Contents

This quick-start guide shows key features of MultiAssayExperiment using a subset of the TCGA adrenocortical carcinoma (ACC) dataset. This dataset provides five assays on 92 patients, although all five assays were not performed for every patient:

  1. RNASeq2GeneNorm: gene mRNA abundance by RNA-seq
  2. gistict: GISTIC genomic copy number by gene
  3. RPPAArray: protein abundance by Reverse Phase Protein Array
  4. Mutations: non-silent somatic mutations by gene
  5. miRNASeqGene: microRNA abundance by microRNA-seq.
data(miniACC)
miniACC
## A MultiAssayExperiment object of 5 listed
##  experiments with user-defined names and respective classes. 
##  Containing an ExperimentList class object of length 5: 
##  [1] RNASeq2GeneNorm: SummarizedExperiment with 198 rows and 79 columns 
##  [2] gistict: SummarizedExperiment with 198 rows and 90 columns 
##  [3] RPPAArray: SummarizedExperiment with 33 rows and 46 columns 
##  [4] Mutations: matrix with 97 rows and 90 columns 
##  [5] miRNASeqGene: SummarizedExperiment with 471 rows and 80 columns 
## Features: 
##  experiments() - obtain the ExperimentList instance 
##  colData() - the primary/phenotype DFrame 
##  sampleMap() - the sample availability DFrame 
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment 
##  *Format() - convert into a long or wide DFrame 
##  assays() - convert ExperimentList to a SimpleList of matrices

Component slots

colData - information biological units

A DataFrame describing the characteristics of biological units, for example clinical data for patients. In the prepared datasets from The Cancer Genome Atlas, each row is one patient and each column is a clinical, pathological, subtype, or other variable. The $ function provides a shortcut for accessing or setting colData columns.

colData(miniACC)[1:4, 1:4]
## DataFrame with 4 rows and 4 columns
##                 patientID years_to_birth vital_status days_to_death
##               <character>      <integer>    <integer>     <integer>
## TCGA-OR-A5J1 TCGA-OR-A5J1             58            1          1355
## TCGA-OR-A5J2 TCGA-OR-A5J2             44            1          1677
## TCGA-OR-A5J3 TCGA-OR-A5J3             23            0            NA
## TCGA-OR-A5J4 TCGA-OR-A5J4             23            1           423
table(miniACC$race)
## 
##                     asian black or african american 
##                         2                         1 
##                     white 
##                        78

Key points: * One row per patient * Each row maps to zero or more observations in each experiment in the ExperimentList, below.

ExperimentList - experiment data

A base list or ExperimentList object containing the experimental datasets for the set of samples collected. This gets converted into a class ExperimentList during construction.

experiments(miniACC)
## ExperimentList class object of length 5: 
##  [1] RNASeq2GeneNorm: SummarizedExperiment with 198 rows and 79 columns 
##  [2] gistict: SummarizedExperiment with 198 rows and 90 columns 
##  [3] RPPAArray: SummarizedExperiment with 33 rows and 46 columns 
##  [4] Mutations: matrix with 97 rows and 90 columns 
##  [5] miRNASeqGene: SummarizedExperiment with 471 rows and 80 columns

Key points: * One matrix-like dataset per list element (although they do not even need to be matrix-like, see for example the RaggedExperiment package) * One matrix column per assayed specimen. Each matrix column must correspond to exactly one row of colData: in other words, you must know which patient or cell line the observation came from. However, multiple columns can come from the same patient, or there can be no data for that patient. * Matrix rows correspond to variables, e.g. genes or genomic ranges * ExperimentList elements can be genomic range-based (e.g. SummarizedExperiment::RangedSummarizedExperiment-class or RaggedExperiment::RaggedExperiment-class) or ID-based data (e.g. SummarizedExperiment::SummarizedExperiment-class, Biobase::eSet-class base::matrix-class, DelayedArray::DelayedArray-class, and derived classes) * Any data class can be included in the ExperimentList, as long as it supports: single-bracket subsetting ([), dimnames, and dim. Most data classes defined in Bioconductor meet these requirements.

sampleMap - relationship graph

sampleMap is a graph representation of the relationship between biological units and experimental results. In simple cases where the column names of ExperimentList data matrices match the row names of colData, the user won’t need to specify or think about a sample map, it can be created automatically by the MultiAssayExperiment constructor. sampleMap is a simple three-column DataFrame:

  1. assay column: the name of the assay, and found in the names of ExperimentList list names
  2. primary column: identifiers of patients or biological units, and found in the row names of colData
  3. colname column: identifiers of assay results, and found in the column names of ExperimentList elements Helper functions are available for creating a map from a list. See ?listToMap
sampleMap(miniACC)
## DataFrame with 385 rows and 3 columns
##               assay      primary                      colname
##            <factor>  <character>                  <character>
## 1   RNASeq2GeneNorm TCGA-OR-A5J1 TCGA-OR-A5J1-01A-11R-A29S-07
## 2   RNASeq2GeneNorm TCGA-OR-A5J2 TCGA-OR-A5J2-01A-11R-A29S-07
## 3   RNASeq2GeneNorm TCGA-OR-A5J3 TCGA-OR-A5J3-01A-11R-A29S-07
## 4   RNASeq2GeneNorm TCGA-OR-A5J5 TCGA-OR-A5J5-01A-11R-A29S-07
## 5   RNASeq2GeneNorm TCGA-OR-A5J6 TCGA-OR-A5J6-01A-31R-A29S-07
## ...             ...          ...                          ...
## 381    miRNASeqGene TCGA-PA-A5YG TCGA-PA-A5YG-01A-11R-A29W-13
## 382    miRNASeqGene TCGA-PK-A5H8 TCGA-PK-A5H8-01A-11R-A29W-13
## 383    miRNASeqGene TCGA-PK-A5H9 TCGA-PK-A5H9-01A-11R-A29W-13
## 384    miRNASeqGene TCGA-PK-A5HA TCGA-PK-A5HA-01A-11R-A29W-13
## 385    miRNASeqGene TCGA-PK-A5HB TCGA-PK-A5HB-01A-11R-A29W-13

Key points: * relates experimental observations (colnames) to colData * permits experiment-specific sample naming, missing, and replicate observations

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metadata

Metadata can be used to keep additional information about patients, assays performed on individuals or on the entire cohort, or features such as genes, proteins, and genomic ranges. There are many options available for storing metadata. First, MultiAssayExperiment has its own metadata for describing the entire experiment:

metadata(miniACC)
## $title
## [1] "Comprehensive Pan-Genomic Characterization of Adrenocortical Carcinoma"
## 
## $PMID
## [1] "27165744"
## 
## $sourceURL
## [1] "http://s3.amazonaws.com/multiassayexperiments/accMAEO.rds"
## 
## $RPPAfeatureDataURL
## [1] "http://genomeportal.stanford.edu/pan-tcga/show_target_selection_file?filename=Allprotein.txt"
## 
## $colDataExtrasURL
## [1] "http://www.cell.com/cms/attachment/2062093088/2063584534/mmc3.xlsx"

Additionally, the DataFrame class used by sampleMap and colData, as well as the ExperimentList class, similarly support metadata. Finally, many experimental data objects that can be used in the ExperimentList support metadata. These provide flexible options to users and to developers of derived classes.

Subsetting

Single bracket [

In pseudo code below, the subsetting operations work on the rows of the following indices: 1. i experimental data rows 2. j the primary names or the column names (entered as a list or List) 3. k assay

multiassayexperiment[i = rownames, j = primary or colnames, k = assay]

Subsetting operations always return another MultiAssayExperiment. For example, the following will return any rows named “MAPK14” or “IGFBP2”, and remove any assays where no rows match:

miniACC[c("MAPK14", "IGFBP2"), , ]
## harmonizing input:
##   removing 170 sampleMap rows not in names(experiments)

The following will keep only patients of pathological stage iv, and all their associated assays:

miniACC[, miniACC$pathologic_stage == "stage iv", ]

And the following will keep only the RNA-seq dataset, and only patients for which this assay is available:

miniACC[, , "RNASeq2GeneNorm"]
## harmonizing input:
##   removing 306 sampleMap rows not in names(experiments)
##   removing 13 colData rownames not in sampleMap 'primary'

Subsetting by genomic ranges

If any ExperimentList objects have features represented by genomic ranges (e.g. RangedSummarizedExperiment, RaggedExperiment), then a GRanges object in the first subsetting position will subset these objects as in GenomicRanges::findOverlaps().

Double bracket [[

The “double bracket” method ([[) is a convenience function for extracting a single element of the MultiAssayExperiment ExperimentList. It avoids the use of experiments(mae)[[1L]]. For example, both of the following extract the ExpressionSet object containing RNA-seq data:

miniACC[[1L]]  #or equivalently, miniACC[["RNASeq2GeneNorm"]]
## class: SummarizedExperiment 
## dim: 198 79 
## metadata(3): experimentData annotation protocolData
## assays(1): exprs
## rownames(198): DIRAS3 MAPK14 ... SQSTM1 KCNJ13
## rowData names(0):
## colnames(79): TCGA-OR-A5J1-01A-11R-A29S-07
##   TCGA-OR-A5J2-01A-11R-A29S-07 ... TCGA-PK-A5HA-01A-11R-A29S-07
##   TCGA-PK-A5HB-01A-11R-A29S-07
## colData names(0):

Patients with complete data

complete.cases() shows which patients have complete data for all assays:

summary(complete.cases(miniACC))
##    Mode   FALSE    TRUE 
## logical      49      43

The above logical vector could be used for patient subsetting. More simply, intersectColumns() will select complete cases and rearrange each ExperimentList element so its columns correspond exactly to rows of colData in the same order:

accmatched = intersectColumns(miniACC)

Note, the column names of the assays in accmatched are not the same because of assay-specific identifiers, but they have been automatically re-arranged to correspond to the same patients. In these TCGA assays, the first three - delimited positions correspond to patient, ie the first patient is TCGA-OR-A5J2:

colnames(accmatched)
## CharacterList of length 5
## [["RNASeq2GeneNorm"]] TCGA-OR-A5J2-01A-11R-A29S-07 ...
## [["gistict"]] TCGA-OR-A5J2-01A-11D-A29H-01 ... TCGA-PK-A5HA-01A-11D-A29H-01
## [["RPPAArray"]] TCGA-OR-A5J2-01A-21-A39K-20 ... TCGA-PK-A5HA-01A-21-A39K-20
## [["Mutations"]] TCGA-OR-A5J2-01A-11D-A29I-10 ...
## [["miRNASeqGene"]] TCGA-OR-A5J2-01A-11R-A29W-13 ...

Row names that are common across assays

intersectRows() keeps only rows that are common to each assay, and aligns them in identical order. For example, to keep only genes where data are available for RNA-seq, GISTIC copy number, and somatic mutations:

accmatched2 <- intersectRows(miniACC[, , c("RNASeq2GeneNorm",
                                           "gistict",
                                           "Mutations")])
## harmonizing input:
##   removing 126 sampleMap rows not in names(experiments)
rownames(accmatched2)
## CharacterList of length 3
## [["RNASeq2GeneNorm"]] DIRAS3 G6PD KDR ERBB3 AKT1S1 ... RET CDKN2A MACC1 CHGA
## [["gistict"]] DIRAS3 G6PD KDR ERBB3 AKT1S1 ... PREX1 RET CDKN2A MACC1 CHGA
## [["Mutations"]] DIRAS3 G6PD KDR ERBB3 AKT1S1 ... PREX1 RET CDKN2A MACC1 CHGA

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Extraction

assay and assays

The assay and assays methods follow SummarizedExperiment convention. The assay (singular) method will extract the first element of the ExperimentList and will return a matrix.

class(assay(miniACC))
## [1] "matrix"

The assays (plural) method will return a SimpleList of the data with each element being a matrix.

assays(miniACC)
## List of length 5
## names(5): RNASeq2GeneNorm gistict RPPAArray Mutations miRNASeqGene

Key point: * Whereas the [[ returned an assay as its original class, assay() and assays() convert the assay data to matrix form.

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Summary of slots and accessors

Slot in the MultiAssayExperiment can be accessed or set using their accessor functions:

Slot Accessor
ExperimentList experiments()
colData colData() and $ *
sampleMap sampleMap()
metadata metadata()

__*__ The $ operator on a MultiAssayExperiment returns a single column of the colData.

Transformation / reshaping

The longFormat or wideFormat functions will “reshape” and combine experiments with each other and with colData into one DataFrame. These functions provide compatibility with most of the common R/Bioconductor functions for regression, machine learning, and visualization.

longFormat

In long format a single column provides all assay results, with additional optional colData columns whose values are repeated as necessary. Here assay is the name of the ExperimentList element, primary is the patient identifier (rowname of colData), rowname is the assay rowname (in this case genes), colname is the assay-specific identifier (column name), value is the numeric measurement (gene expression, copy number, presence of a non-silent mutation, etc), and following these are the vital_status and days_to_death colData columns that have been added:

longFormat(miniACC[c("TP53", "CTNNB1"), , ], 
           colDataCols = c("vital_status", "days_to_death"))
## harmonizing input:
##   removing 126 sampleMap rows not in names(experiments)
## DataFrame with 518 rows and 7 columns
##               assay      primary     rowname                      colname
##         <character>  <character> <character>                  <character>
## 1   RNASeq2GeneNorm TCGA-OR-A5J1        TP53 TCGA-OR-A5J1-01A-11R-A29S-07
## 2   RNASeq2GeneNorm TCGA-OR-A5J1      CTNNB1 TCGA-OR-A5J1-01A-11R-A29S-07
## 3   RNASeq2GeneNorm TCGA-OR-A5J2        TP53 TCGA-OR-A5J2-01A-11R-A29S-07
## 4   RNASeq2GeneNorm TCGA-OR-A5J2      CTNNB1 TCGA-OR-A5J2-01A-11R-A29S-07
## 5   RNASeq2GeneNorm TCGA-OR-A5J3        TP53 TCGA-OR-A5J3-01A-11R-A29S-07
## ...             ...          ...         ...                          ...
## 514       Mutations TCGA-PK-A5HA      CTNNB1 TCGA-PK-A5HA-01A-11D-A29I-10
## 515       Mutations TCGA-PK-A5HB        TP53 TCGA-PK-A5HB-01A-11D-A29I-10
## 516       Mutations TCGA-PK-A5HB      CTNNB1 TCGA-PK-A5HB-01A-11D-A29I-10
## 517       Mutations TCGA-PK-A5HC        TP53 TCGA-PK-A5HC-01A-11D-A30A-10
## 518       Mutations TCGA-PK-A5HC      CTNNB1 TCGA-PK-A5HC-01A-11D-A30A-10
##          value vital_status days_to_death
##      <numeric>    <integer>     <integer>
## 1     563.4006            1          1355
## 2    5634.4669            1          1355
## 3     165.4811            1          1677
## 4   62658.3913            1          1677
## 5     956.3028            0            NA
## ...        ...          ...           ...
## 514          0            0            NA
## 515          0            0            NA
## 516          0            0            NA
## 517          0            0            NA
## 518          0            0            NA

wideFormat

In wide format, each feature from each assay goes in a separate column, with one row per primary identifier (patient). Here, each variable becomes a new column:

wideFormat(miniACC[c("TP53", "CTNNB1"), , ], 
           colDataCols = c("vital_status", "days_to_death"))
## harmonizing input:
##   removing 126 sampleMap rows not in names(experiments)
## DataFrame with 92 rows and 9 columns
##          primary vital_status days_to_death RNASeq2GeneNorm_CTNNB1
##      <character>    <integer>     <integer>              <numeric>
## 1   TCGA-OR-A5J1            1          1355              5634.4669
## 2   TCGA-OR-A5J2            1          1677             62658.3913
## 3   TCGA-OR-A5J3            0            NA              6337.4256
## 4   TCGA-OR-A5J4            1           423                     NA
## 5   TCGA-OR-A5J5            1           365               5979.055
## ...          ...          ...           ...                    ...
## 88  TCGA-PK-A5H9            0            NA              5258.9863
## 89  TCGA-PK-A5HA            0            NA              8120.1654
## 90  TCGA-PK-A5HB            0            NA              5257.8148
## 91  TCGA-PK-A5HC            0            NA                     NA
## 92  TCGA-P6-A5OG            1           383              6390.0997
##     RNASeq2GeneNorm_TP53 gistict_CTNNB1 gistict_TP53 Mutations_CTNNB1
##                <numeric>      <numeric>    <numeric>        <numeric>
## 1               563.4006              0            0                0
## 2               165.4811              1            0                1
## 3               956.3028              0            0                0
## 4                     NA              0            1                0
## 5              1169.6359              0            0                0
## ...                  ...            ...          ...              ...
## 88              890.8663              0            0                0
## 89              683.5722              0           -1                0
## 90              237.3697             -1           -1                0
## 91                    NA              1            1                0
## 92              815.3446              1           -1               NA
##     Mutations_TP53
##          <numeric>
## 1                0
## 2                1
## 3                0
## 4                0
## 5                0
## ...            ...
## 88               0
## 89               0
## 90               0
## 91               0
## 92              NA

MultiAssayExperiment class construction and concatenation

MultiAssayExperiment constructor function

The MultiAssayExperiment constructor function can take three arguments:

  1. experiments - An ExperimentList or list of data
  2. colData - A DataFrame describing the patients (or cell lines, or other biological units)
  3. sampleMap - A DataFrame of assay, primary, and colname identifiers

The miniACC object can be reconstructed as follows:

MultiAssayExperiment(experiments=experiments(miniACC),
    colData=colData(miniACC),
    sampleMap=sampleMap(miniACC),
    metadata=metadata(miniACC))
## A MultiAssayExperiment object of 5 listed
##  experiments with user-defined names and respective classes. 
##  Containing an ExperimentList class object of length 5: 
##  [1] RNASeq2GeneNorm: SummarizedExperiment with 198 rows and 79 columns 
##  [2] gistict: SummarizedExperiment with 198 rows and 90 columns 
##  [3] RPPAArray: SummarizedExperiment with 33 rows and 46 columns 
##  [4] Mutations: matrix with 97 rows and 90 columns 
##  [5] miRNASeqGene: SummarizedExperiment with 471 rows and 80 columns 
## Features: 
##  experiments() - obtain the ExperimentList instance 
##  colData() - the primary/phenotype DFrame 
##  sampleMap() - the sample availability DFrame 
##  `$`, `[`, `[[` - extract colData columns, subset, or experiment 
##  *Format() - convert into a long or wide DFrame 
##  assays() - convert ExperimentList to a SimpleList of matrices

prepMultiAssay - Constructor function helper

The prepMultiAssay function allows the user to diagnose typical problems when creating a MultiAssayExperiment object. See ?prepMultiAssay for more details.

c - concatenate to MultiAssayExperiment

The c function allows the user to concatenate an additional experiment to an existing MultiAssayExperiment. The optional sampleMap argument allows concatenating an assay whose column names do not match the row names of colData. For convenience, the mapFrom argument allows the user to map from a particular experiment provided that the order of the colnames is in the same. A warning will be issued to make the user aware of this assumption. For example, to concatenate a matrix of log2-transformed RNA-seq results:

miniACC2 <- c(miniACC, log2rnaseq = log2(assays(miniACC)$RNASeq2GeneNorm), mapFrom=1L)
## Warning: Assuming column order in the data provided 
##  matches the order in 'mapFrom' experiment(s) colnames
assays(miniACC2)
## List of length 6
## names(6): RNASeq2GeneNorm gistict RPPAArray Mutations miRNASeqGene log2rnaseq

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Examples

UpsetR “Venn” diagram

We see that 43 samples have all 5 assays, 32 are missing reverse-phase protein (RPPAArray), 2 are missing Mutations, 1 is missing gistict, 12 have only mutations and gistict, etc:

library(UpSetR)
upsetSamples(miniACC)

Kaplan-meier plot stratified by a clinical variable

The colData can provide clinical data for things like a Kaplan-Meier plot for overall survival stratified by nodal stage. To simplify things, first add a “y” column to the colData, containing the Surv object for survival analysis:

Note: survfit method does not work well with DataFrame. To bypass the error, here we covert colData to a data.frame.

suppressPackageStartupMessages({
  library(survival)
  library(survminer)
})
coldat <- as.data.frame(colData(miniACC))
coldat$y <- Surv(miniACC$days_to_death, miniACC$vital_status)
colData(miniACC) <- DataFrame(coldat)

And remove any patients missing overall survival information:

miniACC <- miniACC[, complete.cases(coldat$y), ]
coldat <- as(colData(miniACC), "data.frame")
fit <- survfit(y ~ pathology_N_stage, data = coldat)
ggsurvplot(fit, data = coldat, risk.table = TRUE)

Multivariate Cox regression including RNA-seq, copy number, and pathology

Choose the EZH2 gene for demonstration. This subsetting will drop assays with no row named EZH2:

wideacc <- wideFormat(miniACC["EZH2", , ], 
    colDataCols = c("vital_status", "days_to_death", "pathology_N_stage"))
## harmonizing input:
##   removing 76 sampleMap rows not in names(experiments)
wideacc$y <- Surv(wideacc$days_to_death, wideacc$vital_status)
head(wideacc)
## DataFrame with 6 rows and 7 columns
##        primary vital_status days_to_death pathology_N_stage
##    <character>    <integer>     <integer>       <character>
## 1 TCGA-OR-A5J1            1          1355                n0
## 2 TCGA-OR-A5J2            1          1677                n0
## 3 TCGA-OR-A5J4            1           423                n1
## 4 TCGA-OR-A5J5            1           365                n0
## 5 TCGA-OR-A5J7            1           490                n0
## 6 TCGA-OR-A5J8            1           579                n0
##   RNASeq2GeneNorm_EZH2 gistict_EZH2      y
##              <numeric>    <numeric> <Surv>
## 1              75.8886            0 1355:1
## 2             326.5332            1 1677:1
## 3                   NA           -2  423:1
## 4             366.3826            1  365:1
## 5             747.6935            1  490:1
## 6             426.4401            1  579:1

Perform a multivariate Cox regression with EZH2 copy number (gistict), log2-transformed EZH2 expression (RNASeq2GeneNorm), and nodal status (pathology_N_stage) as predictors:

coxph(Surv(days_to_death, vital_status) ~ gistict_EZH2 +
          log2(RNASeq2GeneNorm_EZH2) + pathology_N_stage,  data=wideacc)
## Call:
## coxph(formula = Surv(days_to_death, vital_status) ~ gistict_EZH2 + 
##     log2(RNASeq2GeneNorm_EZH2) + pathology_N_stage, data = wideacc)
## 
##                                coef exp(coef) se(coef)      z        p
## gistict_EZH2               -0.03723   0.96345  0.28205 -0.132 0.894986
## log2(RNASeq2GeneNorm_EZH2)  0.97731   2.65729  0.28105  3.477 0.000506
## pathology_N_stagen1         0.37749   1.45862  0.56992  0.662 0.507743
## 
## Likelihood ratio test=16.28  on 3 df, p=0.0009942
## n= 26, number of events= 26 
##    (8 observations deleted due to missingness)

We see that EZH2 expression is significantly associated with overal survival (p < 0.001), but EZH2 copy number and nodal status are not. This analysis could easily be extended to the whole genome for discovery of prognostic features by repeated univariate regressions over columns, penalized multivariate regression, etc.

For further detail, see the main MultiAssayExperiment vignette.

Session info

sessionInfo()
## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats4    stats     graphics  grDevices utils     datasets 
## [8] methods   base     
## 
## other attached packages:
##  [1] survminer_0.4.6             ggpubr_0.2.3               
##  [3] magrittr_1.5                ggplot2_3.2.1              
##  [5] survival_2.44-1.1           UpSetR_1.4.0               
##  [7] RaggedExperiment_1.10.0     MultiAssayExperiment_1.12.0
##  [9] SummarizedExperiment_1.16.0 DelayedArray_0.12.0        
## [11] BiocParallel_1.20.0         matrixStats_0.55.0         
## [13] Biobase_2.46.0              GenomicRanges_1.38.0       
## [15] GenomeInfoDb_1.22.0         IRanges_2.20.0             
## [17] S4Vectors_0.24.0            BiocGenerics_0.32.0        
## [19] BiocStyle_2.14.0           
## 
## loaded via a namespace (and not attached):
##  [1] tidyr_1.0.0            splines_3.6.1          R.utils_2.9.0         
##  [4] assertthat_0.2.1       BiocManager_1.30.9     highr_0.8             
##  [7] GenomeInfoDbData_1.2.2 yaml_2.2.0             pillar_1.4.2          
## [10] backports_1.1.5        lattice_0.20-38        glue_1.3.1            
## [13] digest_0.6.22          XVector_0.26.0         ggsignif_0.6.0        
## [16] colorspace_1.4-1       htmltools_0.4.0        Matrix_1.2-17         
## [19] R.oo_1.22.0            plyr_1.8.4             pkgconfig_2.0.3       
## [22] broom_0.5.2            bookdown_0.14          zlibbioc_1.32.0       
## [25] xtable_1.8-4           purrr_0.3.3            scales_1.0.0          
## [28] km.ci_0.5-2            KMsurv_0.1-5           tibble_2.1.3          
## [31] generics_0.0.2         ellipsis_0.3.0         withr_2.1.2           
## [34] lazyeval_0.2.2         crayon_1.3.4           evaluate_0.14         
## [37] R.methodsS3_1.7.1      nlme_3.1-141           R.cache_0.13.0        
## [40] R.rsp_0.43.2           data.table_1.12.6      tools_3.6.1           
## [43] lifecycle_0.1.0        stringr_1.4.0          munsell_0.5.0         
## [46] compiler_3.6.1         rlang_0.4.1            grid_3.6.1            
## [49] RCurl_1.95-4.12        bitops_1.0-6           labeling_0.3          
## [52] rmarkdown_1.16         gtable_0.3.0           R6_2.4.0              
## [55] zoo_1.8-6              gridExtra_2.3          knitr_1.25            
## [58] dplyr_0.8.3            survMisc_0.5.5         zeallot_0.1.0         
## [61] stringi_1.4.3          Rcpp_1.0.2             vctrs_0.2.0           
## [64] tidyselect_0.2.5       xfun_0.10

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