Contents

This vignette describes how to use the stageR package that has been developed for stage-wise analysis of high throughput gene expression data in R. A stage-wise analysis was shown to be beneficial in terms of biological interpretation and statistical performance when multiple hypotheses per gene are of interest. The stage-wise analysis has been adopted from (Heller et al. 2009) and consists of a screening stage and a confirmation stage. In the screening stage, genes are screened by calculating p-values that aggregate evidence across the different hypotheses of interest for the gene. The screening p-values are then adjusted for FDR control after which significance of the screening hypothesis is assessed. In the confirmation stage, only genes passing the screening stage are considered for analysis. For those genes, every hypothesis of interest is assessed separately and multiple testing correction is performed across hypotheses within a gene to control the FWER on the BH-adjusted significance level of the screening stage. stageR provides an automated way to perform stage-wise testing, given p-values for the screening and confirmation stages. A number of FWER control procedures that take into account the logical relations among the hypotheses are implemented. Since the logical relations may be specific to the experiment, the user can also specify an adjustment deemed appropriate.

The vignette analyses two datasets. The Hammer dataset (Hammer et al. 2010) is a differential gene expression analysis for an experiment with a complex design. This type of analyses are supported by the stageR class. The Ren dataset (Ren et al. 2012) analyses differential transcript usage (DTU) in tumoral versus normal tissue in Chinese patients. Transcript-level analyses are supported by the stageRTx class.

1 Installing and loading the package

The release version of the package is hosted on Bioconductor, and can be installed with the following code

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

The development version of the package is hosted on GitHub and can be installed with the devtools library using devtools::install_github("statOmics/stageR").

After installing, we will load the package.

library(stageR)
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2 Differential gene expression: Hammer dataset

library(edgeR) ; library(Biobase) ; library(limma) ; library(utils) ; library(DEXSeq)
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As a case study for differential gene expression analysis, we analyse the Hammer dataset (Hammer et al. 2010). The dataset is provided with the stageR package and was originally downloaded from the ReCount project website (Frazee, Langmead, and Leek 2011).

data(hammer.eset, package="stageR")
eset <- hammer.eset ; rm(hammer.eset)

The Hammer experiment investigated the effect of a spinal nerve ligation (SNL) versus control samples in rats at two weeks and two months after treatment. For every time \(\times\) treatment combination, 2 biological replicates were used. The hypotheses of interest are

We use a contrast for the differential expression at the first and second timepoint and a difference in fold change between the two timepoints, respectively. Therefore we create a design matrix consisting of two timepoints, two treatments and two biological replicates in every treatment \(\times\) time combination. Note there has been a typo in the phenoData, so we will correct this first.

pData(eset)$Time #typo. Will do it ourself
## [1] 2 months 2 months 2 months 2months  2 weeks  2 weeks  2 weeks  2 weeks 
## Levels: 2months 2 months 2 weeks
time <- factor(rep(c("mo2","w2"),each=4),levels=c("w2","mo2"))
pData(eset)$protocol
## [1] control control L5 SNL  L5 SNL  control control L5 SNL  L5 SNL 
## Levels: control L5 SNL
treat <- factor(c("control","control","SNL","SNL","control","control","SNL","SNL"),levels=c("control","SNL"))
design <- model.matrix(~time*treat)
rownames(design) = paste0(time,treat,rep(1:2,4))
colnames(design)[4] = "timeMo2xTreatSNL"
design
##             (Intercept) timemo2 treatSNL timeMo2xTreatSNL
## mo2control1           1       1        0                0
## mo2control2           1       1        0                0
## mo2SNL1               1       1        1                1
## mo2SNL2               1       1        1                1
## w2control1            1       0        0                0
## w2control2            1       0        0                0
## w2SNL1                1       0        1                0
## w2SNL2                1       0        1                0
## attr(,"assign")
## [1] 0 1 2 3
## attr(,"contrasts")
## attr(,"contrasts")$time
## [1] "contr.treatment"
## 
## attr(,"contrasts")$treat
## [1] "contr.treatment"

We perform indpendent filtering (Bourgon, Gentleman, and Huber 2010) of the genes and retain genes that are expressed with at least 2 counts per million in 2 samples. The data is then normalised with TMM normalisation (Robinson and Oshlack 2010) to correct for differences in sequencing depth and RNA population between the samples.

cpmOffset <- 2
keep <- rowSums(cpm(exprs(eset))>cpmOffset)>=2 #2cpm in 2 samples
dge <- DGEList(exprs(eset)[keep,])
colnames(dge) = rownames(design)
dge <- calcNormFactors(dge)

2.1 Conventional analysis

We will first analyse the data with limma-voom (Law et al. 2014) in a standard way: the three contrasts are assessed separately on an FDR level of \(5\%\).

## regular analysis
voomObj <- voom(dge,design,plot=TRUE)

fit <- lmFit(voomObj,design)
contrast.matrix <- makeContrasts(treatSNL, treatSNL+timeMo2xTreatSNL, timeMo2xTreatSNL, levels=design)
## Warning in makeContrasts(treatSNL, treatSNL + timeMo2xTreatSNL,
## timeMo2xTreatSNL, : Renaming (Intercept) to Intercept
fit2 <- contrasts.fit(fit, contrast.matrix)
fit2 <- eBayes(fit2)
res <- decideTests(fit2)
summary.TestResults(res) #nr of significant up-/downregulated genes
##        treatSNL treatSNL + timeMo2xTreatSNL timeMo2xTreatSNL
## Down       3433                        3418                0
## NotSig     5768                        6304            12893
## Up         3692                        3171                0
colSums(summary.TestResults(res)[c(1,3),]) #total nr of significant genes
##                    treatSNL treatSNL + timeMo2xTreatSNL 
##                        7125                        6589 
##            timeMo2xTreatSNL 
##                           0

The conventional analysis does not find any genes that have a different effect of the treatment between the two timepoints (i.e. the interaction effect test), while many genes are differentially expressed between treatment and control within every timepoint.

To get a global picture of the effect of SNL on the transcriptome, we can check how many genes are significantly altered following SNL.

uniqueGenesRegular <- which(res[,1]!=0 | res[,2]!=0 | res[,3]!=0)
length(uniqueGenesRegular) #total nr of significant genes
## [1] 8199

In total, 8199 genes are found to be differentially expressed following a spinal nerve ligation. However, FDR was only controlled at the contrast level and not at the gene level so we cannot state a target FDR level together with this number.

2.2 Stage-wise analysis

The stage-wise analysis first considers an omnibus test that tests whether any of the three contrasts are significant, i.e. it tests whether there has been any effect of the treatment whatsoever. For the screening hypothesis, we use the topTableF function from the limma package to perform an F-test across the three contrasts. The screening hypothesis p-values are then stored in the vector pScreen.

alpha <- 0.05
nGenes <- nrow(dge)
tableF <- topTableF(fit2, number=nGenes, sort.by="none") #screening hypothesis
## topTableF is obsolete and will be removed in a future version of limma. Please considering using topTable instead.
pScreen <- tableF$P.Value
names(pScreen) = rownames(tableF)

In the confirmation stage, every contrast is assessed separately. The confirmation stage p-values are adjusted to control the FWER across the hypotheses within a gene and are subsequently corrected to the BH-adjusted significance level of the screening stage. This allows a direct comparison of the adjusted p-values to the provided significance level alpha for both screening and confirmation stage adjusted p-values. The function stageR constructs an object from the stageR class and requires a (preferably named) vector of p-values for the screening hypothesis pScreen and a (preferably named) matrix of p-values for the confirmation stage pConfirmation with columns corresponding to the different contrasts of interest. Note that the rows in pConfirmation correspond to features (genes) and the features should be identically sorted in pScreen and pConfirmation. The constructor function will check whether the length of pScreen is identical to the number of rows in pConfirmation and return an error if this is not the case. Finally, the pScreenAdjusted argument specifies whether the screening p-values have already been adjusted according to FDR control.

pConfirmation <- sapply(1:3,function(i) topTable(fit2, coef=i, number=nGenes, sort.by="none")$P.Value)
dimnames(pConfirmation) <- list(rownames(fit2),c("t1","t2","t1t2"))
stageRObj <- stageR(pScreen=pScreen, pConfirmation=pConfirmation, pScreenAdjusted=FALSE)

The function stageWiseAdjustment then adjusts the p-values according to a stage-wise analysis. The method argument specifies the FWER correction procedure to be used in the confirmation stage. More details on the different methods can be found in the help file for stageWiseAdjustment. The alpha argument specifies the target OFDR level that is used for controlling the fraction of false positive genes across all rejected genes over the entire stage-wise testing procedure. The adjusted p-values for genes that did not pass the screening stage are by default set to NA.

Note that when a gene passed the screening hypothesis in the Hammer experiment, only one null hypothesis can still be true: there has to be DE at timepoint 1 or timepoint 2; if the DE only occurs on one timepoint there also exist an interaction; if DE occurs at both timepoints, the \(H_0\) of no interaction can still be true. Thus, according to Shaffer’s MSRB procedure (Shaffer 1986), no correction is required in the confirmation stage for this experiment to control the FWER. This can be specified with the method="none" argument.

stageRObj <- stageWiseAdjustment(object=stageRObj, method="none", alpha=0.05)

We can explore the results of the stage-wise analysis by querying the object returned by stageWiseAdjustment. Note that the confirmation stage adjusted p-values returned by the function are only valid for the OFDR level provided. If a different OFDR level is of interest, the stage-wise testing adjustment of p-values should be re-run entirely with the other OFDR level specified in stageWiseAdjustment. The adjusted p-values from the confirmation stage can be accessed with the getAdjustedPValues function

head(getAdjustedPValues(stageRObj, onlySignificantGenes=FALSE, order=FALSE))
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
##                      padjScreen           t1           t2      t1t2
## ENSRNOG00000000001 1.078986e-05 4.550174e-06 0.0003156565 0.4228668
## ENSRNOG00000000010 2.220561e-01           NA           NA        NA
## ENSRNOG00000000017 4.119722e-05 2.992824e-05 0.0005530845 0.8296248
## ENSRNOG00000000024 9.929107e-02           NA           NA        NA
## ENSRNOG00000000028 2.338292e-05 1.347330e-05 0.0004053057 1.0000000
## ENSRNOG00000000029 3.991249e-02 1.726360e-02 0.3710217648 0.6619969
head(getAdjustedPValues(stageRObj, onlySignificantGenes=TRUE, order=TRUE))
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
##                      padjScreen           t1           t2         t1t2
## ENSRNOG00000004805 7.188747e-11 2.503902e-14 2.416459e-12 1.0000000000
## ENSRNOG00000004874 2.713897e-10 3.909855e-13 6.540645e-12 0.2086166172
## ENSRNOG00000004899 5.747483e-10 7.664403e-12 3.661990e-12 0.0009906281
## ENSRNOG00000009768 5.747483e-10 9.712181e-13 5.713093e-11 0.2057276503
## ENSRNOG00000004731 6.050652e-10 3.442620e-12 1.895910e-11 0.6365765690
## ENSRNOG00000001416 7.466126e-10 3.065430e-12 1.191188e-10 0.0124723717

and may either return all p-values or only those from the significant genes, as specified by the onlySignificantGenes argument which can then be ordered or not as specified by the order argument.

Finally, the getResults function returns a binary matrix where rows correspond to features and columns correspond to hypotheses, including the screening hypothesis. For every feature \(\times\) hypothesis combination, it indicates whether the test is significant (1) or not (0) according to the stage-wise testing procedure.

res <- getResults(stageRObj)
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
head(res)
##                    padjScreen t1 t2 t1t2
## ENSRNOG00000000001          1  1  1    0
## ENSRNOG00000000010          0  0  0    0
## ENSRNOG00000000017          1  1  1    0
## ENSRNOG00000000024          0  0  0    0
## ENSRNOG00000000028          1  1  1    0
## ENSRNOG00000000029          1  1  0    0
colSums(res) #stage-wise analysis results
## padjScreen         t1         t2       t1t2 
##       7901       6890       6574        665

The adjustment argument from the stageWiseAdjustment function allows the user to specify the FWER adjustment correction. It requires a numeric vector of the same length as the number of columns in pConfirmation. The first element of the vector is the adjustment for the most significant p-value of the gene, the second element for the second most significant p-value etc. Since the Hammer dataset did not require any adjustment, identical results are obtained when manually specifying the adjustments to equal \(1\).

stageRObj <- stageR(pScreen=pScreen, pConfirmation=pConfirmation, pScreenAdjusted=FALSE)
adjustedPSW <- stageWiseAdjustment(object=stageRObj, method="user", alpha=0.05, adjustment=c(1,1,1))
res <- getResults(adjustedPSW)
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
colSums(res)
## padjScreen         t1         t2       t1t2 
##       7901       6890       6574        665

3 Differential transcript expression/usage

Multiple hypotheses of interest per gene also arise in transcript-level studies, where the different hypotheses correspond to the different isoforms from a gene. We analyse differential transcript usage for a case study that investigated expression in prostate cancer tumoral tissue versus normal tissue in 14 Chinese patients (Ren et al. 2012). The raw sequences have been preprocessed with kallisto (Bray et al. 2016) and transcript-level abundance estimates can be downloaded from The Lair project (Pimentel et al. 2016) website. We used the unnormalized, unfiltered abundances for the analysis. A subset of the dataset comes with the stageR package and can be accessed with data(esetProstate) after loading stageR. The ExpressionSet contains the metadata for the samples in pData(esetProstate) and corresponding gene identifiers for the transcripts are stored in fData(esetProstate). The dataset contains 945 transcripts from 456 genes.

data("esetProstate", package="stageR") #from stageR package
head(pData(esetProstate))
##           condition patient
## ERR031017         N      10
## ERR031018         T      10
## ERR031019         N      11
## ERR299295         T      11
## ERR299296         N      12
## ERR031022         T      12
head(fData(esetProstate))
##                      transcript            gene
## ENST00000002501 ENST00000002501 ENSG00000003249
## ENST00000005374 ENST00000005374 ENSG00000006625
## ENST00000007510 ENST00000007510 ENSG00000004777
## ENST00000008440 ENST00000008440 ENSG00000010072
## ENST00000010299 ENST00000010299 ENSG00000009780
## ENST00000011684 ENST00000011684 ENSG00000008323

We will perform some basic data exploration on the transcripts in the dataset. Since the dataset was preprocessed for the purposes of this vignette, every gene has at least two transcripts, and all transcripts are expressed in at least 1 sample.

tx2gene <- fData(esetProstate)
colnames(tx2gene) <- c("transcript","gene")
barplot(table(table(tx2gene$gene)), main="Distribution of number of tx per gene")

#the dataset contains
length(unique(tx2gene$gene)) #nr genes
## [1] 456
median(table(as.character(tx2gene$gene))) #median nr of tx/gene
## [1] 2

3.1 Conventional analysis

We will show how to use the stageR package to analyse DTU with a stage-wise approach. We start with a regular DEXseq analysis to obtain p-values for every transcript and q-values for every gene. Since both control and tumoral tissue are derived from the same patient for all 14 patients, we add a block effect for the patient to account for the correlation between samples within every patient.

### regular DEXSeq analysis
sampleData <- pData(esetProstate)
geneForEachTx <- tx2gene[match(rownames(exprs(esetProstate)),tx2gene[,1]),2]
dxd <- DEXSeqDataSet(countData = exprs(esetProstate),
                     sampleData = sampleData,
                     design = ~ sample + exon + patient + condition:exon,
                     featureID = rownames(esetProstate),
                     groupID = as.character(geneForEachTx))
## converting counts to integer mode
## Warning in DESeqDataSet(rse, design, ignoreRank = TRUE): some variables in
## design formula are characters, converting to factors
dxd <- estimateSizeFactors(dxd)
dxd <- estimateDispersions(dxd)
dxd <- testForDEU(dxd, reducedModel=~ sample + exon + patient)
## 2 rows did not converge in beta, labelled in mcols(object)$fullBetaConv. Use larger maxit argument with nbinomLRT
dxr <- DEXSeqResults(dxd)
qvalDxr <- perGeneQValue(dxr)

3.2 Stage-wise analysis

The code above is a conventional DEXSeq analysis for analysing differential transcript usage. It would proceed by either assessing the significant genes according to the gene-wise q-values or by assessing the significant transcripts according to the transcript-level p-values, after adjustment for multiple testing. Performing and interpreting both analyses does not provide appropriate FDR control and thus should be avoided. However, interpretation on the gene level combined with transcript-level results can provide useful biological insights and this can be achieved through stage-wise testing. In the following code, we show how to automatically perform a stage-wise analysis using stageR. We start by constructing

  • a named vector of gene-wise q-values pScreen
  • a named matrix with transcript-level p-values pConfirmation
  • a data.frame with transcript identifiers and corresponding gene identifiers tx2gene

These three objects provide everything we need to construct an instance from the stageRTx class for the stage-wise analysis. Note that a different class and thus a different constructor function is used for transcript-level analyses in comparison to DE analysis for complex designs.

pConfirmation <- matrix(dxr$pvalue,ncol=1)
dimnames(pConfirmation) <- list(c(dxr$featureID),c("transcript"))
pScreen <- qvalDxr
tx2gene <- fData(esetProstate)

Next we build an object from the stageRTx class and indicate that the screening hypothesis p-values were already adjusted by setting pScreenAdjusted=TRUE. Similar as in the DGE example, we port this object to the stageWiseAdjustment function for correcting the p-values. We control the analysis on a \(5\%\) target OFDR (alpha=0.05). method="dtu" indicates the adapted Holm-Shaffer FWER correction that was specifically tailored for DTU analysis as described in the manuscript. In brief, the Holm procedure (Holm 1979) is used from the third transcript onwards and the two most significant p-values are tested on a \(\alpha_I/(n_g-2)\) significance level, with \(\alpha_I\) the BH adjusted significance level from the screening stage and \(n_g\) the number of transcripts for gene \(g\). The method will return NA p-values for genes with only one transcript if the stage-wise testing method equals "dtu".

stageRObj <- stageRTx(pScreen=pScreen, pConfirmation=pConfirmation, pScreenAdjusted=TRUE, tx2gene=tx2gene)
stageRObj <- stageWiseAdjustment(object=stageRObj, method="dtu", alpha=0.05)

We can then explore the results using a range of accessor functions. The significant genes can be returned with the getSignificantGenes function.

head(getSignificantGenes(stageRObj))
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
##                 FDR adjusted p-value
## ENSG00000063245          0.002725907
## ENSG00000106948          0.003579438
## ENSG00000117751          0.027993010
## ENSG00000120910          0.029061467
## ENSG00000124831          0.010006953
## ENSG00000005483          0.038112163

Similar, the significant transcripts can be returned with getSignificantTx.

head(getSignificantTx(stageRObj))
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
##                 stage-wise adjusted p-value
## ENST00000085079                 0.000000000
## ENST00000223791                 0.001100416
## ENST00000236412                 0.000000000
## ENST00000240139                 0.000000000
## ENST00000257745                 0.000000000
## ENST00000261017                 0.033809231

The stage-wise adjusted p-values are returned using the getAdjustedPValues function. The screening (gene) hypothesis p-values were adjusted according to the BH FDR criterion, and the confirmation (transcript) hypothesis p-values were adjusted to control for the full stage-wise analysis, by adopting the correction method specified in stageWiseAdjustment. Hence, the confirmation adjusted p-values returned from this function can be directly compared to the significance level alpha as provided in the stageWiseAdjustment function. getAdjustedPValues returns a matrix where the different rows correspond to transcripts and the respective gene and transcript identifiers are given in the first two columns. Transcript-level adjusted p-values for genes not passing the screening stage are set to NA by default. Note, that the stage-wise adjusted p-values are only valid for the provided significance level and must not be compared to a different significance level. If this would be of interest, the entire stage-wise testing adjustment should be re-run with the other significance level provided in alpha.

padj <- getAdjustedPValues(stageRObj, order=TRUE, onlySignificantGenes=FALSE)
## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.
head(padj)
##            geneID            txID        gene   transcript
## 1 ENSG00000063245 ENST00000085079 0.002725907 0.0000000000
## 2 ENSG00000063245 ENST00000270460 0.002725907 0.0000000000
## 3 ENSG00000106948 ENST00000307564 0.003579438 0.0003366718
## 4 ENSG00000106948 ENST00000223791 0.003579438 0.0011004161
## 5 ENSG00000106948 ENST00000312033 0.003579438 1.0000000000
## 6 ENSG00000149136 ENST00000278412 0.006951241 0.0000000000

The output indeed shows that 2 genes and three transcripts are significant because their adjusted p-values are below the specified alpha level of \(0.05\). The third gene in the list is not significant and thus the p-value of the transcript is set to NA.

3.2.1 Note on a stage-wise DEXSeq analysis.

By default, DEXSeq performs an independent filtering step. This may result in a number of genes that have been filtered and thus no q-value for these genes is given in the output of perGeneQValue. This can cause an error in the stage-wise analysis, since we have confirmation stage p-values for transcripts but no q-value for their respective genes. In order to avoid this, one should filter these transcripts in the pConfirmation and tx2gene objects.

rowsNotFiltered <- tx2gene[,2]%in%names(qvalDxr)
pConfirmation <- matrix(pConfirmation[rowsNotFiltered,],ncol=1,dimnames=list(dxr$featureID[rowsNotFiltered],"transcript"))
tx2gene <- tx2gene[rowsNotFiltered,]

After which the stage-wise analysis may proceed.

References

Bourgon, Richard, Robert Gentleman, and Wolfgang Huber. 2010. “Independent filtering increases detection power for high-throughput experiments.” Proceedings of the National Academy of Sciences of the United States of America 107 (21): 9546–51. https://doi.org/10.1073/pnas.0914005107.
Bray, Nicolas L, Harold Pimentel, Páll Melsted, and Lior Pachter. 2016. “Near-optimal probabilistic RNA-seq quantification.” Nature Biotechnology 34 (5): 525–27. https://doi.org/10.1038/nbt.3519.
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