GSVA: gene set variation analysis
13 April 2025
Abstract
Gene set variation analysis (GSVA) is a particular type of gene set enrichment method that works on single samples and enables pathway-centric analyses of molecular data by performing a conceptually simple but powerful change in the functional unit of analysis, from genes to gene sets. The GSVA package provides the implementation of four single-sample gene set enrichment methods, concretely zscore, plage, ssGSEA and its own called GSVA. While this methodology was initially developed for gene expression data, it can be applied to other types of molecular profiling data. In this vignette we illustrate how to use the GSVA package with bulk microarray and RNA-seq expression data.
Package
GSVA 2.1.17
License: GPL (>= 2)
1 Quick start
GSVA is an R package distributed as part of the Bioconductor project. To install the package, start R and enter:
install.packages("BiocManager")
BiocManager::install("GSVA")Once GSVA is installed, it can be loaded with the following command.
library(GSVA)Given a gene expression data matrix, which we shall call X, with rows
corresponding to genes and columns to samples, such as this one simulated from
random Gaussian data:
p <- 10000 ## number of genes
n <- 30 ## number of samples
## simulate expression values from a standard Gaussian distribution
X <- matrix(rnorm(p*n), nrow=p,
dimnames=list(paste0("g", 1:p), paste0("s", 1:n)))
X[1:5, 1:5]
s1 s2 s3 s4 s5
g1 0.6255889 0.04564445 0.2463573 -0.70853958 -0.8643317
g2 1.4940572 0.13121533 1.1538494 0.16811523 0.8833759
g3 0.4771449 -0.21894061 0.1630454 -0.02304398 0.5643420
g4 -0.3394901 -0.32695829 0.2312632 -1.08156241 -0.1758333
g5 -1.3406257 0.67485964 0.4889498 -0.10952106 1.5236269Given a collection of gene sets stored, for instance, in a list object, which
we shall call gs, with genes sampled uniformly at random without replacement
into 100 different gene sets:
## sample gene set sizes
gs <- as.list(sample(10:100, size=100, replace=TRUE))
## sample gene sets
gs <- lapply(gs, function(n, p)
paste0("g", sample(1:p, size=n, replace=FALSE)), p)
names(gs) <- paste0("gs", 1:length(gs))We can calculate GSVA enrichment scores as follows. First we should build
a parameter object for the desired methodology. Here we illustrate it with
the GSVA algorithm of Hänzelmann, Castelo, and Guinney (2013) by calling the
function gsvaParam(), but other parameter object constructor functions
are available; see in the next section below.
gsvaPar <- gsvaParam(X, gs)
gsvaPar
A GSVA::gsvaParam object
expression data:
matrix [10000, 30]
rows: g1, g2, ..., g10000 (10000 total)
cols: s1, s2, ..., s30 (30 total)
using assay: none
using annotation:
geneIdType: Null
gene sets:
list
names: gs1, gs2, ..., gs100 (100 total)
unique identifiers: g590, g4648, ..., g1325 (4208 total)
gene set size: [1, Inf]
kcdf: auto
kcdfNoneMinSampleSize: 200
tau: 1
maxDiff: TRUE
absRanking: FALSE
checkNA: auto
missing data: noThe first argument to the gsvaParam() function constructing this parameter
object is the gene expression data matrix, and the second is the collection of
gene sets. In this example, we provide expression data and gene sets into
base R matrix and list objects, respectively, to the gsvaParam() function,
but it can take also different specialized containers that facilitate the access
and manipulation of molecular and phenotype data, as well as their associated
metadata.
Second, we call the gsva() function with the parameter object as first
argument. Other additional arguments to the gsva() function are verbose to
control progress reporting and BPPPARAM to perform calculations in parallel
through the package BiocParallel.
gsva.es <- gsva(gsvaPar, verbose=FALSE)
dim(gsva.es)
[1] 100 30
gsva.es[1:5, 1:5]
s1 s2 s3 s4 s5
gs1 0.08897954 -0.022999439 0.1024198 -0.203267207 -0.09001394
gs2 -0.02660668 0.004798259 0.1250146 0.004166502 -0.16064976
gs3 -0.17660381 0.037220504 -0.1262037 -0.019167018 -0.02558168
gs4 -0.35765558 0.154533049 0.1531882 -0.054275986 0.03955377
gs5 0.45626805 0.004635269 -0.3362622 0.049503539 0.168626062 Introduction
Gene set variation analysis (GSVA) provides an estimate of pathway activity by transforming an input gene-by-sample expression data matrix into a corresponding gene-set-by-sample expression data matrix. This resulting expression data matrix can be then used with classical analytical methods such as differential expression, classification, survival analysis, clustering or correlation analysis in a pathway-centric manner. One can also perform sample-wise comparisons between pathways and other molecular data types such as microRNA expression or binding data, copy-number variation (CNV) data or single nucleotide polymorphisms (SNPs).
The GSVA package provides an implementation of this approach for the following methods:
plage (Tomfohr, Lu, and Kepler 2005). Pathway level analysis of gene expression (PLAGE) standardizes expression profiles over the samples and then, for each gene set, it performs a singular value decomposition (SVD) over its genes. The coefficients of the first right-singular vector are returned as the estimates of pathway activity over the samples. Note that, because of how SVD is calculated, the sign of its singular vectors is arbitrary.
zscore (Lee et al. 2008). The z-score method standardizes expression profiles over the samples and then, for each gene set, combines the standardized values as follows. Given a gene set \(\gamma=\{1,\dots,k\}\) with standardized values \(z_1,\dots,z_k\) for each gene in a specific sample, the combined z-score \(Z_\gamma\) for the gene set \(\gamma\) is defined as: \[ Z_\gamma = \frac{\sum_{i=1}^k z_i}{\sqrt{k}}\,. \]
ssgsea (Barbie et al. 2009). Single sample GSEA (ssGSEA) is a non-parametric method that calculates a gene set enrichment score per sample as the normalized difference in empirical cumulative distribution functions (CDFs) of gene expression ranks inside and outside the gene set. By default, the implementation in the GSVA package follows the last step described in (Barbie et al. 2009, online methods, pg. 2) by which pathway scores are normalized, dividing them by the range of calculated values. This normalization step may be switched off using the argument
ssgsea.normin the call to thegsva()function; see below.gsva (Hänzelmann, Castelo, and Guinney 2013). This is the default method of the package and similarly to ssGSEA, is a non-parametric method that uses the empirical CDFs of gene expression ranks inside and outside the gene set, but it starts by calculating an expression-level statistic that brings gene expression profiles with different dynamic ranges to a common scale.
The interested user may find full technical details about how these methods work in their corresponding articles cited above. If you use any of them in a publication, please cite them with the given bibliographic reference.
3 Overview of the GSVA functionality
The workhorse of the GSVA package is the function gsva(), which takes
a parameter object as its main input. There are four classes of parameter
objects corresponding to the methods listed above, and may have different
additional parameters to tune, but all of them require at least the following
two input arguments:
- A normalized gene expression dataset, which can be provided in one of the
following containers:
- A
matrixof expression values with genes corresponding to rows and samples corresponding to columns. - An
ExpressionSetobject; see package Biobase. - A
SummarizedExperimentobject, see package SummarizedExperiment.
- A
- A collection of gene sets; which can be provided in one of the following
containers:
- A
listobject where each element corresponds to a gene set defined by a vector of gene identifiers, and the element names correspond to the names of the gene sets. - A
GeneSetCollectionobject; see package GSEABase.
- A
One advantage of providing the input data using specialized containers such as
ExpressionSet, SummarizedExperiment and GeneSetCollection is that the
gsva() function will automatically map the gene identifiers between the
expression data and the gene sets (internally calling the function
mapIdentifiers() from the package GSEABase), when they come
from different standard nomenclatures, i.e., Ensembl versus Entrez, provided
the input objects contain the appropriate metadata; see next section.
If either the input gene expression data is provided as a matrix object or
the gene sets are provided in a list object, or both, it is then the
responsibility of the user to ensure that both objects contain gene identifiers
following the same standard nomenclature.
Before the actual calculations take place, the gsva() function will apply
the following filters:
Discard genes in the input expression data matrix with constant expression.
Discard genes in the input gene sets that do not map to a gene in the input gene expression data matrix.
Discard gene sets that, after applying the previous filters, do not meet a minimum and maximum size, which by default is one for the minimum size and has no limit for the maximum size.
If, as a result of applying these three filters, either no genes or gene sets
are left, the gsva() function will prompt an error. A common cause for such
an error at this stage is that gene identifiers between the expression data
matrix and the gene sets do not belong to the same standard nomenclature and
could not be mapped. This may happen because either the input data were not
provided using some of the specialized containers described above or the
necessary metadata in those containers that allows the software to successfully
map gene identifiers, is missing.
The method employed by the gsva() function is determined by the class of the
parameter object that it receives as an input. An object constructed using the
gsvaParam() function runs the method described by
Hänzelmann, Castelo, and Guinney (2013), but this can be changed using the parameter
constructor functions plageParam(), zscoreParam(), or ssgseaParam(),
corresponding to the methods briefly described in the introduction; see also
their corresponding help pages.
When using gsvaParam(), the user can additionally tune the following
parameters, whose default values cover most of the use cases:
kcdf: The first step of the GSVA algorithm brings gene expression profiles to a common scale by calculating an expression statistic through the estimation of the CDF across samples. The way in which such an estimation is performed by GSVA is controlled by thekcdfparameter, which accepts the following four possible values: (1)"auto", the default value, lets GSVA automatically decide the estimation method; (2)"Gaussian", use a Gaussian kernel, suitable for continuous expression data, such as microarray fluorescent units in logarithmic scale and RNA-seq log-CPMs, log-RPKMs or log-TPMs units of expression; (2)"Poisson", use a Poisson kernel, suitable for integer counts, such as those derived from RNA-seq alignments; (3)"none", which will perform a direct estimation of the CDF without a kernel function.kcdfNoneMinSampleSize: Whenkcdf="auto", this parameter decides at what minimum sample sizekcdf="none", i.e., the estimation of the empirical cumulative distribution function (ECDF) of expression levels across samples is performed directly without using a kernel; see the previouskcdfparameter. By defaultkcdfNoneMinSampleSize=200.tau: Exponent defining the weight of the tail in the random walk. By defaulttau=1.maxDiff: The last step of the GSVA algorithm calculates the gene set enrichment score from two Kolmogorov-Smirnov random walk statistics. This parameter is a logical flag that allows the user to specify two possible ways to do such calculation: (1)TRUE, the default value, where the enrichment score is calculated as the magnitude difference between the largest positive and negative random walk deviations. This default value gives larger enrichment scores to gene sets whose genes are concordantly activated in one direction only; (2)FALSE, where the enrichment score is calculated as the maximum distance of the random walk from zero. This approach produces a distribution of enrichment scores that is bimodal, but it can be give large enrichment scores to gene sets whose genes are not concordantly activated in one direction only.absRanking: Logical flag used only whenmaxDiff=TRUE. By default,absRanking=FALSEand it implies that a modified Kuiper statistic is used to calculate enrichment scores, taking the magnitude difference between the largest positive and negative random walk deviations. WhenabsRanking=TRUEthe original Kuiper statistic is used, by which the largest positive and negative random walk deviations are added together.sparse: Logical flag used only when the input expression data is stored in a sparse matrix (e.g., adgCMatrixor aSingleCellExperimentobject storing the expression data in adgCMatrix). In such as case, whensparse=TRUE(default), a sparse version of the GSVA algorithm will be applied. Otherwise, whensparse=FALSE, the classical version of the GSVA algorithm will be used.
In general, the default values for the previous parameters are suitable for most analysis settings, which usually consist of some kind of normalized continuous expression values.
4 Gene set definitions and containers
Gene sets constitute a simple, yet useful, way to define pathways because we use pathway membership definitions only, neglecting the information on molecular interactions. Gene set definitions are a crucial input to any gene set enrichment analysis because if our gene sets do not capture the biological processes we are studying, we will likely not find any relevant insights in our data from an analysis based on these gene sets.
There are multiple sources of gene sets, the most popular ones being The Gene Ontology (GO) project and The Molecular Signatures Database (MSigDB). Sometimes gene set databases will not include the ones we need. In such a case we should either curate our own gene sets or use techniques to infer them from data.
The most basic data container for gene sets in R is the list class of objects,
as illustrated before in the quick start section, where we defined a toy collection
of three gene sets stored in a list object called gs:
class(gs)
[1] "list"
length(gs)
[1] 100
head(lapply(gs, head))
$gs1
[1] "g590" "g4648" "g5092" "g9660" "g8373" "g2893"
$gs2
[1] "g7140" "g7342" "g9331" "g8056" "g5866" "g7020"
$gs3
[1] "g9605" "g2451" "g1609" "g1140" "g5532" "g7760"
$gs4
[1] "g3861" "g4433" "g6316" "g1077" "g3111" "g2968"
$gs5
[1] "g7431" "g2970" "g7338" "g452" "g4285" "g7282"
$gs6
[1] "g6726" "g7335" "g9088" "g3221" "g9352" "g6099"Using a Bioconductor organism-level package such as org.Hs.eg.db we can easily build a list object containing a collection of gene sets defined as GO terms with annotated Entrez gene identifiers, as follows:
library(org.Hs.eg.db)
goannot <- select(org.Hs.eg.db, keys=keys(org.Hs.eg.db), columns="GO")
head(goannot)
ENTREZID GO EVIDENCE ONTOLOGY
1 1 GO:0002764 IBA BP
2 1 GO:0005576 HDA CC
3 1 GO:0005576 IDA CC
4 1 GO:0005576 TAS CC
5 1 GO:0005615 HDA CC
6 1 GO:0005886 IBA CC
genesbygo <- split(goannot$ENTREZID, goannot$GO)
length(genesbygo)
[1] 18640
head(genesbygo)
$`GO:0000002`
[1] "291" "1890" "4205" "4358" "4976" "6742" "9361" "10000" "55186"
[10] "55186" "80119" "84275" "84275" "92667"
$`GO:0000009`
[1] "55650" "79087"
$`GO:0000012`
[1] "1161" "2074" "3981" "7141" "7374" "7515"
[7] "23411" "54840" "54840" "54840" "55247" "55775"
[13] "55775" "200558" "100133315"
$`GO:0000014`
[1] "2021" "2067" "2072" "4361" "4361" "5932" "6419" "6419" "6419"
[10] "9941" "10111" "28990" "64421"
$`GO:0000015`
[1] "2023" "2023" "2026" "2027" "387712"
$`GO:0000016`
[1] "3938" "3938" "3938"A more sophisticated container for gene sets is the GeneSetCollection
object class defined in the GSEABase package, which also
provides the function getGmt() to import
gene matrix transposed (GMT) files such as those
provided by MSigDB into a
GeneSetCollection object. The experiment data package
GSVAdata provides one such object with the old (3.0) version
of the C2 collection of curated genesets from
MSigDB, which can be loaded as
follows.
library(GSEABase)
library(GSVAdata)
data(c2BroadSets)
class(c2BroadSets)
[1] "GeneSetCollection"
attr(,"package")
[1] "GSEABase"
c2BroadSets
GeneSetCollection
names: NAKAMURA_CANCER_MICROENVIRONMENT_UP, NAKAMURA_CANCER_MICROENVIRONMENT_DN, ..., ST_PHOSPHOINOSITIDE_3_KINASE_PATHWAY (3272 total)
unique identifiers: 5167, 100288400, ..., 57191 (29340 total)
types in collection:
geneIdType: EntrezIdentifier (1 total)
collectionType: BroadCollection (1 total)The documentation of GSEABase contains a description of the
GeneSetCollection class and its associated methods.
5 Importing gene sets from GMT files
An important source of gene sets is the Molecular Signatures Database (MSigDB) (Subramanian et al. 2005), which stores them in plain text files following the so-called gene matrix transposed (GMT) format. In the GMT format, each line stores a gene set with the following values separated by tabs:
- A unique gene set identifier.
- A gene set description.
- One or more gene identifiers.
Because each different gene set may consist of a different number of genes,
each line in a GMT file may contain a different number of tab-separated values.
This means that the GMT format is not a tabular format, and therefore cannot be
directly read with base R functions such as read.table() or read.csv().
We need a specialized function to read GMT files. We can find such a function
in the GSEABase package with getGmt(), or in the
qusage package with read.gmt().
GSVA also provides such a function called readGMT(), which takes as first
argument the filename or URL of a, possibly compressed, GMT file. The call
below illustrates how to read a GMT file from MSigDB providing its URL,
concretely the one corresponding to the C7 collection of immunologic signature
gene sets. Note that we also load the package GSEABase because,
by default, the value returned by readGMT() is a GeneSetCollection object
defined in that package.
library(GSEABase)
library(GSVA)
URL <- "https://data.broadinstitute.org/gsea-msigdb/msigdb/release/2024.1.Hs/c7.immunesigdb.v2024.1.Hs.symbols.gmt"
c7.genesets <- readGMT(URL)GeneSetCollection
names: GOLDRATH_EFF_VS_MEMORY_CD8_TCELL_DN, GOLDRATH_EFF_VS_MEMORY_CD8_TCELL_UP, ..., KAECH_NAIVE_VS_MEMORY_CD8_TCELL_UP (4872 total)
unique identifiers: ABCA2, ABCC5, ..., LINC00841 (20457 total)
types in collection:
geneIdType: SymbolIdentifier (1 total)
collectionType: NullCollection (1 total)By default, readGMT() returns a GeneSetCollection object, but this can be
switched to list object by setting the argument valueType="list". It will
also attempt to figure out the type of identifier used in the gene set and set
the corresponding metadata in the resulting object. However, this can be also
manually set either through the parameter geneIdType or in a call to the
setter method gsvaAnnotation():
gsvaAnnotation(c7.genesets) <- SymbolIdentifier("org.Hs.eg.db")This operation can actually also be done with list objects and it will add
the metadata through an R attribute that later the gsva() function will be
able to read. For understanding the different types of available gene
identifier metadata constructor functions, please consult the help page of
GeneIdentifierType in the GSEABase package.
The specification of the GMT format
establishes that duplicated gene set names are not allowed. For this reason,
the getGmt() function from the
GSEABase package prompts an error
when duplicated gene names are found, while the read.gmt() function from the
qusage package silently accepts them
in a list with duplicated element names.
The GSVA readGMT() function deals with duplicated gene set names as follows.
By default, readGMT() warns the user about a duplicated gene set name and
keeps only the first occurrence of the duplicated gene set in the returned
object. We can illustrate this situation with an old GMT file from the MSigDB
database that happens to have duplicated gene set names and which a small
subset of it is stored in the GSVAdata package.
fname <- system.file("extdata", "c2.subsetdups.v7.5.symbols.gmt.gz",
package="GSVAdata")
c2.dupgenesets <- getGmt(fname, geneIdType=SymbolIdentifier())
Error in validObject(.Object): invalid class "GeneSetCollection" object: each setName must be distinct
c2.dupgenesets
Error: object 'c2.dupgenesets' not foundWe can see that getGmt() prompts an error. We can see below that this does
not happen with readGMT() and that, by default, all but the first occurrence
of the duplicated gene set have been removed.
c2.dupgenesets <- readGMT(fname, geneIdType=SymbolIdentifier())
Warning in deduplicateGmtLines(lines, deduplUse): GMT contains duplicated gene
set names; deduplicated using method: first
c2.dupgenesets
GeneSetCollection
names: CORONEL_RFX7_DIRECT_TARGETS_UP, FOROUTAN_TGFB_EMT_UP, ..., CHANDRAN_METASTASIS_TOP50_DN (109 total)
unique identifiers: ABAT, DIP2A, ..., MSRB2 (6929 total)
types in collection:
geneIdType: SymbolIdentifier (1 total)
collectionType: NullCollection (1 total)
any(duplicated(names(c2.dupgenesets)))
[1] FALSEThe parameter deduplUse in the readGMT() function allow one to apply other
policies to deal with duplicated gene set names, see the help page of
readGMT() with ?readGMT for full details on this parameter.
6 Quantification of pathway activity in bulk microarray and RNA-seq data
Here we illustrate how GSVA provides an analogous quantification of pathway activity in both microarray and RNA-seq data by using two such datasets that have been derived from the same biological samples. More concretely, we will use gene expression data of lymphoblastoid cell lines (LCL) from HapMap individuals that have been profiled using both technologies (Huang et al. 2007, @pickrell_understanding_2010). These data form part of the experimental package GSVAdata and the corresponding help pages contain details on how the data were processed. We start loading these data and verifying that they indeed contain expression data for the same genes and samples, as follows:
library(Biobase)
data(commonPickrellHuang)
stopifnot(identical(featureNames(huangArrayRMAnoBatchCommon_eset),
featureNames(pickrellCountsArgonneCQNcommon_eset)))
stopifnot(identical(sampleNames(huangArrayRMAnoBatchCommon_eset),
sampleNames(pickrellCountsArgonneCQNcommon_eset)))Next, for the current analysis we use the subset of canonical pathways from the C2 collection of MSigDB Gene Sets v3.0. These correspond to the following pathways from KEGG, REACTOME and BIOCARTA:
canonicalC2BroadSets <- c2BroadSets[c(grep("^KEGG", names(c2BroadSets)),
grep("^REACTOME", names(c2BroadSets)),
grep("^BIOCARTA", names(c2BroadSets)))]
canonicalC2BroadSets
GeneSetCollection
names: KEGG_GLYCOLYSIS_GLUCONEOGENESIS, KEGG_CITRATE_CYCLE_TCA_CYCLE, ..., BIOCARTA_ACTINY_PATHWAY (833 total)
unique identifiers: 55902, 2645, ..., 8544 (6744 total)
types in collection:
geneIdType: EntrezIdentifier (1 total)
collectionType: BroadCollection (1 total)Additionally, we extend this collection of gene sets with two formed by genes
with sex-specific expression, which also form part of the GSVAdata
experiment data package. Here we use the constructor function GeneSet from the
GSEABase package to build the objects that we add to the
GeneSetCollection object canonicalC2BroadSets.
data(genderGenesEntrez)
MSY <- GeneSet(msYgenesEntrez, geneIdType=EntrezIdentifier(),
collectionType=BroadCollection(category="c2"),
setName="MSY")
MSY
setName: MSY
geneIds: 266, 84663, ..., 353513 (total: 34)
geneIdType: EntrezId
collectionType: Broad
bcCategory: c2 (Curated)
bcSubCategory: NA
details: use 'details(object)'
XiE <- GeneSet(XiEgenesEntrez, geneIdType=EntrezIdentifier(),
collectionType=BroadCollection(category="c2"),
setName="XiE")
XiE
setName: XiE
geneIds: 293, 8623, ..., 1121 (total: 66)
geneIdType: EntrezId
collectionType: Broad
bcCategory: c2 (Curated)
bcSubCategory: NA
details: use 'details(object)'
canonicalC2BroadSets <- GeneSetCollection(c(canonicalC2BroadSets, MSY, XiE))
canonicalC2BroadSets
GeneSetCollection
names: KEGG_GLYCOLYSIS_GLUCONEOGENESIS, KEGG_CITRATE_CYCLE_TCA_CYCLE, ..., XiE (835 total)
unique identifiers: 55902, 2645, ..., 1121 (6810 total)
types in collection:
geneIdType: EntrezIdentifier (1 total)
collectionType: BroadCollection (1 total)We calculate now GSVA enrichment scores for these gene sets using first the
normalized microarray data and then the normalized RNA-seq integer count data.
Note that the only requirement to do the latter is to set the argument
kcdf="Poisson", which is "Gaussian" by default. Note, however, that if our
RNA-seq normalized expression levels would be continuous, such as log-CPMs,
log-RPKMs or log-TPMs, the default value of the kcdf argument should remain
unchanged.
huangPar <- gsvaParam(huangArrayRMAnoBatchCommon_eset, canonicalC2BroadSets,
minSize=5, maxSize=500)
esmicro <- gsva(huangPar)
pickrellPar <- gsvaParam(pickrellCountsArgonneCQNcommon_eset,
canonicalC2BroadSets, minSize=5, maxSize=500,
kcdf="Poisson")
esrnaseq <- gsva(pickrellPar)We are going to assess how gene expression profiles correlate between microarray
and RNA-seq data and compare those correlations with the ones derived at pathway
level. To compare gene expression values of both technologies, we will transform
first the RNA-seq integer counts into log-CPM units of expression using the
cpm() function from the edgeR package.
library(edgeR)
lcpms <- cpm(exprs(pickrellCountsArgonneCQNcommon_eset), log=TRUE)We calculate Spearman correlations between gene expression profiles of the previous log-CPM values and the microarray RMA values.
genecorrs <- sapply(1:nrow(lcpms),
function(i, expmicro, exprnaseq)
cor(expmicro[i, ], exprnaseq[i, ], method="spearman"),
exprs(huangArrayRMAnoBatchCommon_eset), lcpms)
names(genecorrs) <- rownames(lcpms)Now calculate Spearman correlations between GSVA enrichment scores derived from the microarray and the RNA-seq data.
pwycorrs <- sapply(1:nrow(esmicro),
function(i, esmicro, esrnaseq)
cor(esmicro[i, ], esrnaseq[i, ], method="spearman"),
exprs(esmicro), exprs(esrnaseq))
names(pwycorrs) <- rownames(esmicro)Figure 1 below shows the two distributions of these correlations and we can see that GSVA enrichment scores provide an agreement between microarray and RNA-seq data comparable to the one observed between gene-level units of expression.
Figure 1: Comparison of correlation values of gene and pathway expression profiles derived from microarray and RNA-seq data
Finally, in Figure 2 we compare the actual GSVA enrichment scores for two gene sets formed by genes with sex-specific expression. Concretely, one gene set (XIE) formed by genes that escape chromosome X-inactivation in females (Carrel and Willard 2005) and another gene set (MSY) formed by genes located on the male-specific region of chromosome Y (Skaletsky et al. 2003).
Figure 2: Comparison of GSVA enrichment scores obtained from microarray and RNA-seq data for two gene sets formed by genes with sex-specific expression
We can see how microarray and RNA-seq single-sample GSVA enrichment scores correlate very well in these gene sets, with \(\rho=0.80\) for the male-specific gene set and \(\rho=0.79\) for the female-specific gene set. Male and female samples show higher GSVA enrichment scores in their corresponding gene set.
7 Example applications
7.1 Molecular signature identification
In (Verhaak et al. 2010) four subtypes of glioblastoma multiforme (GBM) -proneural, classical, neural and mesenchymal- were identified by the characterization of distinct gene-level expression patterns. Using four gene set signatures specific to brain cell types (astrocytes, oligodendrocytes, neurons and cultured astroglial cells), derived from murine models by Cahoy et al. (2008), we replicate the analysis of Verhaak et al. (2010) by using GSVA to transform the gene expression measurements into enrichment scores for these four gene sets, without taking the sample subtype grouping into account. We start by having a quick glance to the data, which forms part of the GSVAdata package:
data(gbm_VerhaakEtAl)
gbm_eset
ExpressionSet (storageMode: lockedEnvironment)
assayData: 11861 features, 173 samples
element names: exprs
protocolData: none
phenoData
rowNames: TCGA.02.0003.01A.01 TCGA.02.0010.01A.01 ...
TCGA.12.0620.01A.01 (173 total)
varLabels: subtype
varMetadata: labelDescription channel
featureData: none
experimentData: use 'experimentData(object)'
Annotation:
head(featureNames(gbm_eset))
[1] "AACS" "FSTL1" "ELMO2" "CREB3L1" "RPS11" "PNMA1"
table(gbm_eset$subtype)
Classical Mesenchymal Neural Proneural
38 56 26 53
data(brainTxDbSets)
lengths(brainTxDbSets)
astrocytic_up astroglia_up neuronal_up oligodendrocytic_up
85 88 98 70
lapply(brainTxDbSets, head)
$astrocytic_up
[1] "GRHL1" "GPAM" "PAPSS2" "MERTK" "BTG1" "SLC46A1"
$astroglia_up
[1] "BST2" "SERPING1" "ACTA2" "C9orf167" "C1orf31" "ANXA4"
$neuronal_up
[1] "STXBP1" "JPH4" "CACNG3" "BRUNOL6" "CLSTN2" "FAM123C"
$oligodendrocytic_up
[1] "DCT" "ZNF536" "GNG8" "ELOVL6" "NR2C1" "RCBTB1"GSVA enrichment scores for the gene sets contained in brainTxDbSets
are calculated, in this case using mx.diff=FALSE, as follows:
gbmPar <- gsvaParam(gbm_eset, brainTxDbSets, maxDiff=FALSE)
gbm_es <- gsva(gbmPar)Figure 3 shows the GSVA enrichment scores obtained for the up-regulated gene sets across the samples of the four GBM subtypes. As expected, the neural class is associated with the neural gene set and the astrocytic gene sets. The mesenchymal subtype is characterized by the expression of mesenchymal and microglial markers, thus we expect it to correlate with the astroglial gene set. The proneural subtype shows high expression of oligodendrocytic development genes, thus it is not surprising that the oligodendrocytic gene set is highly enriched for ths group. Interestingly, the classical group correlates highly with the astrocytic gene set. In summary, the resulting GSVA enrichment scores recapitulate accurately the molecular signatures from Verhaak et al. (2010).
library(RColorBrewer)
subtypeOrder <- c("Proneural", "Neural", "Classical", "Mesenchymal")
sampleOrderBySubtype <- sort(match(gbm_es$subtype, subtypeOrder),
index.return=TRUE)$ix
subtypeXtable <- table(gbm_es$subtype)
subtypeColorLegend <- c(Proneural="red", Neural="green",
Classical="blue", Mesenchymal="orange")
geneSetOrder <- c("astroglia_up", "astrocytic_up", "neuronal_up",
"oligodendrocytic_up")
geneSetLabels <- gsub("_", " ", geneSetOrder)
hmcol <- colorRampPalette(brewer.pal(10, "RdBu"))(256)
hmcol <- hmcol[length(hmcol):1]
heatmap(exprs(gbm_es)[geneSetOrder, sampleOrderBySubtype], Rowv=NA,
Colv=NA, scale="row", margins=c(3,5), col=hmcol,
ColSideColors=rep(subtypeColorLegend[subtypeOrder],
times=subtypeXtable[subtypeOrder]),
labCol="", gbm_es$subtype[sampleOrderBySubtype],
labRow=paste(toupper(substring(geneSetLabels, 1,1)),
substring(geneSetLabels, 2), sep=""),
cexRow=2, main=" \n ")
par(xpd=TRUE)
text(0.23,1.21, "Proneural", col="red", cex=1.2)
text(0.36,1.21, "Neural", col="green", cex=1.2)
text(0.47,1.21, "Classical", col="blue", cex=1.2)
text(0.62,1.21, "Mesenchymal", col="orange", cex=1.2)
mtext("Gene sets", side=4, line=0, cex=1.5)
mtext("Samples ", side=1, line=4, cex=1.5)
Figure 3: Heatmap of GSVA scores for cell-type brain signatures from murine models (y-axis) across GBM samples grouped by GBM subtype
7.2 Differential expression at pathway level
We illustrate here how to conduct a differential expression analysis at pathway level using the bulk RNA-seq data from (Costa et al. 2021). This dataset consists of stranded 2x75nt paired-end reads sequenced from whole blood stored in dried blood spots (DBS). Costa et al. (2021) generated these data from 21 DBS samples of extremely preterm newborns (neonates born before the 28th week of gestation), where 10 of them had been exposed to a fetal inflammatory response (FIR) before birth. A normalized matrix of logCPM units of expression of these data is stored in a SummarizedExperiment object in the package GSVAdata and can be loaded as follows:
data(geneprotExpCostaEtAl2021)
se <- geneExpCostaEtAl2021
se
class: SummarizedExperiment
dim: 11279 21
metadata(0):
assays(1): logCPM
rownames(11279): 100 10000 ... 9994 9997
rowData names(1): Symbol
colnames(21): BS03 BS04 ... BS23 BS24
colData names(2): FIR SexTo facilitate later on the automatic mapping of gene identifiers between gene
sets and RNA-seq data, we should add annotation metadata to the
SummarizedExperiment object as follows.
gsvaAnnotation(se) <- EntrezIdentifier("org.Hs.eg.db")Here we have used the metadata constructor function EntrezIdentifier()
because we can see that the gene identifiers in these expression data are
entirely formed by numerical digits and these correspond to
NCBI Entrez gene identifiers. The
sample (column) identifiers correspond to anonymized neonates, and the
column (phenotype) metadata describes the exposure to FIR and the sex of
the neonate. We can see that we have expression profiles for all four possible
combinations of FIR exposure and sex.
colData(se)
DataFrame with 21 rows and 2 columns
FIR Sex
<factor> <factor>
BS03 yes female
BS04 yes female
BS05 yes male
BS06 no female
BS07 no female
... ... ...
BS20 no female
BS21 yes male
BS22 no male
BS23 yes male
BS24 no male
table(colData(se))
Sex
FIR female male
no 4 7
yes 4 67.2.1 Data exploration at gene level
We do a brief data exploration at gene level, to have a sense of what we can
expect in our analysis at pathway level. Figure 4
below shows the projection in two dimensions of sample dissimilarity by means
of a
multidimensional scaling (MDS)
plot, produced with the plotMDS() function of the Bioconductor package
limma. We can observe that sample dissimilarity in RNA
expression from DBS samples is driven by the FIR and sex phenotypes, as shown
in Fig. 1C of Costa et al. (2021).
library(limma)
fircolor <- c(no="skyblue", yes="darkred")
sexpch <- c(female=19, male=15)
plotMDS(assay(se), col=fircolor[se$FIR], pch=sexpch[se$Sex])
Figure 4: Gene-level exploration
Multidimensional scaling (MDS) plot at gene level. Red corresponds to FIR=yes and blue to FIR=no, while circles and squares correspond, respectively, to female and male neonates.
7.2.2 Filtering of immunologic gene sets
Costa et al. (2021) report a postnatal activation of the innate immune system and an impairment of the adaptive immunity. For the purpose of exploring these results at pathway level, we will use the C7 collection of immunologic signature gene sets previously downloaded from the MSigDB database. We are going to futher filter this collection of gene sets to those formed by genes upregulated in innate leukocytes and adaptive mature lymphocytes, excluding those reported in studies on myeloid cells and the lupus autoimmune disease.
innatepat <- c("NKCELL_VS_.+_UP", "MAST_CELL_VS_.+_UP",
"EOSINOPHIL_VS_.+_UP", "BASOPHIL_VS_.+_UP",
"MACROPHAGE_VS_.+_UP", "NEUTROPHIL_VS_.+_UP")
innatepat <- paste(innatepat, collapse="|")
innategsets <- names(c7.genesets)[grep(innatepat, names(c7.genesets))]
length(innategsets)
[1] 53
adaptivepat <- c("CD4_TCELL_VS_.+_UP", "CD8_TCELL_VS_.+_UP", "BCELL_VS_.+_UP")
adaptivepat <- paste(adaptivepat, collapse="|")
adaptivegsets <- names(c7.genesets)[grep(adaptivepat, names(c7.genesets))]
excludepat <- c("NAIVE", "LUPUS", "MYELOID")
excludepat <- paste(excludepat, collapse="|")
adaptivegsets <- adaptivegsets[-grep(excludepat, adaptivegsets)]
length(adaptivegsets)
[1] 97
c7.genesets.filt <- c7.genesets[c(innategsets, adaptivegsets)]
length(c7.genesets.filt)
[1] 1507.2.3 Running GSVA
To run GSVA on these data we build first the parameter object.
gsvapar <- gsvaParam(se, c7.genesets.filt, assay="logCPM", minSize=5,
maxSize=300)Second, we run the GSVA algorithm by calling the gsva() function with the
previoulsy built parameter object.
es <- gsva(gsvapar)
es
class: SummarizedExperiment
dim: 150 21
metadata(0):
assays(1): es
rownames(150):
GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP
GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP ...
GSE7460_CD8_TCELL_VS_CD4_TCELL_ACT_UP
GSE7460_CD8_TCELL_VS_TREG_ACT_UP
rowData names(1): gs
colnames(21): BS03 BS04 ... BS23 BS24
colData names(2): FIR SexBecause the input expression data was provided in a SummmarizedExperiment
object, the output of gsva() is again a SummarizedExperiment object,
with two main differences with respect to the one given as input: (1)
the one or more matrices of molecular data in the assay slot of the input
object have been replaced by a single matrix of GSVA enrichment scores under
the assay name es; and (2) the collection of mapped and filtered gene sets
is included in the object and can be accessed using the methods geneSets()
and geneSetSizes().
assayNames(se)
[1] "logCPM"
assayNames(es)
[1] "es"
assay(es)[1:3, 1:3]
BS03
GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP -0.06960698
GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP 0.28080100
GSE18804_SPLEEN_MACROPHAGE_VS_TUMORAL_MACROPHAGE_UP -0.13668932
BS04
GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP 0.05293804
GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP -0.13064317
GSE18804_SPLEEN_MACROPHAGE_VS_TUMORAL_MACROPHAGE_UP 0.16337856
BS05
GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP -0.13353343
GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP -0.08696271
GSE18804_SPLEEN_MACROPHAGE_VS_TUMORAL_MACROPHAGE_UP -0.17543490head(lapply(geneSets(es), head))
$GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP
[1] "8540" "1645" "302" "314" "328" "9582"
$GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP
[1] "51703" "136" "29880" "240" "64682" "313"
$GSE18804_SPLEEN_MACROPHAGE_VS_TUMORAL_MACROPHAGE_UP
[1] "22" "9429" "55860" "1645" "347902" "302"
$GSE22886_NEUTROPHIL_VS_DC_UP
[1] "101" "84658" "222487" "2334" "57538" "200315"
$GSE22886_NEUTROPHIL_VS_MONOCYTE_UP
[1] "8748" "222487" "306" "25825" "699" "762"
$GSE2585_THYMIC_MACROPHAGE_VS_MTEC_UP
[1] "10347" "10449" "2015" "3268" "10327" "334" head(geneSetSizes(es))
GSE18804_SPLEEN_MACROPHAGE_VS_BRAIN_TUMORAL_MACROPHAGE_UP
122
GSE18804_SPLEEN_MACROPHAGE_VS_COLON_TUMORAL_MACROPHAGE_UP
141
GSE18804_SPLEEN_MACROPHAGE_VS_TUMORAL_MACROPHAGE_UP
147
GSE22886_NEUTROPHIL_VS_DC_UP
105
GSE22886_NEUTROPHIL_VS_MONOCYTE_UP
82
GSE2585_THYMIC_MACROPHAGE_VS_MTEC_UP
142 7.2.4 Data exploration at pathway level
We do again a data exploration, this time at pathway level. Figure 5 below, shows an MDS plot of GSVA enrichment scores. We can see again that most variability is driven by the FIR phenotype, but this time the sex phenotype does not seem to affect sample dissimilarity at pathway level, probably because the collection of gene sets we have used does not include gene sets formed by genes with sex-specific expression.
plotMDS(assay(es), col=fircolor[es$FIR], pch=sexpch[es$Sex])
Figure 5: Pathway-level exploration
Multidimensional scaling (MDS) plot at pathway level. Red corresponds to FIR=yes and blue to FIR=no, while circles and squares correspond, respectively, to female and male neonates.
7.2.5 Differential expression
We will perform now a differential expression analysis at pathway level using the Bioconductor packages limma (Smyth 2004) and sva, the latter to adjust for sample heterogeneity using surrogate variable analysis (Leek and Storey 2007)
library(sva)
library(limma)
## build design matrix of the model to which we fit the data
mod <- model.matrix(~ FIR, colData(es))
## build design matrix of the corresponding null model
mod0 <- model.matrix(~ 1, colData(es))
## estimate surrogate variables (SVs) with SVA
sv <- sva(assay(es), mod, mod0)
Number of significant surrogate variables is: 4
Iteration (out of 5 ):1 2 3 4 5
## add SVs to the design matrix of the model of interest
mod <- cbind(mod, sv$sv)
## fit linear models
fit <- lmFit(assay(es), mod)
## calculate moderated t-statistics using the robust regime
fit.eb <- eBayes(fit, robust=TRUE)
## summarize the extent of differential expression at 5% FDR
res <- decideTests(fit.eb)
summary(res)
(Intercept) FIRyes
Down 24 13 39 31 48 57
NotSig 119 97 64 82 69 91
Up 7 40 47 37 33 2As shown in Figure 6 below, GSVA scores tend to have
higher precision for larger gene sets1 Thanks to Gordon Smyth for pointing this out to us.,
albeit this trend breaks at the end of gene set sizes in this case. This trend
is usually more clear when GSVA scores are derived from gene sets including
smaller sizes (our smallest gene set here is about 100 genes), and from less
heterogenous expression data. Here we use the getter method geneSetSizes()
to obtain the vector of sizes of the gene sets filtered after the GSVA
calculations on the output of the gsva() function.
gssizes <- geneSetSizes(es)
plot(sqrt(gssizes), sqrt(fit.eb$sigma), xlab="Sqrt(gene sets sizes)",
ylab="Sqrt(standard deviation)", las=1, pch=".", cex=4)
lines(lowess(sqrt(gssizes), sqrt(fit.eb$sigma)), col="red", lwd=2)
Figure 6: Pathway-level differential expression analysis
Residual standard deviation of GSVA scores as a function of gene set size. Larger gene sets tend to have higher precision.
When this trend is present, we may improve the statistical power to detect
differentially expressed (DE) pathways by using the limma-trend pipeline
(Phipson et al. 2016). More concretely, we should call the eBayes() function
with the argument trend=x, where x is a vector of values corresponding to
the sizes of the gene sets. As we have already seen, the values of these sizes
can be easily obtained using GSVA’s function geneSetSizes() on the output of
the gsva() function. Here below, we call again eBayes() using the trend
parameter. In this case, however, the change in the number of FIR DE pathways
is negligible.
fit.eb.trend <- eBayes(fit, robust=TRUE, trend=gssizes)
res <- decideTests(fit.eb.trend)
summary(res)
(Intercept) FIRyes
Down 26 14 38 31 50 55
NotSig 118 96 65 79 67 92
Up 6 40 47 40 33 3We can select DE pathways with FDR < 5% as follows.
tt <- topTable(fit.eb.trend, coef=2, n=Inf)
DEpwys <- rownames(tt)[tt$adj.P.Val <= 0.05]
length(DEpwys)
[1] 54
head(DEpwys)
[1] "GSE3039_CD4_TCELL_VS_ALPHABETA_CD8_TCELL_UP"
[2] "GSE3982_NEUTROPHIL_VS_CENT_MEMORY_CD4_TCELL_UP"
[3] "GSE3982_EOSINOPHIL_VS_CENT_MEMORY_CD4_TCELL_UP"
[4] "GSE36392_EOSINOPHIL_VS_NEUTROPHIL_IL25_TREATED_LUNG_UP"
[5] "GSE3982_NEUTROPHIL_VS_TH2_UP"
[6] "GSE22886_NEUTROPHIL_VS_DC_UP" Figure 7 below shows a heatmap of the GSVA enrichment scores of the subset of the 54 DE pathways, clustered by pathway and sample. We may observe that, consistently with the findings of Costa et al. (2021), FIR-affected neonates display an enrichment of upregulated pathways associated with innate immunity, and an enrichment of downregulated pathways associated with adaptive immunity, with respect to FIR-unaffected neonates.
## get DE pathway GSVA enrichment scores, removing the covariates effect
DEpwys_es <- removeBatchEffect(assay(es[DEpwys, ]),
covariates=mod[, 2:ncol(mod)],
design=mod[, 1:2])
Coefficients not estimable: FIRyes
## cluster samples
sam_col_map <- fircolor[es$FIR]
names(sam_col_map) <- colnames(DEpwys_es)
sampleClust <- hclust(as.dist(1-cor(DEpwys_es, method="spearman")),
method="complete")
## cluster pathways
gsetClust <- hclust(as.dist(1-cor(t(DEpwys_es), method="pearson")),
method="complete")
## annotate pathways whether they are involved in the innate or in
## the adaptive immune response
labrow <- rownames(DEpwys_es)
mask <- rownames(DEpwys_es) %in% innategsets
labrow[mask] <- paste("(INNATE)", labrow[mask], sep="_")
mask <- rownames(DEpwys_es) %in% adaptivegsets
labrow[mask] <- paste("(ADAPTIVE)", labrow[mask], sep="_")
labrow <- gsub("_", " ", gsub("GSE[0-9]+_", "", labrow))
## pathway expression color scale from blue (low) to red (high)
library(RColorBrewer)
pwyexpcol <- colorRampPalette(brewer.pal(10, "RdBu"))(256)
pwyexpcol <- pwyexpcol[length(pwyexpcol):1]
## generate heatmap
heatmap(DEpwys_es, ColSideColors=fircolor[es$FIR], xlab="Samples",
ylab="Pathways", margins=c(2, 20), labCol="", labRow=labrow,
col=pwyexpcol, scale="row", Colv=as.dendrogram(sampleClust),
Rowv=as.dendrogram(gsetClust))
Figure 7: Pathway-level signature of FIR
Heatmap of GSVA enrichment scores from pathways being called DE with 5% FDR between FIR-affected and unaffected neonates.
8 Interactive web app
The gsva() function can be also used through an interactive web app developed
with shiny. To start it just type on the R console:
res <- igsva()It will open your browser with the web app shown here below. The button
SAVE & CLOSE will close the app and return the resulting object on the
R console. Hence, the need to call igsva() on the right-hand side of an
assignment if you want to store the result in your workspace. Alternatively,
you can use the DOWNLOAD button to download the result in a CSV file.
In the starting window of the web app, after running GSVA, a non-parametric
kernel density estimation of sample profiles of GSVA scores will be shown.
By clicking on one of the lines, the cumulative distribution of GSVA scores
for the corresponding samples will be shown in the GeneSets tab, as
illustrated in the image below.
9 Contributing
GSVA has benefited from contributions by multiple developers, see https://github.com/rcastelo/GSVA/graphs/contributors for a list of them. Contributions to the software codebase of GSVA are welcome as long as contributors abide to the terms of the Bioconductor Contributor Code of Conduct. If you want to contribute to the development of GSVA please open an issue to start discussing your suggestion or, in case of a bugfix or a straightforward feature, directly a pull request.
Session information
Here is the output of sessionInfo() on the system on which this document was
compiled running pandoc 2.7.3:
sessionInfo()
R version 4.5.0 RC (2025-04-04 r88126)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS
Matrix products: default
BLAS: /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
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
time zone: America/New_York
tzcode source: system (glibc)
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] sva_3.55.0 BiocParallel_1.41.5
[3] genefilter_1.89.0 mgcv_1.9-3
[5] nlme_3.1-168 RColorBrewer_1.1-3
[7] edgeR_4.5.10 limma_3.63.13
[9] GSVAdata_1.43.1 SummarizedExperiment_1.37.0
[11] GenomicRanges_1.59.1 GenomeInfoDb_1.43.4
[13] MatrixGenerics_1.19.1 matrixStats_1.5.0
[15] hgu95a.db_3.13.0 GSEABase_1.69.1
[17] graph_1.85.3 annotate_1.85.0
[19] XML_3.99-0.18 org.Hs.eg.db_3.21.0
[21] AnnotationDbi_1.69.1 IRanges_2.41.3
[23] S4Vectors_0.45.4 Biobase_2.67.0
[25] BiocGenerics_0.53.6 generics_0.1.3
[27] GSVA_2.1.17 BiocStyle_2.35.0
loaded via a namespace (and not attached):
[1] blob_1.2.4 Biostrings_2.75.4
[3] fastmap_1.2.0 SingleCellExperiment_1.29.2
[5] digest_0.6.37 rsvd_1.0.5
[7] lifecycle_1.0.4 survival_3.8-3
[9] statmod_1.5.0 KEGGREST_1.47.1
[11] RSQLite_2.3.9 magrittr_2.0.3
[13] compiler_4.5.0 rlang_1.1.6
[15] sass_0.4.10 tools_4.5.0
[17] yaml_2.3.10 knitr_1.50
[19] S4Arrays_1.7.3 bit_4.6.0
[21] DelayedArray_0.33.6 abind_1.4-8
[23] HDF5Array_1.35.16 grid_4.5.0
[25] beachmat_2.23.7 xtable_1.8-4
[27] Rhdf5lib_1.29.2 tinytex_0.56
[29] cli_3.6.4 rmarkdown_2.29
[31] crayon_1.5.3 httr_1.4.7
[33] rjson_0.2.23 DBI_1.2.3
[35] cachem_1.1.0 rhdf5_2.51.2
[37] splines_4.5.0 parallel_4.5.0
[39] BiocManager_1.30.25 XVector_0.47.2
[41] vctrs_0.6.5 Matrix_1.7-3
[43] jsonlite_2.0.0 bookdown_0.42
[45] BiocSingular_1.23.0 bit64_4.6.0-1
[47] irlba_2.3.5.1 magick_2.8.6
[49] locfit_1.5-9.12 h5mread_0.99.4
[51] jquerylib_0.1.4 codetools_0.2-20
[53] UCSC.utils_1.3.1 ScaledMatrix_1.15.0
[55] htmltools_0.5.8.1 rhdf5filters_1.19.2
[57] GenomeInfoDbData_1.2.14 R6_2.6.1
[59] sparseMatrixStats_1.19.0 evaluate_1.0.3
[61] lattice_0.22-7 png_0.1-8
[63] SpatialExperiment_1.17.0 memoise_2.0.1
[65] bslib_0.9.0 Rcpp_1.0.14
[67] SparseArray_1.7.7 xfun_0.52
[69] pkgconfig_2.0.3 References
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