Gene set enrichment analysis with topGO

#

Gene set enrichment analysis with topGO

# Introduction

The `topGO` package is designed to facilitate semi-automated enrichment analysis for Gene Ontology (GO) terms. The process consists of input of normalised gene expression measurements, gene-wise correlation or differential expression analysis, enrichment analysis of GO terms, interpretation and visualisation of the results.

One of the main advantages of `topGO` is the unified gene set testing framework it offers. Besides providing an easy to use set of functions for performing GO enrichment analysis, it also enables the user to easily implement new statistical tests or new algorithms that deal with the GO graph structure. This unified framework also facilitates the comparison between different GO enrichment methodologies.

There are a number of test statistics and algorithms dealing with the GO graph structured ready to use in `topGO`. Table @ref(tab:algos) presents the compatibility table between the test statistics and GO graph methods.

Algorithms currently supported by `topGO`
| fisher | ks | t | globaltest | sum
--- | --- | --- | --- | --- | ---
classic | ✅ | ✅ | ✅ | ✅ | ✅
elim | ✅ | ✅ | ✅ | ✅ | ✅
weight | ✅ | 🔴 | 🔴 | 🔴 | 🔴
weight01 | ✅ | ✅ | ✅ | ✅ | ✅
lea | ✅ | ✅ | ✅ | ✅ | ✅
parentchild | ✅ | 🔴 | 🔴 | 🔴 | 🔴

The `elim` and `weight` algorithms were introduced in (Alexa et al. 2006). The default algorithm used by the `topGO` package is a mixture between the `elim` and the `weight` algorithms and it will be referred as `weight01`. The `parentChild` algorithm was introduced by (Grossmann et al. 2007).

We assume the user has a good understanding of GO, see (Consortium 2001; Yon Rhee et al. 2008), and is familiar with gene set enrichment tests. Also this document requires basic knowledge of R language.

The next section presents a quick tour into `topGO` and is thought to be independent of the rest of this manuscript. The remaining sections provide details on the functions used in the sample section as well as showing more advance functionality implemented in the `topGO` package.

# Installation

This section briefly describe the necessary to get `topGO` running on your system. We assume that the user have the R program (see the R project at https://www.r-project.org) already installed and its familiar with it. You will need to have R 2.10.0 or later to be able to install and run `topGO`.

The `topGO` package is available from the Bioconductor repository at https://www.bioconductor.org. To be able to install the package one needs first to install the core Bioconductor packages. If you have already installed Bioconductor packages on your system then you can skip the two lines below.

    if (!requireNamespace("BiocManager", quietly=TRUE))
        install.packages("BiocManager")
    BiocManager::install()

Once the core Bioconductor packages are installed, we can install the `topGO` package by

    BiocManager::install("topGO")

# Quick start guide

This section describes a simple working session using `topGO`. There are only a handful of commands necessary to perform a gene set enrichment analysis which will be briefly presented below.

A typical session can be divided into three steps:

1. Data preparation: List of genes identifiers, gene scores, list of differentially expressed genes or a criteria for selecting genes based on their scores, as well as gene-to-GO annotations are all collected and stored in a single `R` object.

2. Running the enrichment tests: Using the object created in the first step the user can perform enrichment analysis using any feasible mixture of statistical tests and methods that deal with the GO topology.

3. Analysis of the results: The results obtained in the second step are analysed using summary functions and visualisation tools.

Before going through each of those steps the user needs to decide which biological question he would like to investigate. The aim of the study, as well as the nature of the available data, will dictate which test statistic/methods need to used.

In this section we will test the enrichment of GO terms with differentially expressed genes using two statistical tests, namely Kolmogorov-Smirnov test and Fisher’s exact test.

## Data preparation

In the first step a convenient `R` object of class `topGOdata` is created containing all the information required for the remaining two steps. The user needs to provide the gene universe, GO annotations and either a criteria for selecting interesting genes (e.g. differentially expressed genes) from the gene universe or a score associated with each gene.

In this session we will test the enrichment of GO terms with differentially expressed genes. Thus, the starting point is a list of genes and the respective \(p\)-values for differential expression. A toy example of a list of gene \(p\)-values is provided by the `geneList` object.

    library(topGO)
    library(ALL)
    data(ALL)
    data(geneList)

The `geneList` data is based on a differential expression analysis of the ALL (Acute Lymphoblastic Leukemia) dataset that was extensively studied in the literature on microarray analysis (Chiaretti, S., et al. 2004). Our toy example contains just a small amount, 323, of genes and their corresponding \(p\)-values. The next data one needs are the gene groups itself, the GO terms in our case, and the mapping that associate each gene with one or more GO term(s). The information on where to find the GO annotations is stored in the `ALL` object and it is easily accessible.

    affyLib <- paste(annotation(ALL), "db", sep = ".")
    library(package = affyLib, character.only = TRUE)

The microarray used in the experiment is the hgu95av2 from Affymetrix, as we can see from the `affyLib` object. When we loaded the `geneList` object a selection function used for defining the list of differentially expressed genes is also loaded under the name of `topDiffGenes`. The function assumes that the provided argument is a named vector of \(p\)-values. With the help of this function we can see that there are 50 genes with a raw \(p\)-value less than \(0.01\) out of a total of 323 genes.

    sum(topDiffGenes(geneList))
    #> [1] 50

We now have all data necessary to build an object of type `topGOdata`. This object will contain all gene identifiers and their scores, the GO annotations, the GO hierarchical structure and all other information needed to perform the desired enrichment analysis.

    sampleGOdata <- new("topGOdata",
                        description = "Simple session", ontology = "BP",
                        allGenes = geneList, geneSel = topDiffGenes,
                        nodeSize = 10,
                        annot = annFUN.db, affyLib = affyLib)

The names of the arguments used for building the `topGOdata` object should be self-explanatory. We quickly mention that `nodeSize = 10` is used to prune the GO hierarchy from the terms which have less than \(10\) annotated genes and that `annFUN.db` function is used to extract the gene-to-GO mappings from the `affyLib` object. Section @ref(sec:topGOdata) describes the parameters used to build the `topGOdata` in details.

A summary of the `sampleGOdata` object can be seen by typing the object name at the R prompt. Having all the data stored into this object facilitates the access to identifiers, annotations and to basic data statistics.

    sampleGOdata
    #>
    #> ------------------------- topGOdata object -------------------------
    #>
    #>  Description:
    #>    -  Simple session
    #>
    #>  Ontology:
    #>    -  BP
    #>
    #>  323 available genes (all genes from the array):
    #>    - symbol:  1095_s_at 1130_at 1196_at 1329_s_at 1340_s_at  ...
    #>    - score :  1 1 0.62238 0.541224 1  ...
    #>    - 50  significant genes.
    #>
    #>  315 feasible genes (genes that can be used in the analysis):
    #>    - symbol:  1095_s_at 1130_at 1196_at 1329_s_at 1340_s_at  ...
    #>    - score :  1 1 0.62238 0.541224 1  ...
    #>    - 50  significant genes.
    #>
    #>  GO graph (nodes with at least  10  genes):
    #>    - a graph with directed edges
    #>    - number of nodes = 993
    #>    - number of edges = 2056
    #>
    #> ------------------------- topGOdata object -------------------------

## Performing the enrichment tests

Once we have an object of class `topGOdata` we can start with the enrichment analysis. We will use two types of test statistics: Fisher’s exact test which is based on gene counts, and a Kolmogorov-Smirnov like test which computes enrichment based on gene scores. We can use both these tests since each gene has a score (representing how differentially expressed a gene is) and by the means of `topDiffGenes` functions the genes are categorized into differentially expressed or not differentially expressed genes. All these are stored into `sampleGOdata` object.

The function `runTest` is used to apply the specified test statistic and method to the data. It has three main arguments. The first argument needs to be an object of class `topGOdata`. The second and third argument are of type character; they specify the method for dealing with the GO graph structure and the test statistic, respectively.

First, we perform a classical enrichment analysis by testing the over-representation of GO terms within the group of differentially expressed genes. For the method `classic` each GO category is tested independently.

    resultFisher <- runTest(sampleGOdata,
                            algorithm = "classic", statistic = "fisher")

`runTest` returns an object of class `topGOresult`. A short summary of this object is shown below.

    resultFisher
    #>
    #> Description: Simple session
    #> Ontology: BP
    #> 'classic' algorithm with the 'fisher' test
    #> 993 GO terms scored: 71 terms with p < 0.01
    #> Annotation data:
    #>     Annotated genes: 315
    #>     Significant genes: 50
    #>     Min. no. of genes annotated to a GO: 10
    #>     Nontrivial nodes: 901

Next we will test the enrichment using the Kolmogorov-Smirnov test. We will use the both the `classic` and the `elim` method.

    resultKS <- runTest(sampleGOdata, algorithm = "classic", statistic = "ks")
    resultKS.elim <- runTest(sampleGOdata, algorithm = "elim", statistic = "ks")

Please note that not all statistical tests work with every method. The compatibility matrix between the methods and statistical tests is shown in Table @ref(tab:algos)).

The \(p\)-values computed by the `runTest` function are unadjusted for multiple testing. We do not advocate against adjusting the \(p\)-values of the tested groups, however in many cases adjusted \(p\)-values might be misleading.

## Analysis of results

After the enrichment tests are performed the researcher needs tools for analysing and interpreting the results. `GenTable` is an easy to use function for analysing the most significant GO terms and the corresponding \(p\)-values. In the following example, we list the top \(10\) significant GO terms identified by the `elim` method. At the same time we also compare the ranks and the \(p\)-values of these GO terms with the ones obtained by the `classic` method.

    allRes <- GenTable(sampleGOdata, classicFisher = resultFisher,
                       classicKS = resultKS, elimKS = resultKS.elim,
                       orderBy = "elimKS", ranksOf = "classicFisher", topNodes = 10)

The `GenTable` function returns a data frame containing the top `topNodes` GO terms identified by the `elim` algorithm, see `orderBy` argument. The data frame includes some statistics on the GO terms and the \(p\)-values corresponding to each of the `topGOresult` object specified as arguments. Table @ref(tab:sampleGOresults) shows the results.

Significance of GO terms according to `classic` and `elim` methods.
GO.ID | Term | Annotated | Significant | Expected | Rank in classicFisher | classicFisher | classicKS | elimKS
--- | --- | --- | --- | --- | --- | --- | --- | ---
GO:0051301 | cell division | 146 | 16 | 23.17 | 879 | 0.99179 | 1.8e-07 | 5.8e-07
GO:0032743 | positive regulation of interleukin-2 pro… | 10 | 8 | 1.59 | 1 | 8.5e-06 | 1.6e-05 | 1.6e-05
GO:0050852 | T cell receptor signaling pathway | 10 | 8 | 1.59 | 2 | 8.5e-06 | 1.6e-05 | 1.6e-05
GO:0033077 | T cell differentiation in thymus | 13 | 9 | 2.06 | 5 | 1.4e-05 | 2.5e-05 | 2.5e-05
GO:0043368 | positive T cell selection | 10 | 7 | 1.59 | 8 | 0.00014 | 0.00021 | 0.00021
GO:0070670 | response to interleukin-4 | 11 | 6 | 1.75 | 36 | 0.00296 | 0.00051 | 0.00051
GO:0032465 | regulation of cytokinesis | 15 | 2 | 2.38 | 601 | 0.72041 | 0.00088 | 0.00088
GO:0090068 | positive regulation of cell cycle proces… | 54 | 5 | 8.57 | 831 | 0.95907 | 0.00142 | 0.00142
GO:0008608 | attachment of spindle microtubules to ki… | 25 | 1 | 3.97 | 870 | 0.98902 | 0.00147 | 0.00147
GO:0030183 | B cell differentiation | 12 | 6 | 1.90 | 43 | 0.00520 | 0.00193 | 0.00193

For accessing the GO term’s \(p\)-values from a `topGOresult` object the user should use the `score` functions. As a simple example, we look at the differences between the results of the `classic` and the `elim` methods in the case of the Kolmogorov-Smirnov test. The `elim` method was design to be more conservative then the `classic` method and therefore one expects the \(p\)-values returned by the former method are lower bounded by the \(p\)-values returned by the later method. The easiest way to visualize this property is to scatter plot the two sets of \(p\)-values against each other.

    pValue.classic <- score(resultKS)
    pValue.elim <- score(resultKS.elim)[names(pValue.classic)]

    gstat <- termStat(sampleGOdata, names(pValue.classic))
    gSize <- gstat$Annotated / max(gstat$Annotated) * 4
    gCol <- colMap(gstat$Significant)

    plot(pValue.classic, pValue.elim,
         xlab = "p-value classic", ylab = "p-value elim",
         pch = 19, cex = gSize, col = gCol)

\(p\)-values scatter plot for the `classic` (\(x\) axis) and `elim` (\(y\) axis) methods. On the right panel the \(p\)-values are plotted on a linear scale. The left panned plots the same \(p\)-values on a logarithmic scale. The size of the dot is proportional with the number of annotated genes for the respective GO term and its coloring represents the number of significantly differentially expressed genes, with the dark red points having more genes then the yellow ones.

We can see in Figure @ref(fig:scatterClassicElim) that there are indeed differences between the two methods. Some GO terms found significant by the `classic` method are less significant in the `elim`, as expected. However, in some cases, we can visible identify a few GO terms for which the `elim` \(p\)-value is less conservative then the `classic` \(p\)-value. If such GO terms exist, we can identify them and find the number of annotated genes:

    sel.go <- names(pValue.classic)[pValue.elim < pValue.classic]
    cbind(termStat(sampleGOdata, sel.go),
          elim = pValue.elim[sel.go],
          classic = pValue.classic[sel.go])
    #>            Annotated Significant Expected       elim   classic
    #> GO:0006139       118          23    18.73 0.13414662 0.3205307
    #> GO:0022607       107          18    16.98 0.16203435 0.2122289
    #> GO:0044085       113          20    17.94 0.24408774 0.3005141
    #> GO:0090304       115          23    18.25 0.09909579 0.1744541

It is quite interesting that such cases appear - the above table will not be empty. These GO terms are rather general (having many annotated genes) and their \(p\)-values are not significant at the \(0.05\) level. Therefore these GO terms would not appear in the list of top significant terms. More significant GO terms are less likely to be influenced by this non monotonic behavior.

Another insightful way of looking at the results of the analysis is to investigate how the significant GO terms are distributed over the GO graph. Figure @ref(fig:sampleGOelim) shows the the subgraph induced by the \(5\) most significant GO terms as identified by the `elim` algorithm. Significant nodes are represented as rectangles. The plotted graph is the upper induced graph generated by these significant nodes.

    showSigOfNodes(sampleGOdata, score(resultKS.elim),
                   firstSigNodes = 5, useInfo = 'all')

The subgraph induced by the top \(5\) GO terms identified by the `elim` algorithm for scoring GO terms for enrichment. Rectangles indicate the \(5\) most significant terms. Rectangle color represents the relative significance, ranging from dark red (most significant) to bright yellow (least significant). For each node, some basic information is displayed. The first two lines show the GO identifier and a trimmed GO name. In the third line the raw p-value is shown. The forth line is showing the number of significant genes and the total number of genes annotated to the respective GO term.

# Loading genes and annotations data

## Getting started

To demonstrate the package functionality we will use the ALL (Acute Lymphoblastic Leukemia) gene expression data from (Chiaretti, S., et al. 2004). The dataset consists of \(128\) microarrays from different patients with ALL measured using the HGU95aV2 Affymetrix chip. Additionally, custom annotations and artificial datasets will be used to demonstrate specific features.

We first load the required libraries and data:

    library(topGO)
    library(ALL)
    data(ALL)

When the `topGO` package is loaded, three environments `GOBPTerm`, `GOMFTerm` and `GOCCTerm` are created and bound to the package environment. These environments are build based on the `GOTERM` environment from package `GO.db`. They are used for fast recovering of the information specific to each of the three ontologies: BP, MF and CC. In order to access all GO groups that belong to a specific ontology, e.g. Biological Process (BP), one can type:

    BPterms <- ls(GOBPTerm)
    head(BPterms)
    #> [1] "GO:0000001" "GO:0000011" "GO:0000012" "GO:0000017" "GO:0000018" "GO:0000019"

Usually one needs to remove probes/genes with low expression value as well as probes with very small variability across samples. The package `genefilter` provides tools for filtering genes. In this analysis we choose to filter as many genes as possible for computational reasons; working with a smaller gene universe allows us to exemplify more of the functionalities implemented in the `topGO` package and at the same time allows this document to be compiled in a relatively short time. The effect of gene filtering is discussed in more details in Section @ref(subsec:GOannotations).

    library(genefilter)
    selProbes <- genefilter(ALL, filterfun(pOverA(0.20, log2(100)),
                                           function(x) (IQR(x) > 0.25)))
    eset <- ALL[selProbes, ]
    eset
    #> ExpressionSet (storageMode: lockedEnvironment)
    #> assayData: 4101 features, 128 samples
    #>   element names: exprs
    #> protocolData: none
    #> phenoData
    #>   sampleNames: 01005 01010 ... LAL4 (128 total)
    #>   varLabels: cod diagnosis ... date last seen (21 total)
    #>   varMetadata: labelDescription
    #> featureData: none
    #> experimentData: use 'experimentData(object)'
    #>   pubMedIds: 14684422 16243790
    #> Annotation: hgu95av2

The filter selects only 4101 probesets out of 12625 probesets available on the hgu95av2 array.

#### The gene universe and the set of interesting genes

The set of all genes from the array/study will be referred from now on as the gene universe. Having the gene universe, the user can define a list of interesting genes or to compute gene-wise scores that quantify the significance of each gene. When gene-wise scores are available the list of interesting genes is defined to be the set of gene with a significant score. The `topGO` package deals with these two cases in a unified way once the main data container, the `topGOdata` object, is constructed. The only time the user needs to distinguish between these two cases is during the construction of the data container.

Usually, the gene universe is defined as all feasible genes measured by the microarray. In the case of the ALL dataset we have 4101 feasible genes, the ones that were not removed by the filtering procedure.

## The `topGOdata` object

The central step in using the `topGO` package is to create a `topGOdata` object. This object will contain all information necessary for the GO analysis, namely the list of genes, the list of interesting genes, the gene scores (if available) and the part of the GO ontology (the GO graph) which needs to be used in the analysis. The `topGOdata` object will be the input of the testing procedures, the evaluation and visualisation functions.

To build such an object the user needs the following:

- A list of gene identifiers and optionally the gene-wise scores. The score can be the \(t\)-test statistic (or the \(p\)-value) for differential expression, correlation with a phenotype, or any other relevant score.

- A mapping between gene identifiers and GO terms. In most cases this mapping is directly available in Bioconductor as a microarray specific annotation package. In this case the user just needs to specify the name of the annotation to be used. For example, the annotation package needed for the ALL dataset is hgu95av2.db.

  Of course, Bioconductor does not include up-to-date annotation packages for all platforms. Users who work with custom arrays or wish to use a specific mapping between genes and GO terms, have the possibility to load custom annotations. This is described in Section @ref(subsec:annotations).

- The GO hierarchical structure. This structure is obtained from the `GO.db` package. At the moment `topGO` supports only the ontology definition provided by `GO.db`.

We further describe the arguments of the `initialize` function (`new()`) used to construct an instance of this data container object.

- `ontology`: character string specifying the ontology of interest (BP, MF or CC)

- `description`: character string containing a short description of the study [optional].

- `allGenes`: named vector of type numeric or factor. The names attribute contains the genes identifiers. The genes listed in this object define the gene universe.

- `geneSelectionFun`: function to specify which genes are interesting based on the gene scores. It should be present iff the `allGenes` object is of type numeric.

- `nodeSize`: an integer larger or equal to \(1\). This parameter is used to prune the GO hierarchy from the terms which have less than `nodeSize` annotated genes (after the true path rule is applied).

- `annotationFun`: function which maps genes identifiers to GO terms. There are a couple of annotation function included in the package trying to address the user’s needs. The annotation functions take three arguments. One of those arguments is specifying where the mappings can be found, and needs to be provided by the user. Here we give a short description of each:

  - `annFUN.db`: this function is intended to be used as long as the chip used by the user has an annotation package available in Bioconductor.

  - `annFUN.org`: this function is using the mappings from the “org.XX.XX” annotation packages. Currently, the function supports the following gene identifiers: Entrez, GenBank, Alias, Ensembl, Gene Symbol, GeneName and UniGene.

  - `annFUN.gene2GO`: this function is used when the annotations are provided as a gene-to-GOs mapping.

  - `annFUN.GO2gene`: this function is used when the annotations are provided as a GO-to-genes mapping.

  - `annFUN.file`: this function will read the annotationsof the type gene2GO or GO2genes from a text file.

- `...`: list of arguments to be passed to the `annotationFun`

## Custom annotations

This section describes how custom GO annotations can be used for building a `topGOdata` object.

Annotations need to be provided either as gene-to-GOs or as GO-to-genes mappings. An example of such mapping can be found in the “topGO/examples” directory. The file “geneid2go.map” contains gene-to-GOs mappings. For each gene identifier are listed the GO terms to which this gene is specifically annotated. We use the `readMappings()` function to parse this file.

    geneID2GO <- readMappings(file = system.file("examples/geneid2go.map", package = "topGO"))
    str(head(geneID2GO))
    #> List of 6
    #>  $ 068724: chr [1:5] "GO:0005488" "GO:0003774" "GO:0001539" "GO:0006935" ...
    #>  $ 119608: chr [1:6] "GO:0005634" "GO:0030528" "GO:0006355" "GO:0045449" ...
    #>  $ 049239: chr [1:13] "GO:0016787" "GO:0017057" "GO:0005975" "GO:0005783" ...
    #>  $ 067829: chr [1:16] "GO:0045926" "GO:0016616" "GO:0000287" "GO:0030145" ...
    #>  $ 106331: chr [1:10] "GO:0043565" "GO:0000122" "GO:0003700" "GO:0005634" ...
    #>  $ 214717: chr [1:7] "GO:0004803" "GO:0005634" "GO:0008270" "GO:0003677" ...

The object returned by `readMappings` is a named list of character vectors. The list names give the genes identifiers. Each element of the list is a character vector and contains the GO identifiers annotated to the specific gene. It is sufficient for the mapping to contain only the most specific GO annotations. However, `topGO` can also take as an input files in which all or some ancestors of the most specific GO annotations are included. This redundancy is not making for a faster running time and if possible it should be avoided.

The user can read the annotations from text files or they can build an object such as `geneID2GO` directly into R. The text file format required by the `readMappings` function is very simple. It consists of one line for each gene with the following syntax:

    gene_ID<TAB>GO_ID1, GO_ID2, GO_ID3, ....

Reading GO-to-genes mappings from a file is also possible using the `readMappings` function. However, it is the user responsibility to know the direction of the mappings. The user can easily transform a mapping from gene-to-GOs to GO-to-genes (or vice-versa) using the function `inverseList()`:

    GO2geneID <- inverseList(geneID2GO)
    str(head(GO2geneID))
    #> List of 6
    #>  $ GO:0000122: chr "106331"
    #>  $ GO:0000139: chr [1:6] "133103" "111846" "109956" "161395" ...
    #>  $ GO:0000166: chr [1:10] "067829" "157764" "100302" "074582" ...
    #>  $ GO:0000186: chr "181104"
    #>  $ GO:0000209: chr "159461"
    #>  $ GO:0000228: chr "214717"

## Predefined list of interesting genes

If the user has some a priori knowledge about a set of interesting genes, he can test the enrichment of GO terms with regard to this list of interesting genes. In this scenario, when only a list of interesting genes is provided, the user can use only tests statistics that are based on gene counts, like Fisher’s exact test, Z score and alike.

To demonstrate how custom annotation can be used this section is based on the toy dataset, the `geneID2GO` data, from Section @ref(subsec:annotations). The gene universe in this case is given by the list names:

    geneNames <- names(geneID2GO)
    head(geneNames)
    #> [1] "068724" "119608" "049239" "067829" "106331" "214717"

Since for the available genes we do not have any measurement and thus no criteria to select interesting genes, we randomly select \(10\%\) genes from the gene universe and consider them as interesting genes.

    myInterestingGenes <- sample(geneNames, length(geneNames) / 10)
    geneList <- factor(as.integer(geneNames %in% myInterestingGenes))
    names(geneList) <- geneNames
    str(geneList)
    #>  Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
    #>  - attr(*, "names")= chr [1:100] "068724" "119608" "049239" "067829" ...

The `geneList` object is a named factor that indicates which genes are interesting and which not. It should be straightforward to compute such a named vector in a real case situation, where the user has his own predefined list of interesting genes.

We now have all the elements to construct a `topGOdata` object.

To build the `topGOdata` object, we will use the MF ontology. The mapping is given by the `geneID2GO` list which will be used with the `annFUN.gene2GO` function.

    GOdata <- new("topGOdata", ontology = "MF", allGenes = geneList,
                  annot = annFUN.gene2GO, gene2GO = geneID2GO)

The building of the `GOdata` object can take some time, depending on the number of annotated genes and on the chosen ontology. In our example the running time is quite fast given that we have a rather small size gene universe which also imply a moderate size GO ontology, especially since we are using the MF ontology.

The advantage of having (information on) the gene scores (or better genes measurements) as well as a way to define which are the interesting genes, in the `topGOdata` object is that one can apply various group testing procedure, which let us test multiple hypothesis or tune with different parameters.

By typing `GOdata` at the R prompt, the user can see a summary of the data.

    GOdata
    #>
    #> ------------------------- topGOdata object -------------------------
    #>
    #>  Description:
    #>    -
    #>
    #>  Ontology:
    #>    -  MF
    #>
    #>  100 available genes (all genes from the array):
    #>    - symbol:  068724 119608 049239 067829 106331  ...
    #>    - 10  significant genes.
    #>
    #>  86 feasible genes (genes that can be used in the analysis):
    #>    - symbol:  068724 119608 049239 067829 106331  ...
    #>    - 10  significant genes.
    #>
    #>  GO graph (nodes with at least  1  genes):
    #>    - a graph with directed edges
    #>    - number of nodes = 225
    #>    - number of edges = 290
    #>
    #> ------------------------- topGOdata object -------------------------

One important point to notice is that not all the genes that are provided by `geneList`, the initial gene universe, can be annotated to the GO. This can be seen by comparing the number of all available genes, the genes present in `geneList`, with the number of feasible genes. We are therefore forced at this point to restrict the gene universe to the set of feasible genes for the rest of the analysis.

The summary on the GO graph shows the number of GO terms and the relations between them of the specified GO ontology. This graph contains only GO terms which have at least one gene annotated to them.

## Using the genes score

In many cases the set of interesting genes can be computed based on a score assigned to all genes, for example based on the \(p\)-value returned by a study of differential expression. In this case, the `topGOdata` object can store the genes score and a rule specifying the list of interesting genes. The advantage of having both the scores and the procedure to select interesting genes encapsulated in the `topGOdata` object is that the user can choose different types of tests statistics for the GO analysis without modifying the input data.

A typical example for the ALL dataset is the study where we need to discriminate between ALL cells delivered from either B-cell or T-cell precursors.

    y <- as.integer(sapply(eset$BT, function(x) return(substr(x, 1, 1) == 'T')))
    table(y)

There are 95 B-cell ALL samples and 95 T-cell ALL samples in the dataset. A two-sided \(t\)-test can by applied using the function `getPvalues` (a wrapping function for the `mt.teststat` from the `multtest` package). By default the function computes FDR (false discovery rate) adjusted \(p\)-value in order to account for multiple testing. A different type of correction can be specified using the `correction` argument.

    geneList <- getPvalues(exprs(eset), classlabel = y, alternative = "greater")

`geneList` is a named numeric vector. The gene identifiers are stored in the names attribute of the vector. This set of genes defines the gene universe.

Next, a function for specifying the list of interesting genes must be defined. This function needs to select genes based on their scores (in our case the adjusted \(p\)-values) and must return a logical vector specifying which gene is selected and which not. The function must have one argument, named `allScore` and must not depend on any attributes of this object. In this example we will consider as interesting genes all genes with an adjusted \(p\)-value lower than \(0.01\). This criteria is implemented in the following function:

    topDiffGenes <- function(allScore) {
      return(allScore < 0.01)
    }
    x <- topDiffGenes(geneList)
    sum(x) ## the number of selected genes

With all these steps done, the user can now build the `topGOdata` object. For a short description of the arguments used by the `initialize` function see Section @ref(subsec:sigGenes)

    GOdata <- new("topGOdata",
                  description = "GO analysis of ALL data; B-cell vs T-cell",
                  ontology = "BP",
                  allGenes = geneList,
                  geneSel = topDiffGenes,
                  annot = annFUN.db,
                  nodeSize = 5,
                  affyLib = affyLib)

It is often the case that many GO terms which have few annotated genes are detected to be significantly enriched due to artifacts in the statistical test. These small sized GO terms are of less importance for the analysis and in many cases they can be omitted. By using the `nodeSize` argument the user can control the size of the GO terms used in the analysis. Once the genes are annotated to the each GO term and the true path rule is applied the nodes with less than `nodeSize` annotated genes are removed from the GO hierarchy. We found that values between \(5\) and \(10\) for the `nodeSize` parameter yield more stable results. The default value for the `nodeSize` parameter is \(1\), meaning that no pruning is performed.

Note that the only difference in the initialisation of an object of class `topGOdata` to the case in which we start with a predefined list of interesting genes is the use of the `geneSel` argument. All further analysis depends only on the `GOdata` object.

## Filtering and missing GO annotations

Before going further with the enrichment analysis we analyse which of the probes available on the array can be used in the analysis.

We want to see if the filtering performed in Section @ref(subsec:preprocessing) removes important probes. There are a total of \(12625\) probes on the \(hgu95av2\) chip. One assumes that only the noisy probes, probes with low expression values or small variance across samples are filtered out from the analysis.

The number of probes have a direct effect on the multiple testing adjustment of \(p\)-values. Too many probes will result in too conservative adjusted \(p\)-values which can bias the result of tests like Fisher’s exact test. Thus, it is important to carefully analyse this step.

    allProb <- featureNames(ALL)
    groupProb <- integer(length(allProb)) + 1
    groupProb[allProb %in% genes(GOdata)] <- 0
    groupProb[!selProbes] <- 2
    groupProb <- factor(groupProb,
                        labels = c("Used", "Not annotated", "Filtered"))

    tt <- table(groupProb)
    tt
    #> groupProb
    #>          Used Not annotated      Filtered
    #>          3883           218          8524

Out of the filtered probes only \(95\%\) have annotation to GO terms. The filtering procedure removes \(8524\) probes which is a very large percentage of probes (more than \(50\%\)), but we did this intentionally to reduce the expression set for computational purposes.

We perform a differential expression analysis on all available probes and we check if differentially expressed genes are left out from the enrichment analysis.

    library(lattice)
    pValue <- getPvalues(exprs(ALL), classlabel = y, alternative = "greater")
    geneVar <- apply(exprs(ALL), 1, var)
    dd <- data.frame(x = geneVar[allProb],
                     y = log10(pValue[allProb]),
                     groups = groupProb)
    legendLab <- paste(names(table(groupProb)),
                       " (#", table(groupProb), ")", sep = "")
    xyplot(y ~ x | groups, data = dd, groups = groups,
           xlab = "Variance", ylab = "Log of p-values",
           layout = c(2, 2),
           key = list(text = list(lab = legendLab),
                      points = list(pch = 20, cex = 2,
                                    col = Rows(trellis.par.get("superpose.symbol"), 1:3)$col),
                      size = 7, padding.text = 3,
                      x = .65, y = .7, corner = c(0, 0), border = TRUE, cex = 1),
           panel = function(x, y, ...) {
             selY <- y <= -2
             panel.xyplot(x[selY], y[selY], pch = 2, ...)
             panel.xyplot(x[!selY], y[!selY], pch = 20, ...)
             panel.abline(h = -2, lty = 2, col = "black")
           })

Scatter plot of FDR adjusted \(p\)-values against variance of probes. Points below the horizontal line are significant probes.

Figure @ref(fig:whichProbes) shows for the three groups of probes the adjusted \(p\)-values and the gene-wise variance. Probes with large changes between conditions have large variance and low \(p\)-value. In an ideal case, one would expect to have a large density of probes in the lower right corner of Used panel and few probes in this region in the other two panels. We can see that the filtering process throws out some significant probes and in a real analysis a more conservative filtering needs to be applied. However, there are also many differentially expressed probes without GO annotation which cannot be used in the analysis.

# Working with the `topGOdata` object

Once the `topGOdata` object is created the user can use various methods defined for this class to access the information encapsulated in the object.

The `description` slot contains information about the experiment. This information can be accessed or replaced using the method with the same name.

    description(GOdata)
    description(GOdata) <- paste(description(GOdata),
                                 "Object modified on:",
                                 format(Sys.time(), "%d %b %Y"), sep = " ")
    description(GOdata)

Methods to obtain the list of genes that will be used in the further analysis or methods for obtaining all gene scores are exemplified below.

    a <- genes(GOdata) ## obtain the list of genes
    head(a)
    #> [1] "1000_at"   "1005_at"   "1007_s_at" "1008_f_at" "1009_at"   "100_g_at"
    numGenes(GOdata)
    #> [1] 3883

Next we describe how to retrieve the score of a specified set of genes, e.g. a set of randomly selected genes. If the object was constructed using a list of interesting genes, then the factor vector that was provided at the building of the object will be returned.

    selGenes <- sample(a, 10)
    gs <- geneScore(GOdata, whichGenes = selGenes)
    print(gs)
    #>     37048_at     33935_at   37793_r_at     33614_at     36574_at   37239_r_at     34154_at
    #> 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
    #>   40244_s_at     36641_at     41399_at
    #> 0.0003092377 1.0000000000 1.0000000000

If the user wants an unnamed vector or the score of all genes:

    gs <- geneScore(GOdata, whichGenes = selGenes, use.names = FALSE)
    print(gs)
    #>  [1] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
    #>  [8] 0.0003092377 1.0000000000 1.0000000000

    gs <- geneScore(GOdata, use.names = FALSE)
    str(gs)
    #>  num [1:3883] 0.007953 1 1 1 0.000285 ...

The list of significant genes can be accessed using the method `sigGenes`.

    sg <- sigGenes(GOdata)
    str(sg)
    #>  chr [1:339] "1000_at" "1009_at" "106_at" "1091_at" "1105_s_at" "1110_at" "1140_at" ...
    numSigGenes(GOdata)
    #> [1] 339

Another useful method is `updateGenes` which allows the user to update/change the list of genes (and their scores) from a `topGOdata` object. If one wants to update the list of genes by including only the feasible ones, one can type:

    .geneList <- geneScore(GOdata, use.names = TRUE)
    GOdata ## more available genes
    GOdata <- updateGenes(GOdata, geneList = .geneList, geneSelFun = topDiffGenes)
    GOdata ## the available genes are now the feasible genes

There are also methods available for accessing information related to GO and its structure. First, we want to know which GO terms are available for analysis and to obtain all the genes annotated to a subset of these GO terms.

    graph(GOdata) ## returns the GO graph
    #> A graphNEL graph with directed edges
    #> Number of Nodes = 5772
    #> Number of Edges = 12335

    ug <- usedGO(GOdata)
    head(ug)
    #> [1] "GO:0000018" "GO:0000027" "GO:0000028" "GO:0000038" "GO:0000041" "GO:0000045"

We further select \(10\) random GO terms, count the number of annotated genes and obtain their annotation.

    sel.terms <- sample(usedGO(GOdata), 10)

    num.ann.genes <- countGenesInTerm(GOdata, sel.terms) ## the number of annotated genes
    num.ann.genes

    ann.genes <- genesInTerm(GOdata, sel.terms) ## get the annotations
    head(ann.genes)

When the `sel.terms` argument is missing all GO terms are used. The scores for all genes, possibly annotated with names of the genes, can be obtained using the method `scoresInTerm()`.

    ann.score <- scoresInTerm(GOdata, sel.terms)
    head(ann.score)
    ann.score <- scoresInTerm(GOdata, sel.terms, use.names = TRUE)
    head(ann.score)

Finally, some statistics for a set of GO terms are returned by the method `termStat`. As mentioned previously, if the `sel.terms` argument is missing then the statistics for all available GO terms are returned.

    termStat(GOdata, sel.terms)
    #>            Annotated Significant Expected
    #> GO:1905209         5           0     0.44
    #> GO:0030812         8           1     0.70
    #> GO:0065004        82           4     7.16
    #> GO:0010565        34           6     2.97
    #> GO:0038034        40           4     3.49
    #> GO:0090162        13           1     1.13
    #> GO:0015959         5           1     0.44
    #> GO:0031580         7           6     0.61
    #> GO:0098703        11           0     0.96
    #> GO:0042401        19           4     1.66

# Running the enrichment tests

In this section we explain how we can run the desired enrichment method once the `topGOdata` object is available.

`topGO` package was designed to work with various test statistics and various algorithms which take the GO dependencies into account. At the base of this design stands a S4 class mechanism which facilitates defining and executing a (new) group test. Three types of enrichment tests can be distinguish if we look at the data used by the each test.

- Tests based on gene counts. This is the most popular family of tests, given that it only requires the presence of a list of interesting genes and nothing more. Tests like Fisher’s exact test, Hypergeometric test and binomial test belong to this family (Draghici et al. 2006).
- Tests based on gene scores or gene ranks. It includes Kolmogorov-Smirnov like tests (also known as GSEA), Gentleman’s Category, \(t\)-test, etc. (Ackermann and Strimmer 2009).
- Tests based on gene expression. Tests like Goeman’s globaltest or GlobalAncova separate from the others since they work directly on the expression matrix (Goeman and Bühlmann 2007).

There are also a number of strategies/algorithms to account for the GO topology, see Table @ref(tab:algos), each of them having specific requirements.

For each test type described above and for each algorithm there is S4 class defined in the package. The main idea is to have a class (container) which can store, for a specified gene set(GO category), all data necessary for computing the desired test statistic, and a method
that will iterate over all GO categories. In such a design the user needs to instantiate an object from the class corresponding to the chosen method(test statistic and algorithm) and then run the iterator function on this object.

The defined S4 classes are organised in a hierarchy which is showed in Figure @ref(fig:topGOclasses).

The test statistics class structure.

There are two possibilities(or interfaces) for applying a test statistic to an object of class `topGOdata`. The basic interface, which provides the core of the testing procedure in `topGO`, offers more flexibility to the experienced `R` user allowing him to implement new test statistics or new algorithms. The second interface is more user friendly but at the same time more restrictive in the choice of the tests and algorithms used. We will further explain how these two interfaces work.

## Defining and running the test

The main function for running the GO enrichment is `getSigGroups()` and it takes two arguments. The first argument is an instance of class `topGOdata` and the second argument is an instance of class `groupStats` or any of its descendents.

To better understand this principle consider the following example. Assume we decided to apply the `classic` algorithm. The two classes defined for this algorithm are `classicCount` and `classicScore`. If an object of this class is given as a argument to `getSigGroups()` than the classic algorithm will be used. The `getSigGroups()` function can take a while, depending on the size of the graph (the ontology used), so be patient.

### The `groupStats` classes

Next we show how an instance of the `groupStats` class can represent a gene set and how the test statistic is performed.

We compute the enrichment of lipid metabolic process (GO:0006629) term using Fisher’s exact test. In order to do this we need to define the gene universe, to obtain the genes annotated to GO:0006629, and to define the set of significant genes.

    goID <- "GO:0006629"
    gene.universe <- genes(GOdata)
    go.genes <- genesInTerm(GOdata, goID)[[1]]
    sig.genes <- sigGenes(GOdata)

Now we can instantiate an object of class `classicCount`. Once the object is constructed we can get the \(2\times2\) contingency table or apply the test statistic.

    my.group <- new("classicCount", testStatistic = GOFisherTest, name = "fisher",
                    allMembers = gene.universe, groupMembers = go.genes,
                    sigMembers = sig.genes)

    contTable(my.group)
    #>         sig notSig
    #> anno     41    271
    #> notAnno 298   3273
    runTest(my.group)
    #> [1] 0.004130896

The slot `testStatistic` contains the function (or to be more precise, the method) which computes the test statistic. We used the `GOFisherTest` function which is available in the `topGO` package and as the name states it implements Fisher’s exact test. The user can define his own test statistic function and then apply it using the preferred algorithm. The function, however, should use the methods defined for the `groupStats` class to access the data encapsulated in such an object. (For example a function which computes the \(Z\) score can be easily implemented using as an example the `GOFisherTest` method.)

The `runTest` method is defined for the `groupStats` class and its used to run/compute the test statistic, by calling the `testStatistic` function. The value returned by the `runTest` method in this case is the value returned by `GOFisherTest` method, which is the Fisher’s exact test \(p\)-value. The `contTable` method, showed in the example above, is only defined for the classes based on gene counts and its used to compile the two-dimensional contingency table based on the object.

To show how the same interface is used for the classes based on gene counts we next build an instance for the `elimCount` class. We randomly select \(25\%\) of the annotated genes as genes that should be removed.

    set.seed(123)
    elim.genes <- sample(go.genes, length(go.genes) / 4)
    elim.group <- new("elimCount", testStatistic = GOFisherTest, name = "fisher",
                      allMembers = gene.universe, groupMembers = go.genes,
                      sigMembers = sig.genes, elim = elim.genes)

    contTable(elim.group)
    #>         sig notSig
    #> anno     35    199
    #> notAnno 298   3273
    runTest(elim.group)
    #> [1] 0.0008995721

We see that the interface accounts for the genes that need to be eliminated, once the object is instantiated. The same mechanism applies for the other hierarchy of classes (the score based and expression based classes), except that each hierarchy has its own specialised methods for computing statistics from the data.

Please note that the `groupStats` class or any descendent class does not depend on GO, and an object of such a class can be instantiated using any gene set.

### Performing the test

According to the mechanism described above, one first defines a test statistic for the chosen algorithm, meaning that an instance of object specific for the algorithm is constructed in which only the test statistic must be specified, and then calls a generic function (interface) to run the algorithm.

According to this mechanism, one first defines a test statistic for the chosen algorithm, in this case `classic` and then runs the algorithm (see the second line). The slot `testStatistic` contains the test statistic function. In the above example `GOFisherTest` function which implements Fisher’s exact test and is available in the `topGO` package was used. A user can define his own test statistic function and then apply it using the `classic` algorithm. (For example a function which computes the \(Z\) score can be implemented using as an example the `GOFisherTest` method.)

    test.stat <- new("classicCount",
                     testStatistic = GOFisherTest,
                     name = "Fisher test")
    resultFisher <- getSigGroups(GOdata, test.stat)

A short summary on the used test and the results is printed at the R console.

    resultFisher
    #>
    #> Description: GO analysis of ALL data; B-cell vs T-cell Object modified on: 29 Apr 2026
    #> Ontology: BP
    #> 'classic' algorithm with the 'Fisher test' test
    #> 5772 GO terms scored: 164 terms with p < 0.01
    #> Annotation data:
    #>     Annotated genes: 3883
    #>     Significant genes: 339
    #>     Min. no. of genes annotated to a GO: 5
    #>     Nontrivial nodes: 3993

To use the Kolmogorov-Smirnov (KS) test one needs to provide the gene-wise scores and thus we need to instantiate an object of a class which is able to deal of the scores. Such a class is the `classicScore` class, see Figure @ref(fig:topGOclasses) which will let us run the `classic` algorithm.

    test.stat <- new("classicScore",
                     testStatistic = GOKSTest,
                     name = "KS tests")
    resultKS <- getSigGroups(GOdata, test.stat)

The mechanism presented above for `classic` also hold for `elim` and `weight`. The user should pay attention to the compatibility between the chosen class and the function for computing the test statistic, since no incompatibility test are made when the object is instantiated. For example the `weight` algorithm will not work with classes based on gene-wise scores. To run the `elim` algorithm with KS test one needs to type:

    test.stat <- new("elimScore", testStatistic = GOKSTest,
                     name = "Fisher test", cutOff = 0.01)
    resultElim <- getSigGroups(GOdata, test.stat)

Similarly, for the `weight` algorithm with Fisher’s exact test one types:

    test.stat <- new("weightCount", testStatistic = GOFisherTest,
                     name = "Fisher test", sigRatio = "ratio")
    resultWeight <- getSigGroups(GOdata, test.stat)

## The adjustment of \(p\)-values

The \(p\)-values return by the `getSigGroups` function are row \(p\)-values. There is no multiple testing correction applied to them, unless the test statistic directly incorporate such a correction. Of course, the researcher can perform an adjustment of the \(p\)-values if he considers it is important for the analysis. The reasons for not automatically correcting for multiple testing are:

- In many cases the row \(p\)-values return by an enrichment analysis are not that extreme. A FDR/FWER adjustment procedure can in this case produce very conservative \(p\)-values and declare no, or very few, terms as significant. This is not necessary a bad thing, but it can happen that there are interesting GO terms which didn’t make it over the cutoff but they are omitted and thus valuable information lost. In this case the researcher might be interested in the ranking of the GO terms even though no top term is significant at a specify FDR level.

- One should keep in mind that an enrichment analysis consist of many steps and there are many assumptions done before applying, for example, Fisher’s exact test on a set of GO terms. Performing a multiple testing procedure accounting only on the number of GO terms is far from being enough to control the error rate.

- For the methods that account for the GO topology like `elim` and `weight`, the problem of multiple testing is even more complicated. Here one computes the \(p\)-value of a GO term conditioned on the neighbouring terms. The tests are therefore not independent and the multiple testing theory does not directly apply. We like to interpret the \(p\)-values returned by these methods as corrected or not affected by multiple testing.

## `runTest`: a high-level interface for testing

Over the basic interface we implemented an abstract layer to provide the users with a higher level interface for running the enrichment tests. The interface is composed by a function, namely the `runTest` function, which can be used only with a predefined set of test statistics and algorithms. In fact `runTest` is a warping function for the set of commands used for defining and running a test presented in Section @ref(sub:define_test).

There are three main arguments that this function takes. The first argument is an object of class `topGOdata`. The second argument, named `algorithm`, is of type character and specifies which method for dealing with the GO graph structure will be used. The third argument, named `statistic`, specifies which group test statistic will be used.

To perform a classical enrichment analysis by using the `classic` method and Fisher’s exact test, the user needs to type:

    resultFis <- runTest(GOdata, algorithm = "classic", statistic = "fisher")

Various algorithms can be easily combine with various test statistics. However not all the combinations will work, as seen in Table @ref(tab:algos). In the case of a mismatch the function will throw an error. The `algorithm` argument is optional and if not specified the `weight01` method will be used. Bellow we can see more examples using the `runTest` function.

    weight01.fisher <- runTest(GOdata, statistic = "fisher")
    weight01.t <- runTest(GOdata, algorithm = "weight01", statistic = "t")
    elim.ks <- runTest(GOdata, algorithm = "elim", statistic = "ks")
    weight.ks <- runTest(GOdata, algorithm = "weight", statistic = "ks") # will not work!!!

The last line will return an error because we cannot use the `weight` method with the Kolmogorov-Smirnov test. The methods and the statistical tests which are accessible via the `runTest` function are available via the following two functions:

    whichTests()
    #> [1] "fisher"     "ks"         "t"          "globaltest" "sum"        "ks.ties"
    whichAlgorithms()
    #> [1] "classic"     "elim"        "weight"      "weight01"    "lea"         "parentchild"

There is no advantage of using the `runTest()` over `getSigGroups()`, except that it is more user friendly and it gives cleaner code. However, if the user wants to define his own test statistic or implement a new algorithm based on the available `groupStats` classes, then it would be not possible to use the `runTest()` function.

Finally, the function can pass extra arguments to the initialisation method for an `groupStats` object. Thus, one can specify different cutoffs for the `elim` method, or arguments for the `weight` method.

# Interpretation and visualization of results

This section present the available tools for analysing and interpreting the results of the performed tests. Both `getSigGroups` and `runTest` functions return an object of type `topGOresult`, and most of the following functions work with this object.

## The `topGOresult` object

The structure of the `topGOresult` object is quite simple. It contains the \(p\)-values or the statistics returned by the test and basic informations on the used test statistic/algorithm. The information stored in the `topGOdata` object is not carried over this object, and both of these objects will be needed by the diagnostic tools.

Since the test statistic can return either a \(p\)-value or a statistic of the data, we will refer them as scores!

To access the stored \(p\)-values, the user should use the function `score`. It returns a named numeric vector, were the names are GO identifiers. For example, we can look at the histogram of the results of the Fisher’s exact test and the `classic` algorithm.

By default, the `score` function does not warrant the order in which the \(p\)-values are returned, as we can see if we compare the `resultFis` object with the `resultWeight` object:

    head(score(resultWeight))
    #> GO:0006740 GO:0045661 GO:0045662 GO:0046879 GO:0045663 GO:0006749
    #> 1.00000000 1.00000000 0.51881662 0.89758312 0.69692327 0.09056999

    pvalFis <- score(resultFis)
    head(pvalFis)
    #> GO:0000018 GO:0000038 GO:0000041 GO:0000045 GO:0000070 GO:0000075
    #> 0.21473401 0.01080238 0.71611370 0.80342934 0.92283581 0.28375362
    hist(pvalFis, 50, xlab = "p-values")

However, the `score` method has a parameter, `whichGO`, which takes a list of GO identifiers and returns the scores for these terms in the specified order. Only the scores for the terms found in the intersection between the specified GOs and the GOs stored in the `topGOresult` object are returned. To see how this work lets compute the correlation between the \(p\)-values of the `classic` and `weight` methods:

    pvalWeight <- score(resultWeight, whichGO = names(pvalFis))
    head(pvalWeight)
    #> GO:0000018 GO:0000038 GO:0000041 GO:0000045 GO:0000070 GO:0000075
    #> 1.00000000 0.01080238 0.87799455 0.92980613 0.97683169 0.83776291
    cor(pvalFis, pvalWeight)
    #> [1] 0.5360126

Basic information on input data can be accessed using the `geneData` function. The number of annotated genes, the number of significant genes (if it is the case), the minimal size of a GO category as well as the number of GO categories which have at least one significant gene annotated are listed:

    geneData(resultWeight)
    #>   Annotated Significant    NodeSize    SigTerms
    #>        3883         339           5        3993

## Summarising the results

We can use the `GenTable` function to generate a summary table with the results from one or more tests applied to the same `topGOdata` object. The function can take a variable number of `topGOresult` objects and it returns a `data.frame` containing the top `topNodes` GO terms identified by the method specified with the `orderBy` argument. This argument allows the user decide which \(p\)-values should be used for ordering the GO terms.

    allRes <- GenTable(GOdata, classic = resultFis, KS = resultKS,
                       weight = resultWeight, orderBy = "weight",
                       ranksOf = "classic", topNodes = 20)

Please note that we need to type the full names (the exact name) of the function arguments: `topNodes`, `rankOf`, etc. This is the price paid for flexibility of specifying different number of `topGOresults` objects. The table includes statistics on the GO terms plus the \(p\)-values returned by the other algorithms/test statistics. Table @ref(tab:GOresults) shows the informations included in the `data.frame`.

Significance of GO terms according to different tests.
GO.ID | Term | Annotated | Significant | Expected | Rank in classic | classic | KS | weight
--- | --- | --- | --- | --- | --- | --- | --- | ---
GO:0045586 | regulation of gamma-delta T cell differe… | 12 | 8 | 1.05 | 3 | 1.1e-06 | 0.00018 | 1.1e-06
GO:0050852 | T cell receptor signaling pathway | 84 | 22 | 7.33 | 6 | 1.6e-06 | 0.00035 | 1.6e-06
GO:0031580 | membrane raft distribution | 7 | 6 | 0.61 | 9 | 2.8e-06 | 0.00019 | 2.8e-06
GO:0033077 | T cell differentiation in thymus | 57 | 18 | 4.98 | 2 | 7.3e-07 | 9.2e-06 | 4.2e-06
GO:0048935 | peripheral nervous system neuron develop… | 8 | 6 | 0.70 | 13 | 1.0e-05 | 0.00060 | 1.0e-05
GO:0042102 | positive regulation of T cell proliferat… | 47 | 14 | 4.10 | 20 | 2.7e-05 | 0.00757 | 2.7e-05
GO:0042473 | outer ear morphogenesis | 7 | 5 | 0.61 | 27 | 8.9e-05 | 0.00384 | 8.9e-05
GO:0043651 | linoleic acid metabolic process | 11 | 6 | 0.96 | 33 | 0.00013 | 0.00494 | 0.00013
GO:0060043 | regulation of cardiac muscle cell prolif… | 16 | 7 | 1.40 | 39 | 0.00021 | 0.00289 | 0.00021
GO:0035898 | parathyroid hormone secretion | 5 | 4 | 0.44 | 45 | 0.00027 | 0.00579 | 0.00027
GO:0036109 | alpha-linolenic acid metabolic process | 5 | 4 | 0.44 | 46 | 0.00027 | 0.00255 | 0.00027
GO:0043378 | positive regulation of CD8-positive, alp… | 5 | 4 | 0.44 | 47 | 0.00027 | 0.00403 | 0.00027
GO:0032743 | positive regulation of interleukin-2 pro… | 27 | 9 | 2.36 | 48 | 0.00030 | 0.02110 | 0.00030
GO:0046629 | gamma-delta T cell activation | 19 | 12 | 1.66 | 1 | 4.7e-09 | 5.5e-06 | 0.00069
GO:0042759 | long-chain fatty acid biosynthetic proce… | 14 | 6 | 1.22 | 55 | 0.00069 | 0.01539 | 0.00069
GO:0003096 | renal sodium ion transport | 6 | 4 | 0.52 | 58 | 0.00074 | 0.00786 | 0.00074
GO:0090270 | regulation of fibroblast growth factor p… | 6 | 4 | 0.52 | 59 | 0.00074 | 0.01659 | 0.00074
GO:0070670 | response to interleukin-4 | 33 | 9 | 2.88 | 70 | 0.00154 | 0.01279 | 0.00154
GO:0048304 | positive regulation of isotype switching… | 7 | 4 | 0.61 | 73 | 0.00161 | 0.00991 | 0.00161
GO:0006636 | unsaturated fatty acid biosynthetic proc… | 17 | 6 | 1.48 | 81 | 0.00228 | 0.00784 | 0.00228

## Analysing individual GOs

Next we want to analyse the distribution of the genes annotated to a GO term of interest. In an enrichment analysis one expects that the genes annotated to a significantly enriched GO term have higher scores than the average gene’ score of the gene universe.

One way to check this hypothesis is to compare the distribution of the gene scores annotated to the specified GO term with the distribution of the scores of the complementary gene set (all the genes in the gene universe which are not annotated to the GO term). This can be easily achieved using the `showGroupDensity` function. For example, lets look at the distribution of the genes annotated to the most significant GO term w.r.t. the `weight` algorithm.

    goID <- allRes[1, "GO.ID"]
    print(showGroupDensity(GOdata, goID, ranks = TRUE))

Distribution of the gene’s rank from GO:0031580, compared with the null distribution.

We can see in Figure @ref(fig:geneDensityDiff) that the genes annotated to GO:0045586 have low ranks (genes with low \(p\)-value of the \(t\)-test). The distribution of the ranks is skewed on the left side compared with the reference distribution given by the complementary gene set. This is a nice example in which there is a significant difference in the distribution of scores between the gene set and the complementary set, and we see from Table @ref(tab:GOresults) that this GO is found as significantly enriched by all methods used.

In the above example, the genes with a \(p\)-value equal to \(1\) were omitted. They can be included using the value `FALSE` for the `rm.one` argument in the `showGroupDensity` function.

Another useful function for analysing terms of interest is `printGenes`. The function will generate a table with all the genes/probes annotated to the specified GO term. Various type of identifiers, the gene name and the \(p\)-values/statistics are provided in the table.

    goID <- allRes[10, "GO.ID"]
    gt <- printGenes(GOdata, whichTerms = goID, chip = affyLib, numChar = 40)

Genes annotated to GO:0043378
| Chip ID | LL.id | Symbol.id | Gene name | raw p-value
--- | --- | --- | --- | --- | ---
40511_at | 40511_at | 2625 | GATA3 | GATA binding protein 3 | 1.47e-12
2057_g_at | 2057_g_at | 2260 | FGFR1 | fibroblast growth factor receptor 1 | 1.33e-06
2056_at | 2056_at | 2260 | FGFR1 | fibroblast growth factor receptor 1 | 4.83e-05
424_s_at | 424_s_at | 2260 | FGFR1 | fibroblast growth factor receptor 1 | 0.00607
36168_at | 36168_at | 2260 | FGFR1 | fibroblast growth factor receptor 1 | 1.00000

The `data.frame` containing the genes annotated to GO:0035898 is shown in Table @ref(tab:printGenes1). One or more GO identifiers can be given to the function using the `whichTerms` argument. When more than one GO is specified, the function returns a list of data.frames, otherwise only one `data.frame` is returned. The function has a argument `file` which, when specified, will save the results into a file using the CSV format.

For the moment the function will work only when the chip used has an annotation package available in Bioconductor. It will not work with other type of custom annotations.

## Visualising the GO structure

An insightful way of looking at the results of the analysis is to investigate how the significant GO terms are distributed over the GO graph. We plot the subgraphs induced by the most significant GO terms reported by `classic` and `weight` methods. There are two functions available. The `showSigOfNodes` will plot the induced subgraph to the current graphic device. The `printGraph` is a wrapping function of `showSigOfNodes` and will save the resulting graph into a PDF or PS file.

    showSigOfNodes(GOdata, score(resultFis), firstSigNodes = 5, useInfo = 'all')

The subgraph induced by the top 5 GO terms identified by the `classic` algorithm for scoring GO terms for enrichment. Boxes indicate the 5 most significant terms. Box color represents the relative significance, ranging from dark red (most significant) to light yellow (least significant). Black arrows indicate is-a relationships and red arrows part-of relationships.

    showSigOfNodes(GOdata, score(resultWeight), firstSigNodes = 5, useInfo = 'def')

The subgraph induced by the top 5 GO terms identified by the `weight` algorithm for scoring GO terms for enrichment. Boxes indicate the 5 most significant terms. Box color represents the relative significance, ranging from dark red (most significant) to light yellow (least significant). Black arrows indicate is-a relationships and red arrows part-of relationships.

    printGraph(GOdata, resultFis, firstSigNodes = 5,
               fn.prefix = "tGO", useInfo = "all", pdfSW = TRUE)
    printGraph(GOdata, resultWeight, firstSigNodes = 5,
               fn.prefix = "tGO", useInfo = "def", pdfSW = TRUE)

In the plots, the significant nodes are represented as rectangles. The plotted graph is the upper induced graph generated by these significant nodes. These graph plots are used to see how the significant GO terms are distributed in the hierarchy. It is a very useful tool to realize behaviour of various enrichment methods and to better understand which of the significant GO terms are really of interest.

We can emphasise differences between two methods using the `printGraph` function:

    printGraph(GOdata, resultWeight, firstSigNodes = 10, resultFis,
               fn.prefix = "tGO", useInfo = "def", pdfSW = TRUE)
    printGraph(GOdata, resultElim, firstSigNodes = 15, resultFis,
               fn.prefix = "tGO", useInfo = "all", pdfSW = TRUE)

# Session Information

The version number of R and packages loaded for generating the vignette were:

    #> R version 4.6.0 (2026-04-24)
    #> Platform: x86_64-pc-linux-gnu
    #> Running under: Ubuntu 24.04.4 LTS
    #>
    #> Matrix products: default
    #> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
    #> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
    #>
    #> locale:
    #>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8
    #>  [4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
    #>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C
    #> [10] LC_TELEPHONE=C             LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
    #>
    #> time zone: Etc/UTC
    #> tzcode source: system (glibc)
    #>
    #> attached base packages:
    #> [1] grid      stats4    stats     graphics  grDevices utils     datasets  methods   base
    #>
    #> other attached packages:
    #>  [1] lattice_0.22-9       multtest_2.68.0      genefilter_1.92.0    Rgraphviz_2.56.0
    #>  [5] hgu95av2.db_3.13.0   org.Hs.eg.db_3.22.0  ALL_1.52.0           topGO_2.64.0
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    #> [17] generics_0.1.4       BiocStyle_2.40.0
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Yon Rhee, Seung, Valerie Wood, Kara Dolinski, and Sorin Draghici. 2008. “Use and Misuse of the Gene Ontology Annotations.” Nature Reviews. Genetics advanced online publication (May): 509–15. http://www.ncbi.nlm.nih.gov/pubmed/18475267.