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Determines whether an a priori defined set of genes shows statistically significant, concordant differences between two biological states

Two categories of GSEA procedures:

  • Competitive: compare genes in the test set relative to all other genes.
  • Self-contained: whether the gene-set is more DE than one were to expect under the null of no association between two phenotype conditions (without reference to other genes in the genome). For example the method by Jiang & Gentleman Bioinformatics 2007

See also BRB-ArrayTools -> GSEA.


  • XXX class is associated with the XXX gene sets (GSVA vignette)
  • XXX subtype is characterized by the expression of XXX markers, thus we expect it to correlate with the XXX gene set (GSVA vignette)
  • The XXX subtype shows high expression of XXX genes, thus the XXX gene sets is highly enriched for this group (GSVA vignette)


FDR cutoff

Why does GSEA use a false discovery rate (FDR) of 0.25 rather than the more classic 0.05?



Over-representation analysis. ?goana and ?kegga. See UserGuide 2.14 Gene ontology (GO) and pathway analysis.


fgsea package and download stat

  • ?exampleRanks gives a hint about how it was obtained. It is actually the t-statistic, not logFC.
    fit2 <- eBayes(fit2)
    de <- data.table(topTable(fit2, adjust.method="BH", number=12000, = "B"), 
                     keep.rownames = TRUE)
    plot(de$t, exampleRanks[match(de$rn, names(exampleRanks))]) # 45 degrees straight line
    # [1] -62.22877  52.59930
    # [1] -63.33703  53.28400
    # [1] -11.56067  12.57562
  • vignette
    data(examplePathways) # a list of length 1457 (pathways)
    data(exampleRanks)    # a vector of length 12000 (genes)
    fgseaRes <- fgsea(pathways = examplePathways, 
                       stats    = exampleRanks,
                       minSize  = 4,
                       maxSize  =10) # choose a small gene set in order to see the detail
    head(fgseaRes[order(pval), ], 1)
    #                            pathway         pval         padj   log2err        ES
    # 1: 5991601_Phosphorylation_of_Emi1 2.461461e-07 9.501241e-05 0.6749629 0.9472236
    #         NES size                           leadingEdge
    # 1: 2.082967    6 107995,12534,18817,67141,268697,56371
    plotEnrichment(examplePathways[["5991601_Phosphorylation_of_Emi1"]], exampleRanks)
    # still hard to understand the graph
    # Reduce the total number of genes
    match(examplePathways[["5991601_Phosphorylation_of_Emi1"]], names(exampleRanks)) 
    # [1] 11678 11593 11362 11553 11953 11383    NA    NA
    i <- match(examplePathways[["5991601_Phosphorylation_of_Emi1"]], names(exampleRanks))
    i <- na.omit(i)
    # plotEnrichment(examplePathways[["5991601_Phosphorylation_of_Emi1"]], exampleRanks[i])
    # GSEA statistic is not defined when all genes are selected
    plotEnrichment(examplePathways[["5991601_Phosphorylation_of_Emi1"]], exampleRanks[c(1,i)])
    # Easy to understand
    #    170942     12534     18817     56371     67141    107995    268697 
    # -63.33703  15.16265  13.46935  10.46504  12.70504  28.36914  10.67534

    Note shifting exampleRanks values will change the enrichment scores

                    exampleRanks) + labs(title="Programmed Cell Death") 
                # like sin() with one period
    # [1] -63.33703  53.28400
                    exampleRanks+64) + labs(title="Programmed Cell Death")
                # like a time series plot
                    exampleRanks-54) + labs(title="Programmed Cell Death")
                # same problem if we shift exampleRanks to all negative 

    including NE, NES, pval, etc. So it is not rank-based.

    fgseaRes2 <- fgsea(pathways = examplePathways, 
                       stats    = exampleRanks+2, # OR 2*(exampleRanks+2)
                       minSize  = 4,
                       maxSize  =10) 
    identical(fgseaRes, fgseaRes2)
    # [1] FALSE
    R> fgseaRes[1:3, c("ES", "NES", "pval")]
               ES        NES      pval
    1: -0.3087414 -0.6545067 0.8630705
    2:  0.4209054  1.0360288 0.4312268
    3: -0.4065043 -0.8617561 0.6431535
    R> fgseaRes2[1:3, c("ES", "NES", "pval")]
               ES        NES      pval
    1:  0.4554877  0.8284722 0.7201767
    2:  0.5520914  1.1604366 0.2833333
    3: -0.2908641 -0.5971951 0.9442724

    However, scaling won't change anything.

    fgseaRes3 <- fgsea(pathways = examplePathways, 
                       stats    = 2*exampleRanks,
                       minSize  = 4,
                       maxSize  =10)
    identical(fgseaRes, fgseaRes3)
    # [1] TRUE
  • ?collapsePathways. Collapse list of enriched pathways to independent ones.
  • DESeq results to pathways in 60 Seconds with the fgsea package
  • Performing GSEA using MSigDB gene sets in R

Subramanian algorithm

In the plot, (x-axis) genes are sorted by their expression across all samples. Y-axis represents enrichment score. See HOW TO PERFORM GSEA - A tutorial on gene set enrichment analysis for RNA-seq. Bars represents genes being in the gene set. Genes on the LHS/RHS are more highly expressed in the experimental/control group. Small p means this gene set is enriched in this experimental sample.

Rafael A Irizarry

Gene set enrichment analysis made simple


multiGSEA - Combining GSEA-based pathway enrichment with multi omics data integration.


Single sample


  • singscore
    • Paper Single sample scoring of molecular phenotypes. Our approach does not depend upon background samples and scores are thus stable regardless of the composition and number of samples being scored. In contrast, scores obtained by GSVA, z-score, PLAGE and ssGSEA can be unstable when less data are available (NS < 25). Simulation was conducted.
    • SingscoreAMLMutations
    • TotalScore = UpScore + DownScore
    • centerScore and knownDirection(=TRUE by default) parameters used in generateNull() and simpleScore() functions.
    • On the paper, epithelial and mesenchymal gene sets are up-regulated and TGFβ-EMT signature is bidirectional.
    • The pvalue calculation seems wrong. For example, the first sample D_Ctrl_R1 returns p=0.996 but it should be 2*(1-.996) according to the null distribution plot. However, the 1st sample is a control sample so we don't expect it has a large score; its p-value should be large?
  • Gene-set enrichment analysis workshop. Also use ExperimentHub, SummarizedExperiment, emtdata, GSEABase, msigdb, edgeR, limma, vissE, igraph & patchwork packages.
    • Functions in the GSEABase package help with reading, parsing and processing the signatures.


  • ssGSEAProjection (v9.1.2). Each ssGSEA enrichment score represents the degree to which the genes in a particular gene set are coordinately up- or down-regulated within a sample.
  • single sample GSEA (ssGSEA) from
  • How single sample GSEA works
  • Data formats gct (expression data format), gmt (gene set database format).
  • ssGSEA produced by Broad Gene Pattern is different from one produced by gsva package.
    • Actually they are not compatible. See a plot in singscore paper.
    • Gene Pattern also compute p-values testing the Spearman correlation
  • GSVA and SSGSEA for RNA-Seq TPM data.
    • Generally, negative enrichment values imply down-regulation of a signature / pathway; whereas, positive values imply up-regulation.
    • The idea is to then conduct a differential signature / pathway analysis (using, for example, limma) so that you can have, in addition to differentially expressed genes, differentially expressed signatures / pathways.
  • GSVA vignette. In GSEA Subramanian et al. (2005) it is also observed that the empirical null distribution obtained by permuting phenotypes is bimodal and, for this reason, significance is determined independently using the positive and negative sides of the null distribution.
  • Tips:
  • 纯R代码实现ssGSEA算法评估肿瘤免疫浸润程度. The pheatmap package was used to draw the heatmap. Original paper.
    • fpkm expression data was sorted by gene name & median values. Duplicated genes are removed. The data is transformed by log2(x+1) before sent to gsva()
    • NES scores are scaled and truncated to [-2, 2]. The scores are further scaled to have the range [0,1] before sending it to the heatmap function
  • gsva() from the GSVA package has an option to compute ssGSEA. 单样本基因集富集分析 --- ssGSEA (it includes the formula from Barbie's paper). The output of gsva() is a matrix of ES (# gene sets x # samples). It does not produce plots nor running the permutation tests. Notice the option ssgsea.norm. Note ssgsea.norm = TRUE (default) option will scale ES by the absolute difference of the max and min ES; Unscaled ES / (max(unscaled ES) - min(unscaled ES)). So the scaled ES values depends on the included samples. But it seems the impact of the included samples is small from some real data. See the source code on github and on how to debug an S4 function.
    p <- 10 ## number of genes
    n <- 30 ## number of samples
    nGrp1 <- 15 ## number of samples in group 1
    nGrp2 <- n - nGrp1 ## number of samples in group 2
    ## consider three disjoint gene sets
    geneSets <- list(set1=paste("g", 1:3, sep=""),
                     set2=paste("g", 4:6, sep=""),
                     set3=paste("g", 7:10, sep=""))
    ## sample data from a normal distribution with mean 0 and 1
    y <- matrix(rnorm(n*p), nrow=p, ncol=n,
                dimnames=list(paste("g", 1:p, sep="") , paste("s", 1:n, sep="")))
    ## genes in set1 are expressed at higher levels in the last 'nGrp1+1' to 'n' samples
    y[geneSets$set1, (nGrp1+1):n] <- y[geneSets$set1, (nGrp1+1):n] + 2
    gsva_es <- gsva(y, geneSets, method="ssgsea")
    dim(gsva_es) #  3 x 30
    hist(gsva_es) # bi-modal
    # [1] -0.4390651  0.5609349
    ## build design matrix
    design <- cbind(sampleGroup1=1, sampleGroup2vs1=c(rep(0, nGrp1), rep(1, nGrp2)))
    ## fit the same linear model now to the GSVA enrichment scores
    fit <- lmFit(gsva_es, design)
    ## estimate moderated t-statistics
    fit <- eBayes(fit)
    ## set1 is differentially expressed
    topTable(fit, coef="sampleGroup2vs1")
    #           logFC     AveExpr         t      P.Value    adj.P.Val         B
    # set1  0.5045008 0.272674410  8.065096 4.493289e-12 1.347987e-11 17.067380
    # set2 -0.1474396 0.029578749 -2.315576 2.301957e-02 3.452935e-02 -4.461466
    # set3 -0.1266808 0.001380826 -2.060323 4.246231e-02 4.246231e-02 -4.992049
    heatmaply(gsva_es)   # easy to see a pattern
                         # samples' clusters are not perfect
    heatmaply(gsva_es, scale = "none")  # 'scale' is not working?
    heatmaply(y, Colv = F, Rowv= F, scale = "none") # not easy to see a pattern
  • If we set ssgsea.norm=FALSE, do we get the same results when we compute ssgsea using a subset of samples?
    gsva1 <- gsva(y, geneSets, method="ssgsea", ssgsea.norm = FALSE)
    gsva2 <- gsva(y[, 1:2], geneSets, method="ssgsea", ssgsea.norm = FALSE)
    range(abs(gsva1[, 1:2] - gsva2)) # [1] 0 0
  • Verify ssgsea.norm = TRUE option.
    gsva_es <- gsva(y, geneSets, method="ssgsea")
    gsva1 <- gsva(y, geneSets, method="ssgsea", ssgsea.norm = FALSE)
    gsva2 <- gsva1 / abs(max(gsva1) - min(gsva1)) # abs(max(gsva1) - min(gsva1)) 8.9
    range(gsva_es)              # [1] -0.4390651  0.5609349
    range(abs(gsva_es - gsva2)) # [1] 0 0
  • Only ranks matters! If I replace the sample 1 gene expression values with the ranks, the ssgsea scores are not changed at all.
    y2 <- y
    y2[, 1] <- rank(y2[, 1])
    gsva2 <- gsva(y2, geneSets, method="ssgsea")
    gsva_es[, 1]
    #      set1       set2       set3 
    # 0.1927056  0.1699799 -0.1782934 
    gsva2[, 1]
    #      set1       set2       set3 
    # 0.1927056  0.1699799 -0.1782934 
    all.equal(gsva_es, gsva2)
    # [1] TRUE
    # How about the reverse ranking? No that will change everything.
    # The one with the smallest value was assigned one according to 
    # the definition of 'rank'
    y3[, 1] <- 11 - y2[, 1]
    gsva3 <- gsva(y3, geneSets, method="ssgsea")
    gsva3[, 1]
    #        set1         set2         set3 
    #-0.054991319 -0.009603802  0.191733634
    cbind(y[, 1], y2[, 1], y3[, 1])
    #           [,1] [,2] [,3]
    # g1  -1.2070657    2    9
    # g2   0.2774292    7    4
    # g3   1.0844412   10    1
    # g4  -2.3456977    1   10
    # g5   0.4291247    8    3
    # g6   0.5060559    9    2
    # g7  -0.5747400    4    7
    # g8  -0.5466319    6    5
    # g9  -0.5644520    5    6
    # g10 -0.8900378    3    8
  • Is mx.diff useful? No.
    gsva4 <- gsva(y, geneSets, method="ssgsea", mx.diff = FALSE)
    all.equal(gsva_es, gsva4)
    # [1] TRUE
  • A simple implementation of ssGSEA (single sample gene set enrichment analysis)
  • Use "ssgsea-gui.R". The first question is a folder containing input files GCT. The 2nd question is about gene set database in GMT format. This has to be very restrict. For example, "ptm.sig.db.all.uniprot.human.v1.9.0.gmt" and "ptm.sig.db.all.sitegrpid.human.v1.9.0.gmt" provided in github won't work with the example GCT file.
    # select a folder containing gct files; e.g. PI3K_pert_logP_n2x23936.gct 
    # select a gene set file; e.g. <ptm.sig.db.all.flanking.human.v1.8.1.gmt>

    A new folder (e.g. 2021-03-01) will be created under the same parent folder as the gct file folder.

    tree -L 1 ~/github/ssGSEA2.0/example/gct/2021-03-20/                         
    ├── PI3K_pert_logP_n2x23936_ssGSEA-combined.gct
    ├── PI3K_pert_logP_n2x23936_ssGSEA-fdr-pvalues.gct
    ├── PI3K_pert_logP_n2x23936_ssGSEA-pvalues.gct
    ├── PI3K_pert_logP_n2x23936_ssGSEA-scores.gct
    ├── PI3K_pert_logP_n2x23936_ssGSEA.RData
    ├── parameters.txt
    ├── rank-plots
    ├── run.log
    └── signature_gct
    tree ~/github/ssGSEA2.0/example/gct/2021-03-20/rank-plots | head -3 
    # 102 files. One file per matched gene set
    ├── DISEASE.PSP_Alzheime_2.pdf
    ├── DISEASE.PSP_breast_c_2.pdf
    tree ~/github/ssGSEA2.0/example/gct/2021-03-20/signature_gct | head -3                    
    # 102 files. One file per matched gene set
    ├── DISEASE.PSP_Alzheimer.s_disease_n2x23.gct
    ├── DISEASE.PSP_breast_cancer_n2x14.gct

    Since the GCT file contains 2 samples (the last 2 columns), ssGSEA produces one rank plot for each gene set (with adjusted p-value & the plot could contain multiple samples). The ES scores are saved in <PI3K_pert_logP_n2x23936_ssGSEA-scores> and adjust p-values are saved in <PI3K_pert_logP_n2x23936_ssGSEA-fdr-pvalues>.


  • Some possible problems using ssGSEA to replace GSEA for DE analysis? See a toy example on Single Sample GSEA (ssGSEA) and dynamic range of expression. PS: the rank values table is wrong; they should be reversed.
  • In general terms, PLAGE and z-score are parametric and should perform well with close-to-Gaussian expression profiles, and ssGSEA and GSVA are non-parametric and more robust to departures of Gaussianity in gene expression data. See Method and kcdf arguments in gsva package
  • Some discussions from Find -> "ssgsea"
  • Some papers.
  • 【生信分析 3】教你看懂GSEA和ssGSEA分析结果. No groups/classes in the data (6:33). Output is a heatmap. Each value is computed sample by sample. Rows = gene set. Columns = (sorted by the 1st gene set) samples.


escape - Easy single cell analysis platform for enrichment. Github.


Toward a gold standard for benchmarking gene set enrichment analysis Geistlinger, 2021. GSEABenchmarkeR package in Bioconductor.


Selected papers



Gene-set distance analysis (GSDA): a powerful tool for gene-set association analysis


  • C1: Hallmark
  • C2: Curated gene sets including BioCarta, KEGG, Reactome
  • C5: Oncology


  • Epithelial (170 genes), mesenchymal gene signatures 218-170 genes). Tan et al. 2014 and can be found in the ‘Table S1B. Generic EMT signature for cell line’ (Epi/Mes column) in the supplementary tables file. See here. I save the gene lists in Github.