hsa-miR-191 hsa-miR-148a hsa-miR148b
## [["CNV gistic"]] a b c d e

colnames(myMultiAssay)

## CharacterList of length 4
## [["Affy"]] array1 array2 array3 array4
## [["Methyl 450k"]] methyl1 methyl2 methyl3 methyl4 methyl5
## [["Mirna"]] micro1 micro2 micro3
## [["CNV gistic"]] mysnparray1 mysnparray2 mysnparray3 mysnparray4

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10 Requirements for support of additional data classes

Any data classes in the ExperimentList object must support the following methods:

• dimnames
• [
• dim()

Here is what happens if one of the methods doesn’t:

objlist2 <- objlist
objlist2[[2]] <- as.vector(objlist2[[2]])

tryCatch(
    MultiAssayExperiment(objlist2, patient.data, dfmap),
    error = function(e) {
        conditionMessage(e)
    }
)

## [1] "invalid class \"ExperimentList\" object: \n    'integer' class is not supported, use a rectangular class"

11 Application Programming Interface (API)

For more information on the formal API of MultiAssayExperiment, please see the API wiki document on GitHub. An API package is available for download on GitHub via install("waldronlab/MultiAssayShiny"). It provides visual exploration of available methods in MultiAssayExperiment.

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12 Methods for MultiAssayExperiment

The following methods are defined for MultiAssayExperiment:

methods(class="MultiAssayExperiment")

##  [1] $               $<-             [               [<-            
##  [5] [[              [[<-            anyReplicated   assay          
##  [9] assays          c               coerce          colData        
## [13] colData<-       colnames<-      complete.cases  dimnames       
## [17] experiments     experiments<-   exportClass     hasRowRanges   
## [21] isEmpty         length          mergeReplicates metadata       
## [25] metadata<-      names           names<-         replicated     
## [29] sampleMap       sampleMap<-     show            splitAssays    
## [33] subsetByAssay   subsetByColData subsetByColumn  subsetByRow    
## [37] updateObject   
## see '?methods' for accessing help and source code

13 Citing MultiAssayExperiment

We are excited to announce the official citation for MultiAssayExperiment in Cancer Research.

citation("MultiAssayExperiment")

## 
## To cite MultiAssayExperiment in publications use:
## 
##   Marcel Ramos et al. Software For The Integration Of Multiomics
##   Experiments In Bioconductor. Cancer Research, 2017 November 1;
##   77(21); e39-42. DOI: 10.1158/0008-5472.CAN-17-0344
## 
## A BibTeX entry for LaTeX users is
## 
##   @Article{,
##     title = {Software For The Integration Of Multi-Omics Experiments In Bioconductor},
##     author = {Marcel Ramos and Lucas Schiffer and Angela Re and Rimsha Azhar and Azfar Basunia and Carmen Rodriguez Cabrera and Tiffany Chan and Philip Chapman and Sean Davis and David Gomez-Cabrero and Aedin C. Culhane and Benjamin Haibe-Kains and Kasper Hansen and Hanish Kodali and Marie Stephie Louis and Arvind Singh Mer and Markus Reister and Martin Morgan and Vincent Carey and Levi Waldron},
##     journal = {Cancer Research},
##     year = {2017},
##     volume = {77(21); e39-42},
##   }

14 sessionInfo()

sessionInfo()

## R version 4.1.1 (2021-08-10)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              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       
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] RaggedExperiment_1.18.0     MultiAssayExperiment_1.20.0
##  [3] SummarizedExperiment_1.24.0 Biobase_2.54.0             
##  [5] GenomicRanges_1.46.0        GenomeInfoDb_1.30.0        
##  [7] IRanges_2.28.0              S4Vectors_0.32.0           
##  [9] BiocGenerics_0.40.0         MatrixGenerics_1.6.0       
## [11] matrixStats_0.61.0          BiocStyle_2.22.0           
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.1.1       xfun_0.27              bslib_0.3.1           
##  [4] purrr_0.3.4            lattice_0.20-45        vctrs_0.3.8           
##  [7] generics_0.1.1         htmltools_0.5.2        yaml_2.2.1            
## [10] utf8_1.2.2             rlang_0.4.12           R.oo_1.24.0           
## [13] jquerylib_0.1.4        pillar_1.6.4           DBI_1.1.1             
## [16] glue_1.4.2             R.utils_2.11.0         GenomeInfoDbData_1.2.7
## [19] R.cache_0.15.0         lifecycle_1.0.1        stringr_1.4.0         
## [22] zlibbioc_1.40.0        R.methodsS3_1.8.1      evaluate_0.14         
## [25] knitr_1.36             fastmap_1.1.0          fansi_0.5.0           
## [28] highr_0.9              BiocManager_1.30.16    DelayedArray_0.20.0   
## [31] jsonlite_1.7.2         XVector_0.34.0         R.rsp_0.44.0          
## [34] digest_0.6.28          stringi_1.7.5          bookdown_0.24         
## [37] dplyr_1.0.7            grid_4.1.1             tools_4.1.1           
## [40] bitops_1.0-7           magrittr_2.0.1         sass_0.4.0            
## [43] tibble_3.1.5           RCurl_1.98-1.5         pkgconfig_2.0.3       
## [46] crayon_1.4.1           tidyr_1.1.4            ellipsis_0.3.2        
## [49] Matrix_1.3-4           assertthat_0.2.1       rmarkdown_2.11        
## [52] R6_2.5.1               compiler_4.1.1

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