MultiAssayExperiment: Quick Start Guide
April 26, 2022
Contents
library(MultiAssayExperiment)
library(S4Vectors)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:
- RNASeq2GeneNorm: gene mRNA abundance by RNA-seq
- gistict: GISTIC genomic copy number by gene
- RPPAArray: protein abundance by Reverse Phase Protein Array
- Mutations: non-silent somatic mutations by gene
- 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
## 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 filesComponent slots
colData - information on 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 423table(miniACC$race)##
## asian black or african american white
## 2 1 78Key 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 columnsKey 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:
assaycolumn: the name of the assay, and found in the names ofExperimentListlist namesprimarycolumn: identifiers of patients or biological units, and found in the row names ofcolDatacolnamecolumn: identifiers of assay results, and found in the column names ofExperimentListelements 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..
## 2 RNASeq2GeneNorm TCGA-OR-A5J2 TCGA-OR-A5J2-01A-11R..
## 3 RNASeq2GeneNorm TCGA-OR-A5J3 TCGA-OR-A5J3-01A-11R..
## 4 RNASeq2GeneNorm TCGA-OR-A5J5 TCGA-OR-A5J5-01A-11R..
## 5 RNASeq2GeneNorm TCGA-OR-A5J6 TCGA-OR-A5J6-01A-31R..
## ... ... ... ...
## 381 miRNASeqGene TCGA-PA-A5YG TCGA-PA-A5YG-01A-11R..
## 382 miRNASeqGene TCGA-PK-A5H8 TCGA-PK-A5H8-01A-11R..
## 383 miRNASeqGene TCGA-PK-A5H9 TCGA-PK-A5H9-01A-11R..
## 384 miRNASeqGene TCGA-PK-A5HA TCGA-PK-A5HA-01A-11R..
## 385 miRNASeqGene TCGA-PK-A5HB TCGA-PK-A5HB-01A-11R..Key points:
* relates experimental observations (colnames) to colData
* permits experiment-specific sample naming, missing, and replicate observations
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"
##
## $colDataExtrasURL
## [1] "http://www.cell.com/cms/attachment/2062093088/2063584534/mmc3.xlsx"Additionally, the DataFrame class used by sampleMap and colData, as well
as the ExperimentList class, similarly support metadata. Finally, many
experimental data objects that can be used in the ExperimentList support
metadata. These provide flexible options to users and to developers of derived
classes.
Subsetting
Single bracket [
In pseudo code below, the subsetting operations work on the rows of the
following indices:
1. i experimental data rows
2. j the primary names or the column names (entered as a list or List)
3. k assay
multiassayexperiment[i = rownames, j = primary or colnames, k = assay]Subsetting operations always return another MultiAssayExperiment. For example,
the following will return any rows named “MAPK14” or “IGFBP2”, and remove any
assays where no rows match:
miniACC[c("MAPK14", "IGFBP2"), , ]The following will keep only patients of pathological stage iv, and all their associated assays:
stg4 <- miniACC$pathologic_stage == "stage iv"
# remove NA values from vector
miniACC[, stg4 & !is.na(stg4), ]And the following will keep only the RNA-seq dataset, and only patients for which this assay is available:
miniACC[, , "RNASeq2GeneNorm"]## Warning: 'experiments' dropped; see 'metadata'## 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 43The 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 ... TCGA-PK-A5HA-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")])## Warning: 'experiments' dropped; see 'metadata'## 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 CHGAExtraction
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" "array"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 miRNASeqGeneKey point:
* Whereas the [[ returned an assay as its original class, assay() and
assays() convert the assay data to matrix form.
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 value
## <character> <character> <character> <character> <numeric>
## 1 RNASeq2GeneNorm TCGA-OR-A5J1 TP53 TCGA-OR-A5J1-01A-11R.. 563.401
## 2 RNASeq2GeneNorm TCGA-OR-A5J1 CTNNB1 TCGA-OR-A5J1-01A-11R.. 5634.467
## 3 RNASeq2GeneNorm TCGA-OR-A5J2 TP53 TCGA-OR-A5J2-01A-11R.. 165.481
## 4 RNASeq2GeneNorm TCGA-OR-A5J2 CTNNB1 TCGA-OR-A5J2-01A-11R.. 62658.391
## 5 RNASeq2GeneNorm TCGA-OR-A5J3 TP53 TCGA-OR-A5J3-01A-11R.. 956.303
## ... ... ... ... ... ...
## 514 Mutations TCGA-PK-A5HA CTNNB1 TCGA-PK-A5HA-01A-11D.. 0
## 515 Mutations TCGA-PK-A5HB TP53 TCGA-PK-A5HB-01A-11D.. 0
## 516 Mutations TCGA-PK-A5HB CTNNB1 TCGA-PK-A5HB-01A-11D.. 0
## 517 Mutations TCGA-PK-A5HC TP53 TCGA-PK-A5HC-01A-11D.. 0
## 518 Mutations TCGA-PK-A5HC CTNNB1 TCGA-PK-A5HC-01A-11D.. 0
## vital_status days_to_death
## <integer> <integer>
## 1 1 1355
## 2 1 1355
## 3 1 1677
## 4 1 1677
## 5 0 NA
## ... ... ...
## 514 0 NA
## 515 0 NA
## 516 0 NA
## 517 0 NA
## 518 0 NAwideFormat
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_TP53
## <character> <integer> <integer> <numeric>
## 1 TCGA-OR-A5J1 1 1355 563.401
## 2 TCGA-OR-A5J2 1 1677 165.481
## 3 TCGA-OR-A5J3 0 NA 956.303
## 4 TCGA-OR-A5J4 1 423 NA
## 5 TCGA-OR-A5J5 1 365 1169.636
## ... ... ... ... ...
## 88 TCGA-PK-A5H9 0 NA 890.866
## 89 TCGA-PK-A5HA 0 NA 683.572
## 90 TCGA-PK-A5HB 0 NA 237.370
## 91 TCGA-PK-A5HC 0 NA NA
## 92 TCGA-P6-A5OG 1 383 815.345
## RNASeq2GeneNorm_CTNNB1 gistict_TP53 gistict_CTNNB1 Mutations_TP53
## <numeric> <numeric> <numeric> <numeric>
## 1 5634.47 0 0 0
## 2 62658.39 0 1 1
## 3 6337.43 0 0 0
## 4 NA 1 0 0
## 5 5979.06 0 0 0
## ... ... ... ... ...
## 88 5258.99 0 0 0
## 89 8120.17 -1 0 0
## 90 5257.81 -1 -1 0
## 91 NA 1 1 0
## 92 6390.10 -1 1 NA
## Mutations_CTNNB1
## <numeric>
## 1 0
## 2 1
## 3 0
## 4 0
## 5 0
## ... ...
## 88 0
## 89 0
## 90 0
## 91 0
## 92 NAMultiAssayExperiment class construction and concatenation
MultiAssayExperiment constructor function
The MultiAssayExperiment constructor function can take three arguments:
experiments- AnExperimentListorlistof datacolData- ADataFramedescribing the patients (or cell lines, or other biological units)sampleMap- ADataFrameofassay,primary, andcolnameidentifiers
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
## Functionality:
## experiments() - obtain the ExperimentList instance
## colData() - the primary/phenotype DataFrame
## sampleMap() - the sample coordination DataFrame
## `$`, `[`, `[[` - extract colData columns, subset, or experiment
## *Format() - convert into a long or wide DataFrame
## assays() - convert ExperimentList to a SimpleList of matrices
## exportClass() - save data to flat filesprepMultiAssay - Constructor function helper
The prepMultiAssay function allows the user to diagnose typical problems
when creating a MultiAssayExperiment object. See ?prepMultiAssay for more
details.
c - concatenate to MultiAssayExperiment
The c function allows the user to concatenate an additional experiment to an
existing MultiAssayExperiment. The optional sampleMap argument allows
concatenating an assay whose column names do not match the row names of
colData. For convenience, the mapFrom argument allows the user to map from
a particular experiment provided that the order of the colnames is in
the same. A warning will be issued to make the user aware of this
assumption. For example, to concatenate a matrix of log2-transformed RNA-seq
results:
miniACC2 <- c(miniACC, log2rnaseq = log2(assays(miniACC)$RNASeq2GeneNorm), mapFrom=1L)## Warning: Assuming column order in the data provided
## matches the order in 'mapFrom' experiment(s) colnamesassays(miniACC2)## List of length 6
## names(6): RNASeq2GeneNorm gistict RPPAArray Mutations miRNASeqGene log2rnaseqExamples
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 1 579:1Perform 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 4.2.0 RC (2022-04-19 r82224)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.15-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] survminer_0.4.9 ggpubr_0.4.0
## [3] ggplot2_3.3.5 survival_3.3-1
## [5] UpSetR_1.4.0 RaggedExperiment_1.20.0
## [7] MultiAssayExperiment_1.22.0 SummarizedExperiment_1.26.0
## [9] Biobase_2.56.0 GenomicRanges_1.48.0
## [11] GenomeInfoDb_1.32.0 IRanges_2.30.0
## [13] S4Vectors_0.34.0 BiocGenerics_0.42.0
## [15] MatrixGenerics_1.8.0 matrixStats_0.62.0
## [17] BiocStyle_2.24.0
##
## loaded via a namespace (and not attached):
## [1] ggtext_0.1.1 bitops_1.0-7 R.cache_0.15.0
## [4] tools_4.2.0 backports_1.4.1 bslib_0.3.1
## [7] utf8_1.2.2 R6_2.5.1 DBI_1.1.2
## [10] colorspace_2.0-3 withr_2.5.0 tidyselect_1.1.2
## [13] gridExtra_2.3 compiler_4.2.0 cli_3.3.0
## [16] xml2_1.3.3 DelayedArray_0.22.0 labeling_0.4.2
## [19] bookdown_0.26 sass_0.4.1 scales_1.2.0
## [22] survMisc_0.5.6 stringr_1.4.0 digest_0.6.29
## [25] rmarkdown_2.14 R.utils_2.11.0 XVector_0.36.0
## [28] pkgconfig_2.0.3 htmltools_0.5.2 fastmap_1.1.0
## [31] highr_0.9 rlang_1.0.2 jquerylib_0.1.4
## [34] farver_2.1.0 generics_0.1.2 zoo_1.8-10
## [37] jsonlite_1.8.0 dplyr_1.0.8 car_3.0-12
## [40] R.oo_1.24.0 RCurl_1.98-1.6 magrittr_2.0.3
## [43] GenomeInfoDbData_1.2.8 Matrix_1.4-1 Rcpp_1.0.8.3
## [46] munsell_0.5.0 fansi_1.0.3 abind_1.4-5
## [49] lifecycle_1.0.1 R.methodsS3_1.8.1 stringi_1.7.6
## [52] yaml_2.3.5 carData_3.0-5 zlibbioc_1.42.0
## [55] plyr_1.8.7 grid_4.2.0 crayon_1.5.1
## [58] lattice_0.20-45 splines_4.2.0 gridtext_0.1.4
## [61] magick_2.7.3 knitr_1.38 pillar_1.7.0
## [64] markdown_1.1 ggsignif_0.6.3 glue_1.6.2
## [67] evaluate_0.15 data.table_1.14.2 BiocManager_1.30.17
## [70] vctrs_0.4.1 gtable_0.3.0 purrr_0.3.4
## [73] tidyr_1.2.0 km.ci_0.5-6 assertthat_0.2.1
## [76] xfun_0.30 xtable_1.8-4 broom_0.8.0
## [79] rstatix_0.7.0 tibble_3.1.6 KMsurv_0.1-5
## [82] ellipsis_0.3.2 R.rsp_0.44.0