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.

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.

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 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": 2 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  ...
#>    - 9  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.

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.

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

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

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

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

resultFisher
#> 
#> Description: GO analysis of ALL data; B-cell vs T-cell Object modified on: 30 Oct 2025 
#> 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

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

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

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.

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.

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)

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)