Methods for the Gene Set Regulation Index (GSRI)


Estimate the number of differentially expressed genes in gene sets.


gsri(exprs, groups, geneSet, names=NULL, weight=NULL, nBoot=100,
test=rowt, testArgs=NULL, alpha=0.05, grenander=TRUE, verbose=FALSE,



Matrix or object of class ExpressionSet containing the expression intensities of the microarray. If a matrix the rows represent the genes and the columns the samples, respectively.


Factor with the assignments of the microarray samples to the groups, along which the differential effect should be estimated. Must have as many elements as exprs has samples.


Optional object of class GeneSet or GeneSetCollection defining the gene set(s) used for the analysis. If missing all genes of exprs are considered to be part of the gene set. If an object of class GeneSet only these genes are considered to be part of the gene set. If an object of class GeneSetCollecton the analysis is performed for each gene set of the collection individually.


Optional character vector with the names of the gene set(s). If missing the names are taken from the geneSet argument. Has to have as many unique elements as gene sets in the analysis.


Optional numerical vector of weights specifying the certainty a gene is part of the gene set. If NULL all genes are assumed to have the same weight. Please note that the weights are defined in a relative way and thus any kind of positive weights is feasable. Must have as many elements as eighter the genes defined in geneSet or in exprs.


Integer with the number of bootstrap samples to be drawn in the calculation of the GSRI (default: 100).


A function defining the statistical test used to assess the differential effect between the groups which are given by the groups argument. In this package, a t-test (rowt) and an F-test (rowF) are already supplied, with rowt being the default. Additionally, a custom test function can be used in order to be able to include any feasible statistical test in the analysis. For details, please see the ‘details’ section.


List of optional arguments used by the test function. For details, please see the ‘details’ section and the help for test-functions.


Single numeric specifying the confidence level for the GSRI. The estimated GSRI is the lower bound of the (1-\sQuote{alpha})*100% confidence interval obtained from bootstrapping.


Logical about whether the modified Grenander estimator for the cumulative density should be used instead of a centered ECDF. By default the modified Grenander estimator is used. For more information, please see the ‘details’ section.


Logical indicating whether the progress of the computation should be printed to the screen (default: FALSE). Most useful if geneSet is an object of class GeneSetCollection.


Additional arguments, including:


Integer specifying the minimal number of genes in a gene set in order to perform an analysis. If the gene set has less than minSize in exprs, the gene set is ignored in the analysis.


Integer setting the number of cores used for the computation in combination with the multicore package for a GeneSetCollection. For details, please see the ‘details’ section.


The gsri method estimates the degree of differential expression in gene sets. By assessing the part of the distribution of p-values consistent with the null hypothesis the number of differentially expressed genes is calculated.

Through non-parametric fitting of the uniform component of the p-value distribution, the fraction of regulated genes \sQuote{r} in a gene set is estimated. The GSRI \sQuote{eta} is then defined as the \sQuote{alpha*100}%-quantile of the distribution of \sQuote{r}, obtained from bootstrapping the samples within the groups. The index indicates that with a probability of (1-\sQuote{alpha})% more than a fraction of \sQuote{eta} genes in the gene set is differentially expressed. It can also be employed to test the hypothesis whether at least one gene in a gene set is regulated. Further, different gene sets can be compared or ranked according to the estimated amount of regulation.

Assessing the differential effect is based on p-values obtained from statistical testing at the level of individual genes between the groups. The GSRI approach is independent of the underlying test and can be chosen according to the experimental design. With the t-test (rowt) and F-test (rowF) two widely used statistical test are already part of the package. Additional tests can easily used which are passed with the test argument to the gsri method. For details on how to implement custom test functions, please refer to the help of rowt and rowF or the vignette of this package.

The GSRI approach further allows weighting the influence of individual genes in the estimation. This can be beneficial including for example the certainty that genes are part of a certain gene set derived from experimental findings or annotations.

Defining gene sets is available through the GSEABase package which provides the GeneSet and GeneSetCollection classes a single or multiple gene sets, respectively. This ensures a powerful approach for obtaining gene sets from data objects, data bases, and other bioconductor packages. For details on how to define or retrieve gene sets, please refer to the documentation of the GSEABase package, with a special focus on the GeneSet and GeneSetCollection classes.

The distribution of the p-values of a gene set is assessed in the cumulative density. In addition to a symmetrical empirical cumulative density function (ECDF), the modified Grenander estimator based on the assumption about the concave shape of the cumulative density is implemented and used by default. While the modified Grenander estimator reduces the variance and makes the approach more stable especially for small gene set, it underestimates the number of regulated genes and thus leads to conservative estimates.

In the case that the computation is performed for several gene sets in the form of a GeneSetCollection object, it can be parallelized with the multicore package. Please note that this package is not available on all platforms. Using its capabilities requires attaching multicore prior to the calculation and specification of the nCores argument. For further details, please refer to the documentation of the multicore package. This may be especially relevant in the case that specific seed values for the bootstrapping are of interest.


An object of class Gsri with the slots:


Data frame containing the results of the GSRI estimation, with one row for each gene set.


List of data frames containing the ECDF of the p-values. Each data frame covers one gene set.


List containing the parameter values used in the analysis, with the elements.

For details, please see the help for the Gsri class.


Analysis for all genes of exprs part of the gene set:

signature(exprs="matrix", groups="factor", geneSet="missing")
signature(exprs="ExpressionSet", groups="factor", geneSet="missing")

Analysis for one gene set, defined as an object of class GeneSet:

signature(exprs="matrix", groups="factor", geneSet="GeneSet")
signature(exprs="ExpressionSet", groups="factor", geneSet="GeneSet")

Analysis for several gene sets, defined as an object of class GeneSetCollection:

signature(exprs="matrix", groups="factor", geneSet="GeneSetCollection")
signature(exprs="ExpressionSet", groups="factor", geneSet="GeneSetCollection")

In this case parallel computing capabilities provided by the multicore package may be available, depending on the platform.


The standard deviation of the estimated number of regulated genes as well as the GSRI are obtained through bootstrapping. Thus, the results for these two parameters may differ slightly for several realizations, especially for small numbers of bootstraps (nBoot). Setting the seed of the random number generator avoids this problem and yields exactly the same results for several realizations.


Julian Gehring

Maintainer: Julian Gehring <>

See Also

Package: GSRI-package

Class: Gsri

Methods: gsri getGsri getCdf getParms export sortGsri plot show summary readCls readGct


## Simulate expression data for a gene set of
## 100 genes, 20 samples (10 treatment, 10 control)
## and 30 regulated genes
exprs <- matrix(rnorm(100*20), 100)
exprs[1:30,1:10] <- rnorm(30*10, mean=2)
rownames(exprs) <- paste("g", 1:nrow(exprs), sep="")
groups <- factor(rep(1:2, each=10))

## Estimate the number of differentially expressed genes
res <- gsri(exprs, groups)

## Perform the analysis for different gene set
gs1 <- GeneSet(paste("g", 25:40, sep=""), setName="set1")
gs2 <- GeneSet(paste("g", seq(1, nrow(exprs), by=5), sep=""), setName="set2")
gsc <- GeneSetCollection(gs1, gs2)

res2 <- gsri(exprs, groups, gs1)
res3 <- gsri(exprs, groups, gsc, verbose=TRUE)

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