Tmod: Analysis Of Transcriptional Modules Tmod User Manual
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tmod: Analysis of Transcriptional
Modules
January Weiner
2018-11-28
Abstract
The package tmod provides blood transcriptional modules described by Chaussabel et
al. (2008) and by Li et al. (2014) as well as metabolic profiling clusters from Weiner et
al. (2012). Furthermore, the package includes several tools for testing the significance of
enrichment of modules or other gene sets as well as visualisation of the features (genes,
metabolites etc.) and modules. This user guide is a tutorial and main documentation for
the package.
Contents
1 Introduction
3
2 Dive into tmod: analysis of transcriptomic responses to tuberculosis
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The Gambia data set . . . . . . . . . . . . . . . . . . . . . . .
2.3 Transcriptional module analysis with GSEA . . . . . . . . . . .
2.4 Visualizing results . . . . . . . . . . . . . . . . . . . . . . . .
3 Statistical tests in tmod
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
3.2 First generation tests . . . . . . . . . . . . . . . . . .
3.3 Second generation tests . . . . . . . . . . . . . . . . .
3.3.1 U-test (tmodUtest) . . . . . . . . . . . . . . .
3.3.2 CERNO test (tmodCERNOtest and tmodZtest)
3.3.3 PLAGE . . . . . . . . . . . . . . . . . . . . .
3.4 Permutation tests . . . . . . . . . . . . . . . . . . . .
3.4.1 Introduction . . . . . . . . . . . . . . . . . . .
3.4.2 Permutation testing – a general case . . . . . . .
3.4.3 Permutation testing with tmodGeneSetTest . .
3.5 Comparison of different tests . . . . . . . . . . . . . .
4 Visualisation and presentation of results in tmod
4.1 Introduction . . . . . . . . . . . . . . . . .
4.2 Evidence plots . . . . . . . . . . . . . . . .
4.3 Summary tables . . . . . . . . . . . . . . . .
4.4 Panel plots with tmodPanelPlot . . . . . . .
5 Working with limma
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1
5.1
5.2
5.3
Limma and tmod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Minimum significant difference (MSD) . . . . . . . . . . . . . . . . . . . 31
Comparing tests across experimental conditions . . . . . . . . . . . . . . 35
6 Using tmod for other types of GSEA analyses
41
6.1 Correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 Functional multivariate analysis . . . . . . . . . . . . . . . . . . . . . . 43
6.3 PCA and tag clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7 Using and creating modules and gene sets
7.1 Using built-in gene sets (transcriptional modules) . . . .
7.2 Accessing the tmod module data directly . . . . . . . . .
7.2.1 Module operations . . . . . . . . . . . . . . . .
7.2.2 Using tmod modules in other programs . . . . . .
7.2.3 Custom module definitions . . . . . . . . . . . .
7.3 Obtaining other gene sets . . . . . . . . . . . . . . . . .
7.3.1 MSigDB . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Using the ENSEMBL databases through biomaRt .
7.3.3 Gene ontologies (GO) . . . . . . . . . . . . . . .
7.3.4 KEGG pathways . . . . . . . . . . . . . . . . . .
7.3.5 Manual creation of tmod module objects: MSigDB
8 Case studies
8.1 Metabolic profiling of TB patients . . .
8.1.1 Introduction . . . . . . . . . .
8.1.2 Differential analysis . . . . . .
8.1.3 Functional multivariate analysis
8.2 Case study: RNASeq . . . . . . . . .
References
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2
Chapter 1
Introduction
Gene set enrichment analysis (GSEA) is an increasingly important tool in the biological
interpretation of high throughput data, versatile and powerful. In general, there are three
generations of GSEA algorithms and packages.
First generation approaches test for enrichment in defined sets of differentially expressed genes (often called “foreground”) against the set of all genes (“background”). The
statistical test involved is usually a hypergeometric or Fisher’s exact test. The main problem with this kind of approach is that it relies on arbitrary thresholds (like p-value or log
fold change cut-offs), and the number of genes that go into the “foreground” set depends
on the statistical power involved. Comparison between the same experimental condition
will thus yield vastly different results depending on the number of samples used in the
experiment.
The second generation of GSEA involve tests which do not rely on such arbitrary definitions of what is differentially expressed, and what not, and instead directly or indirectly
employ the information about the statistical distribution of individual genes. A popular
implementation of this type of GSEA is the eponymous GSEA program (Subramanian et
al. 2005). While popular and quite powerful for a range of applications, this software has
important limitations due to its reliance on bootstrapping to obtain an exact p-value. For
one thing, the performance of GSEA dramatically decreases for small sample numbers
(Weiner 3rd and Domaszewska 2016). Moreover, the specifics of the approach prevent it
from being used in applications where a direct test for differential expression is either not
present (for example, in multivariate functional analysis, see Section “Functional multivariate analysis”).
3
The tmod package and the included CERNO1 test belong to the second generation of
algorithms. However, unlike the program GSEA, the CERNO relies exclusively on an
ordered list of genes, and the test statistic has a χ² distribution. Thus, it is suitable for
any application in which an ordered list of genes is generated: for example, it is possible
to apply tmod to weights of PCA components or to variable importance measure of a
machine learning model.
tmod was created with the following properties in mind: (i) test for enrichment which
relies on a list of sorted genes, (ii) with an analytical solution, (iii) flexible, allowing custom
gene sets and analyses, (iv) with visualizations of multiple analysis results, suitable for
time series and suchlike, (v) including transcriptional module definitions not present in
other databases and, finally, (vi) to be suitable for use in R.
1
Coincident Extreme Ranks in Numerical Observations (Yamaguchi et al. 2008)
4
Chapter 2
Dive into tmod: analysis of
transcriptomic responses to tuberculosis
2.1
Introduction
In this chapter, I will use an example data set included in tmod to show the application
of tmod to the analysis of differential gene expression. The data set has been generated
by Maer dorf et al. (2011) and has the GEO ID GSE28623. Is based on whole blood RNA
microarrays from tuberculosis (TB) patients and healthy controls.
Although microarrays were used to generate the data, the principle is the same as in
RNASeq.
2.2
The Gambia data set
In the following, we will use the Egambia data set included in the package. The data
is already background corrected and normalized, so we can proceed with a differential
gene expression analysis. Note that only a bit over 5000 genes from the original set of
over 45000 probes is included.
library(limma)
library(tmod)
5
data(Egambia)
design <- cbind(Intercept=rep(1, 30), TB=rep(c(0,1), each= 15))
E <- as.matrix(Egambia[,-c(1:3)])
fit <- eBayes(lmFit(E, design))
tt <- topTable(fit, coef=2, number=Inf,
genelist=Egambia[,1:3])
The table below shows first couple of results from the table tt.
GENE_SYMBOL
GENE_NAME
FAM20A
FCGR1B
BATF2
ANKRD22
SEPT4
CD274
family with sequence similarity 20,
member A”
Fc fragment of IgG, high affinity Ib,
receptor (CD64)”
basic leucine zipper transcription
factor, ATF-like 2
ankyrin repeat domain 22
septin 4
CD274 molecule
logFC
adj.P.Val
2.956
0.001899
2.391
0.002095
2.681
0.002216
2.764
3.287
2.377
0.002692
0.002692
0.002692
OK, we see some of the genes known to be prominent in the human host response
to TB. We can display one of these using tmod’s showGene function (it’s just a boxplot
combined with a beeswarm, nothing special):
group <- rep( c("CTRL", "TB"), each=15)
showGene(E["20799",], group,
main=Egambia["20799", "GENE_SYMBOL"])
6
FCGR1B
log2 expression
16
15
14
13
12
TB
CTRL
11
Fine, but what about the modules?
2.3
Transcriptional module analysis with GSEA
There are two main functions in tmod to understand which modules or gene sets are significantly enriched1 . There are several statistical tests which can be used from within
tmod (see chapter “Statistical tests in tmod” below), but here we will use the CERNO test,
which is the main reason this package exist. CERNO is particularly fast and robust second
generation approach, recommended for most applications.
CERNO works with an ordered list of genes (only ranks ma er, no other statistic is
necessary); the idea is to test, for each gene set, whether the genes in this gene set are
more likely than others to be at the beginning of that list. The CERNO statistic has a χ2
distribution and therefore no randomization is necessary, making the test really fast.
1
If you work with limma, there are other, more efficient and simpler to use functions. See “Working with
limma” below.
7
l
<- tt$GENE_SYMBOL
resC <- tmodCERNOtest(l)
head(resC, 15)
##
ID
Title cerno
## LI.M37.0
LI.M37.0
immune activation - generic cluster 426.4
## LI.M11.0
LI.M11.0
enriched in monocytes (II) 113.8
## LI.S4
LI.S4
Monocyte surface signature
76.4
## LI.M112.0 LI.M112.0
complement activation (I)
73.7
LI.M75
antiviral IFN signature
65.3
## LI.M16
LI.M16
TLR and inflammatory signaling
46.3
## LI.M67
LI.M67
activated dendritic cells
49.5
LI.M165
enriched in activated dendritic cells (II)
91.7
LI.M37.1
enriched in neutrophils (I)
68.0
## LI.M118.0 LI.M118.0
enriched in monocytes (IV)
54.6
## LI.M75
## LI.M165
## LI.M37.1
## LI.S5
## LI.M4.3
LI.S5
## LI.M20
##
AP-1 transcription factor network
31.9
LI.M81
enriched in myeloid cells and monocytes
57.0
LI.M150
innate antiviral response
31.8
N1
AUC
cES
P.Value adj.P.Val
## LI.M37.0
100 0.746 2.13 1.82e-18
6.31e-16
## LI.M11.0
20 0.777 2.85 5.26e-09
9.09e-07
## LI.S4
10 0.897 3.82 1.61e-08
1.85e-06
## LI.M112.0
11 0.846 3.35 1.72e-07
1.49e-05
## LI.M75
10 0.893 3.26 1.05e-06
7.19e-05
## LI.M16
5 0.979 4.63 1.25e-06
7.19e-05
## LI.M67
6 0.971 4.13 1.69e-06
8.36e-05
## LI.M165
19 0.720 2.41 2.44e-06
1.06e-04
## LI.M37.1
12 0.870 2.83 4.32e-06
1.66e-04
9 0.877 3.03 1.49e-05
5.17e-04
34 0.683 1.81 4.78e-05
1.50e-03
5 0.886 3.44 1.59e-04
4.58e-03
## LI.M118.0
## LI.S5
## LI.M4.3
## LI.M20
5 0.876 3.19 4.09e-04
9.96e-03
## LI.M81
13 0.756 2.19 4.22e-04
9.96e-03
5 0.950 3.18 4.32e-04
9.96e-03
## LI.M150
34.4
LI.M20
## LI.M81
## LI.M150
DC surface signature 123.2
LI.M4.3 myeloid cell enriched receptors and transporters
8
Only first 15 results are shown above.
Columns in the above table contain the following:
• ID The module ID. IDs starting with “LI” come from Li et al. (S. Li et al. 2014),
while IDs starting with “DC” have been defined by Chaussabel et al. (Chaussabel
et al. 2008).
• Title The module description
• cerno The CERNO statistic
• N1 Number of genes in the module
• AUC The area under curve – main size estimate
• cES CERNO statistic divided by 2 × N 1
• P.Value P-value from the hypergeometric test
• adj.P.Val P-value adjusted for multiple testing using the Benjamini-Hochberg correction
These results make a lot of sense: the transcriptional modules found to be enriched in a
comparison of TB patients with healthy individuals are in line with the published findings.
In especially, we see the interferon response, complement system as well as T-cell related
modules.
2.4
Visualizing results
The main working horse for visualizing the results in tmod is the function tmodPanelPlot.
This is really a glorified heatmap which shows both the effect size (size of the blob on
the figure below) and the p-value (intensity of the color). Each column corresponds to a
different comparison. Here, there will be only one column for the only comparison we
made, however we need to wrap it in a list object. However, we can also use a slightly
different representation to also show how many significantly up- and down-regulated2
genes are found in the enriched modules (right panel on the figure below).
2
Formally, we don’t test for regulation here. “Differentially expressed” is the correct expression. I will
use, however, the word “regulated” throughout this manual with the understanding that it only means
“there is a difference between two conditions” because it is shorter.
9
par(mfrow=c(1,2))
tmodPanelPlot(list(Gambia=resC))
## calculate the number of significant genes
## per module
pie <- tmodDecideTests(g=tt$GENE_SYMBOL,
lfc=tt$logFC,
pval=tt$adj.P.Val)
names(pie) <- "Gambia"
Gambia
Gambia
tmodPanelPlot(list(Gambia=resC), pie=pie, grid="b")
enriched in myeloid cells and monocytes (LI.M81)
innate antiviral response (LI.M150)
AP−1 transcription factor network (LI.M20)
myeloid cell enriched receptors and transporters (LI.M4.3)
DC surface signature (LI.S5)
enriched in monocytes (IV) (LI.M118.0)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
enriched in neutrophils (I) (LI.M37.1)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
TLR and inflammatory signaling (LI.M16)
antiviral IFN signature (LI.M75)
enriched in myeloid cells and monocytes (LI.M81)
innate antiviral response (LI.M150)
AP−1 transcription factor network (LI.M20)
myeloid cell enriched receptors and transporters (LI.M4.3)
DC surface signature (LI.S5)
enriched in monocytes (IV) (LI.M118.0)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
enriched in neutrophils (I) (LI.M37.1)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
TLR and inflammatory signaling (LI.M16)
antiviral IFN signature (LI.M75)
P value:
0.01
P value:
0.001
−4
10
10
−5
−6
10
0.01
Effect size:
0.68
0.001
10−4
10−5
10−6
Effect size:
0.98
0.68
0.98
On the right hand side, the red color on the bars indicates that all signficantly regulated
in the enriched modules. The size of the bar corresponds to the AUC, and intensity of the
color corresponds to the p-value. See chapter “Visualisation and presentation of results
in tmod” for more information on this and other functions.
10
Chapter 3
Statistical tests in tmod
3.1
Introduction
There is a substantial numer of different gene set enrichment tests. Several are implemented in tmod (see Table below for a summary). This chapter gives an overview of the
possibilities for gene set enrichment analysis with tmod.
Test
Description
Input type
tmodHGtest
First generation test
tmodUtest
tmodCERNOtest
tmodZtest
Wilcoxon U test
CERNO test
variant of the CERNO
test
eigengene-based
general permutation
based testing
permutation based on a
particular statistic
Two sets, foreground and
background
Ordered gene list
Ordered gene list
Ordered gene list
tmodPLAGEtest
tmodAUC
tmodGeneSetTest
Expression matrix
Matrix of ranks
A statistic (e.g. logFC)
In the following, I will briefly describe the various tests and show examples of usage
on the Gambia data set.
11
3.2
First generation tests
First generation tests were based on an overrepresentation analysis (ORA). In essence,
they rely on spli ing the genes into two groups: the genes of interest (foreground), such
as genes that we consider to be significantly regulated in an experimental condition, and
all the rest (background). For a given gene set, this results in a 2 × 2 contingency table. If
these two factors are independent (i.e., the probability of a gene belonging to a gene set is
independent of the probability of a gene being regulated in the experimental condition),
then we can easily derive expected frequencies for each cell of the table. Several statistical
tests exist to test whether the expected frequencies differ significantly from the observed
frequencies.
In tmod, the function tmodHGtest(), performs a hypergeometric test on two groups
of genes: ‘foreground’ (fg), or the list of differentially expressed genes, and ‘background’
(bg) – the gene universe, i.e., all genes present in the analysis. The gene identifiers used
currently by tmod are HGNC identifiers, and we will use the GENE_SYMBOL field from
the Egambia data set.
In this particular example, however, we have almost no genes which are significantly
differentially expressed after correction for multiple testing: the power of the test with 10
individuals in each group is too low. For the sake of the example, we will therefore relax
our selection. Normally, I’d use a q-value threshold of at least 0.001.
fg <- tt$GENE_SYMBOL[tt$adj.P.Val < 0.05 & abs( tt$logFC ) > 1]
resHG <- tmodHGtest(fg=fg, bg=tt$GENE_SYMBOL)
options(width=60)
resHG
##
ID
## LI.M112.0 LI.M112.0
## LI.M11.0
LI.M11.0
## LI.M75
LI.M75
## LI.S4
LI.S4
## LI.S5
LI.S5
## LI.M165
LI.M165
## LI.M4.3
LI.M4.3
## LI.M16
LI.M16
##
Title
12
## LI.M112.0
complement activation (I)
## LI.M11.0
enriched in monocytes (II)
## LI.M75
antiviral IFN signature
## LI.S4
Monocyte surface signature
## LI.S5
DC surface signature
## LI.M165
enriched in activated dendritic cells (II)
## LI.M4.3
myeloid cell enriched receptors and transporters
## LI.M16
##
TLR and inflammatory signaling
b
B
n
N
E
P.Value adj.P.Val
## LI.M112.0 4 11 47 4826 37.3 2.48e-06
0.000858
## LI.M11.0
4 20 47 4826 20.5 3.41e-05
0.005907
## LI.M75
3 10 47 4826 30.8 9.91e-05
0.008569
## LI.S4
3 10 47 4826 30.8 9.91e-05
0.008569
## LI.S5
4 34 47 4826 12.1 2.96e-04
0.020465
## LI.M165
3 19 47 4826 16.2 7.52e-04
0.039413
## LI.M4.3
2
5 47 4826 41.1 9.11e-04
0.039413
## LI.M16
2
5 47 4826 41.1 9.11e-04
0.039413
The columns in the above table contain the following:
• ID The module ID. IDs starting with “LI” come from Li et al. (S. Li et al. 2014),
while IDs starting with “DC” have been defined by Chaussabel et al. (Chaussabel
et al. 2008).
• Title The module description
• b Number of genes from the given module in the fg set
• B Number of genes from the module in the bg set
• n Size of the fg set
• N Size of the bg set
• E Enrichment, calcualted as (b/n)/(B/N)
• P.Value P-value from the hypergeometric test
• adj.P.Val P-value adjusted for multiple testing using the Benjamini-Hochberg correction
Well, IFN signature in TB is well known. However, the numbers of genes are not high:
n is the size of the foreground, and b the number of genes in fg that belong to the given
module. N and B are the respective totals – size of bg+fg and number of genes that belong
13
to the module that are found in this totality of the analysed genes. If we were using the
full Gambia data set (with all its genes), we would have a different situation.
Lack of significant genes is the main problem of ORA: spli ing the genes into foreground and background relies on an arbitrary threshold which will yield very different
results for different sample sizes.
3.3
Second generation tests
3.3.1
U-test (tmodUtest)
Another approach is to sort all the genes (for example, by the respective p-value) and
perform a U-test on the ranks of (i) genes belonging to the module and (ii) genes that do
not belong to the module. This is a bit slower, but often works even in the case if the power
of the statistical test for differential expression is low. That is, even if only a few genes or
none at all are significant at acceptable thresholds, sorting them by the p-value or another
similar metric can nonetheless allow to get meaningful enrichments1 .
Moreover, we do not need to set arbitrary thresholds, like p-value or logFC cutoff.
The main issue with the U-test is that it detects enrichments as well as depletions –
that is, modules which are enriched at the bo om of the list (e.g. modules which are
never, ever regulated in a particular comparison) will be detected as well. This is often
undesirable. Secondly, large modules will be reported as significant even if the actual
effect size (i.e., AUC) is modest or very small, just because of the sheer number of genes in
a module. Unfortunately, also the reverse is true: modules with a small number of genes,
even if they consist of highly up- or down-regulated genes from the top of the list will not
be detected.
l
<- tt$GENE_SYMBOL
resU <- tmodUtest(l)
head(resU)
##
ID
Title
1
U
N1
The rationale is that the non-significant p-values are not associated with the test that we are actually
performing, but merely used to sort the gene list. Thus, it does not ma er whether they are significant or
not.
14
AUC
## LI.M37.0 LI.M37.0 immune activation - generic cluster 352659 100 0.746
## LI.M37.1 LI.M37.1
enriched in neutrophils (I)
50280
12 0.870
Monocyte surface signature
43220
10 0.897
LI.M75
antiviral IFN signature
42996
10 0.893
## LI.M11.0 LI.M11.0
enriched in monocytes (II)
74652
20 0.777
activated dendritic cells
28095
6 0.971
## LI.S4
## LI.M75
## LI.M67
##
LI.S4
LI.M67
P.Value adj.P.Val
## LI.M37.0 1.60e-17
5.53e-15
## LI.M37.1 4.53e-06
6.57e-04
## LI.S4
6.85e-06
6.57e-04
## LI.M75
8.63e-06
6.57e-04
## LI.M11.0 9.49e-06
6.57e-04
## LI.M67
1.81e-03
3.20e-05
nrow(resU)
## [1] 25
This list makes a lot of sense, and also is more stable than the other one: it does not
depend on modules that contain just a few genes. Since the statistics is different, the b, B,
n, N and E columns in the output have been replaced by the following:
• U The Mann-Whitney U statistics
• N1 Number of genes in the module
• AUC Area under curve – a measure of the effect size
A U-test has been also implemented in limma in the wilcoxGST() function.
3.3.2
CERNO test (tmodCERNOtest and tmodZtest)
There are two tests in tmod which both operate on an ordered list of genes: tmodUtest
and tmodCERNOtest. The U test is simple, however has two main issues. Firstly, The
CERNO test, described by Yamaguchi et al. (2008), is based on Fisher’s method of combining probabilities. In summary, for a given module, the scaled ranks of genes from the
15
module are treated as probabilities. These are then logarithmized, summed and multiplied by -2:
fCERN O = −2 ·
N
∑
i=1
ln
Ri
Ntot
This statitic has the χ2 distribution with 2 · N degrees of freedom, where N is the
number of genes in a given module and Ntot is the total number of genes (Yamaguchi et
al. 2008).
The CERNO test is actually much more practical than other tests for most purposes and
is the recommended approach. A variant called tmodZtest exists in which the p-values
are combined using Stouffer’s method rather than the Fisher’s method.
3.3.3
PLAGE
PLAGE (Tomfohr, Lu, and Kepler 2005) is a gene set enrichment method based on singular
value decomposition (SVD). The idea is that instead of running a statistical test (such as a
t-test) on each gene separately, information present in the gene expression of all genes in a
gene set is first extracted using SVD, and the resulting vector (one per gene set) is treated
as a “pseudo gene” and analysed using the approppriate statistical tool.
In the tmod implementation, for each module a gene expression matrix subset is generated and decomposed using PCA using the eigengene() function. The first component
is returned and a t-test comparing two groups is then performed. This limits the implementation to only two groups, but extending it for more than one group is trivial.
tmodPLAGEtest(Egambia$GENE_SYMBOL, Egambia[,-c(1:3)], group=group)
## Converting group to factor
## Calculating eigengenes...
##
## LI.S4
## LI.M11.0
ID
Title
LI.S4
Monocyte surface signature
LI.M11.0
enriched in monocytes (II)
16
## LI.M16
LI.M16
TLR and inflammatory signaling
## LI.M20
LI.M20
AP-1 transcription factor network
## LI.M67
LI.M67
activated dendritic cells
## LI.M37.0
LI.M37.0
immune activation - generic cluster
LI.M4.3
myeloid cell enriched receptors and transporters
## LI.M118.0 LI.M118.0
enriched in monocytes (IV)
## LI.M4.3
## LI.M37.1
LI.M37.1
enriched in neutrophils (I)
LI.M97
enriched for SMAD2/3 signaling
## LI.M112.0 LI.M112.0
complement activation (I)
## LI.M97
## LI.M105
LI.M105
TBA
LI.M75
antiviral IFN signature
LI.M165
enriched in activated dendritic cells (II)
LI.M81
enriched in myeloid cells and monocytes
## LI.M112.1 LI.M112.1
complement activation (II)
## LI.M75
## LI.M165
## LI.M81
## LI.M86.0
## LI.M66
##
LI.M86.0 chemokines and inflammatory molecules in myeloid cells
LI.M66
TBA
t.t D.CTRL AbsD.CTRL
P.Value adj.P.Val
## LI.S4
-7.17
-2.62
2.62 9.96e-08
3.45e-05
## LI.M11.0
-6.45
-2.35
2.35 5.51e-07
9.53e-05
## LI.M16
-5.34
-1.95
1.95 1.09e-05
1.26e-03
## LI.M20
-4.95
-1.81
1.81 3.21e-05
2.78e-03
## LI.M67
-4.69
-1.71
1.71 6.59e-05
3.88e-03
## LI.M37.0
-4.73
-1.73
1.73 6.89e-05
3.88e-03
## LI.M4.3
-4.63
-1.69
1.69 9.74e-05
3.88e-03
## LI.M118.0 -4.62
-1.69
1.69 9.75e-05
3.88e-03
## LI.M37.1
-4.53
-1.66
1.66 1.01e-04
3.88e-03
## LI.M97
-4.33
-1.58
1.58 1.74e-04
5.52e-03
## LI.M112.0 -4.36
-1.59
1.59 1.75e-04
5.52e-03
## LI.M105
-4.10
-1.50
1.50 3.28e-04
9.44e-03
## LI.M75
-3.91
-1.43
1.43 5.63e-04
1.50e-02
## LI.M165
-3.77
-1.38
1.38 7.80e-04
1.93e-02
## LI.M81
-3.80
-1.39
1.39 9.29e-04
2.14e-02
## LI.M112.1 -3.52
-1.29
1.29 1.64e-03
3.43e-02
## LI.M86.0
-3.50
-1.28
1.28 1.68e-03
3.43e-02
## LI.M66
-3.36
-1.23
1.23 2.24e-03
4.30e-02
17
3.4
Permutation tests
3.4.1
Introduction
The GSEA approach (Subramanian et al. 2005) is based on similar premises as the other
approaches described here. In principle, GSEA is a combination of an arbitrary scoring
of a sorted list of genes and a permutation test. Although the GSEA approach has been
criticized from statistical standpoint (Damian and Gorfine 2004), it remains one of the
most popular tools to analyze gene sets amongst biologists. In the following, it will be
shown how to use a permutation-based test with tmod.
A permutation test is based on a simple principle. The labels of observations (that is,
their group assignments) are permutated and a statistic si is calculated for each i-th permutation. Then, the same statistic so is calculated for the original data set. The proportion
of the permutated sets that yielded a statistic si equal to or higher than so is the p-value
for a statistical hypothesis test.
3.4.2
Permutation testing – a general case
First, we will set up a function that creates a permutation of the Egambia data set and
repeats the limma procedure for this permutation, returning the ordering of the genes.
permset <- function(data, design) {
require(limma)
data <- data[, sample(1:ncol(data)) ]
fit
<- eBayes(lmFit(data, design))
tt
<- topTable(fit, coef=2, number=Inf, sort.by="n")
order(tt$P.Value)
}
In the next step, we will generate 100 random permutations. The sapply function
will return a matrix with a column for each permutation and a row for each gene. The
values indicate the order of the genes in each permutation. We then use the tmod function
tmodAUC to calculate the enrichment of each module for each permutation.
18
# same design as before
design <- cbind(Intercept=rep(1, 30),
TB=rep(c(0,1), each= 15))
E
<- as.matrix(Egambia[,-c(1:3)])
N
<- 250
# small number for the sake of example
set.seed(54321)
perms
<- sapply(1:N, function(x) permset(E, design))
pauc
<- tmodAUC(Egambia$GENE_SYMBOL, perms)
dim(perms)
## [1] 5547
250
We can now calculate the true values of the AUC for each module and compare them
to the results of the permutation. The parameters “order.by” and “qval” ensure that we
will calculate the values for all the modules (even those without any genes in our gene
list!) and in the same order as in the perms variable.
fit <- eBayes(lmFit(E, design))
tt
<- topTable(fit, coef=2, number=Inf,
genelist=Egambia[,1:3])
res <- tmodCERNOtest(tt$GENE_SYMBOL, qval=Inf, order.by="n")
all(res$ID == rownames(perms))
## [1] TRUE
fnsum <- function(m) sum(pauc[m,] >= res[m,"AUC"])
sums <- sapply(res$ID, fnsum)
res$perm.P.Val <- sums / N
res$perm.P.Val.adj <- p.adjust(res$perm.P.Val)
res <- res[order(res$AUC, decreasing=T),]
head(res[order(res$perm.P.Val),
c("ID", "Title", "AUC", "adj.P.Val", "perm.P.Val.adj") ])
##
## LI.M16
ID
Title
AUC adj.P.Val
LI.M16 TLR and inflammatory signaling 0.979
19
7.19e-05
## LI.M59
LI.M59
CCR1, 7 and cell signaling 0.977
5.75e-02
## LI.M67
LI.M67
activated dendritic cells 0.971
8.36e-05
## LI.M150 LI.M150
innate antiviral response 0.950
9.96e-03
## LI.M127 LI.M127
type I interferon response 0.946
1.16e-02
## LI.S4
Monocyte surface signature 0.897
1.85e-06
LI.S4
##
perm.P.Val.adj
## LI.M16
0
## LI.M59
0
## LI.M67
0
## LI.M150
0
## LI.M127
0
## LI.S4
0
Although the results are based on a small number of permutations, the results are
nonetheless strikingly similar. For more permutations, they improve further. The table
below is a result of calculating 100,000 permutations.
ID
Title
AUC
adj.P.Val
LI.M37.0
immune activation - generic cluster 0.7462103
0.00000
LI.M11.0
enriched in monocytes (II) 0.7766542
0.00000
complement activation (I) 0.8455773
0.00000
enriched in neutrophils (I) 0.8703781
0.00000
TBA 0.8949512
0.00000
Monocyte surface signature 0.8974252
0.00000
LI.M150
innate antiviral response 0.9498859
0.00000
LI.M67
activated dendritic cells 0.9714730
0.00000
LI.M16
TLR and inflammatory signaling 0.9790500
0.00000
enriched in monocytes (IV) 0.8774710
0.00295
antiviral IFN signature 0.8927741
0.00295
LI.M112.0
LI.M37.1
LI.M105
LI.S4
LI.M118.0
LI.M75
LI.M127
type I interferon response 0.9455715
0.00295
DC surface signature 0.6833387
0.02336
LI.M188
TBA 0.8684647
0.09894
LI.M165
enriched in activated dendritic cells (II) 0.7197180
0.11600
LI.M240
chromosome Y linked 0.8157171
0.11849
LI.S5
LI.M20
AP-1 transcription factor network 0.8763327
0.12672
LI.M81
enriched in myeloid cells and monocytes 0.7562851
0.13202
regulation of signal transduction 0.7763995
0.14872
myeloid cell enriched receptors and transporters 0.8859573
0.15675
LI.M3
LI.M4.3
20
Unfortunately, the permutation approach has two main drawbacks. Firstly, it requires
a sufficient number of samples – for example, with three samples in each group there are
only 6! = 720 possible permutations. Secondly, the computational load is substantial.
3.4.3
Permutation testing with tmodGeneSetTest
Another approach to permutation testing is through the tmodGeneSetTest() function.
This is an implementation of geneSetTest from the limma package2 . Here, a statistic is
used – for example the fold changes or -log10(pvalue). For each module, the average
value of this statistic in the module is calculated and compared to a number of random
samples of the same size as the module. Below, we are using again the tt object containing
the results of the analysis in the Gambia data set.
tmodGeneSetTest(tt$GENE_SYMBOL, abs(tt$logFC))
##
ID
## LI.M4.3
## LI.M11.0
## LI.M20
Title
d
LI.M4.3 myeloid cell enriched receptors and transporters 4.15
LI.M11.0
enriched in monocytes (II) 5.09
LI.M20
AP-1 transcription factor network 5.55
LI.M37.0
immune activation - generic cluster 9.14
## LI.M67
LI.M67
activated dendritic cells 6.42
## LI.M75
LI.M75
antiviral IFN signature 6.03
## LI.M112.0 LI.M112.0
complement activation (I) 6.64
## LI.M37.0
## LI.M165
LI.M165
## LI.M240
LI.M240
chromosome Y linked 5.39
LI.S4
Monocyte surface signature 5.90
## LI.S4
## LI.S5
enriched in activated dendritic cells (II) 5.23
LI.S5
DC surface signature 4.86
LI.M16
TLR and inflammatory signaling 5.24
LI.M37.1
enriched in neutrophils (I) 3.36
## LI.M118.0 LI.M118.0
enriched in monocytes (IV) 3.75
## LI.M16
## LI.M37.1
## LI.M188
##
LI.M188
M
N1
TBA 3.71
AUC P.Value adj.P.Val
## LI.M4.3
1.216
5 0.886
0.000
0.0000
## LI.M11.0
0.902
20 0.777
0.000
0.0000
## LI.M20
1.414
5 0.876
0.000
0.0000
2
Only the actual geneSetTest part, the wilcoxGST part is implemented in tmodUtest
21
## LI.M37.0
0.815 100 0.746
0.000
## LI.M67
1.480
6 0.971
0.000
0.0000
## LI.M75
1.222
10 0.893
0.000
0.0000
## LI.M112.0 1.273
11 0.846
0.000
0.0000
## LI.M165
0.931
19 0.720
0.000
0.0000
## LI.M240
1.222
8 0.816
0.000
0.0000
## LI.S4
1.224
10 0.897
0.000
0.0000
## LI.S5
0.774
34 0.683
0.000
0.0000
## LI.M16
1.381
5 0.979
0.001
0.0288
## LI.M37.1
0.855
12 0.870
0.002
0.0461
## LI.M118.0 0.959
9 0.877
0.002
0.0461
## LI.M188
6 0.868
0.002
0.0461
1.067
0.0000
In the above table, d is the difference between the mean value of the statistic
(abs(tt$logFC)) in the given module and the mean of the means of the statistic in the
random samples, divided by standard deviation.
The drawback of this approach is that we are permuting the genes (rather than the
samples). This may easily lead to unstable and spurious results, so care should be taken.
3.5
Comparison of different tests
22
Chapter 4
Visualisation and presentation of results
in tmod
4.1
Introduction
By default, results produced by tmod are data frames containing one row per tested gene
set / module. In certain circumstances, when multiple tests are performed, the returned
object is a list in which each element is a results table. In other situations a list can be
created manually. In any case, it is often necessary to extract, compare or summarize one
or more result tables.
4.2
Evidence plots
Let us first investigate in more detail the module LI.M75, the antiviral interferon signature.
We can use the evidencePlot function to see how the module is enriched in the list l.
l
<- tt$GENE_SYMBOL
evidencePlot(l, "LI.M75")
23
0.8
0.4
0.0
Fraction of genes in module
0
1000
2000
3000
4000
5000
List of genes
In essence, this is a receiver-operator characteristic (ROC) curve, and the area under
the curve (AUC) is related to the U-statistic, from which the P-value in the tmodUtest is
calculated, as AUC = n U·n . Both the U statistic and the AUC are reported. Moreover,
1 2
the AUC can be used to calculate effect size according to the Wendt’s formula(Wendt 1972)
for rank-biserial correlation coefficient:
r =1−
2·U
= 1 − 2 · AUC
n1 · n2
In the above diagram, we see that nine out of the 10 genes that belong to the LI.M75
module and which are present in the Egambia data set are ranked among the top 1000
genes (as sorted by p-value).
There are three options of interest for generating evidence plots, shown below. Firstly,
by using the option labels=... it is possible to indicate gene of interest on the plot.
Secondly, option style="g" shows a plot similar to the K-S plots of GSEA. Thirdly, it is
possible to show more than one module on a single plot.
par(mfrow=c(1,2))
evidencePlot(l, m="LI.M75", style="g")
evidencePlot(l, m=c("LI.M37.0", "LI.M75"),
gene.labels=l[1:4], col=c(2,4), legend="right")
24
2000
3000
4000
0.2
FAM20A
FCGR1B
BATF2
ANKRD22
0.4
0.6
0.8
1.0
1000
0.0
Fraction of genes in module
0.6
0.4
0.2
0.0
Fraction of genes in module
0
5000
0
1000
List of genes
4.3
LI.M37.0
LI.M75
2000
3000
4000
5000
List of genes
Summary tables
We can summarize the output from the previously run tests (tmodUtest, tmodCERNOtest
and tmodHGtest) in one table using tmodSummary. For this, we will create a list containing results from all comparisons.
resAll <- list(CERNO=resC, U=resU, HG=resHG)
head(tmodSummary(resAll))
##
ID
## LI.M11.0
Title AUC.CERNO
LI.M11.0
enriched in monocytes (II)
0.777
## LI.M112.0 LI.M112.0
complement activation (I)
0.846
## LI.M118.0 LI.M118.0
enriched in monocytes (IV)
0.877
## LI.M127
type I interferon response
0.946
LI.M13 innate activation by cytosolic DNA sensing
0.913
## LI.M13
## LI.M150
##
LI.M127
LI.M150
innate antiviral response
q.CERNO AUC.U
## LI.M11.0
q.U E.HG
q.HG
9.09e-07 0.777 0.000657 20.5 0.005907
## LI.M112.0 1.49e-05 0.846 0.001811 37.3 0.000858
## LI.M118.0 5.17e-04 0.877 0.001926
NA
NA
## LI.M127
1.16e-02 0.946 0.007486
NA
NA
## LI.M13
3.66e-02
NA
NA
NA
## LI.M150
9.96e-03 0.950 0.007162
NA
NA
NA
The table below shows the results.
25
0.950
4.4
Panel plots with tmodPanelPlot
A list of result tables (or even of a single result table) can be visualized using a heatmaplike plot called here “panel plot”. The idea is to show both, effect sizes and p-values, and,
optionally, also the direction of gene regulation.
In the example below, we will use the resAll object created above, containing the
results from three different tests for enrichment, to compare the results of the individual
tests. However, since the E column of HG test is not easily comparable to the AUC values
(which are between 0 and 1), we need to scale it down.
resAll$HG$E <- log10(resAll$HG$E) - 0.5
tmodPanelPlot(resAll)
26
HG
U
CERNO
DC surface signature (LI.S5)
complement activation (I) (LI.M112.0)
enriched in monocytes (II) (LI.M11.0)
antiviral IFN signature (LI.M75)
Monocyte surface signature (LI.S4)
myeloid cell enriched receptors and transporters (LI.M4.3)
TLR and inflammatory signaling (LI.M16)
enriched in activated dendritic cells (II) (LI.M165)
enriched in monocytes (IV) (LI.M118.0)
activated dendritic cells (LI.M67)
immune activation − generic cluster (LI.M37.0)
enriched in neutrophils (I) (LI.M37.1)
AP−1 transcription factor network (LI.M20)
type I interferon response (LI.M127)
innate antiviral response (LI.M150)
enriched in myeloid cells and monocytes (LI.M81)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
1.1
Each enrichment result corresponds to a reddish blob. The size of the blob corresponds
to the effect size (AUC or log10(Enrichment), as it may be), and color intensity corresponds to the p-value – pale colors show p-values closer to 0.01. It is easily seen how
tmodCERNOtest is the more sensitive option.
We can see that also the intercept term is enriched for genes found in monocytes and
neutrophils. Note that by default, tmodPanelPlot only shows enrichments with p < 0.01,
hence a slight difference from the tmodSummary output. This behavior can be modified
by the pval.thr option.
However, one is usually interested in the direction of regulation. If a gene list is sorted
27
by p-value, the enriched modules may contain both up- or down-regulated genes1 . It
is often desirable to visualize whether genes in a module go up, or go down between
experimental conditions. For this, the function tmodDecideTests is used to obtain the
number of significantly up- or down-regulated genes in a module.
This information must be obtained separately from the differential gene expression
analysis and provided as a list to tmodPanelPlot. The names of this list must be identical
to the names in the results list.
There are three default representations (rug-like, pie and a square pie).
par(mfrow=c(1,3))
pie <- tmodDecideTests(g=tt$GENE_SYMBOL, lfc=tt$logFC, pval=tt$adj.P.Val)
names(pie) <- "CERNO"
tmodPanelPlot(resAll["CERNO"], pie=pie, grid="b")
tmodPanelPlot(resAll["CERNO"], pie=pie, grid="b", pie.style="pie")
CERNO
CERNO
CERNO
tmodPanelPlot(resAll["CERNO"], pie=pie, grid="b", pie.style="boxpie")
enriched in myeloid cells and monocytes (LI.M81)
enriched in myeloid cells and monocytes (LI.M81)
innate antiviral response (LI.M150)
innate antiviral response (LI.M150)
enriched in myeloid cells and monocytes (LI.M81)
innate antiviral response (LI.M150)
AP−1 transcription factor network (LI.M20)
AP−1 transcription factor network (LI.M20)
AP−1 transcription factor network (LI.M20)
myeloid cell enriched receptors and transporters (LI.M4.3)
myeloid cell enriched receptors and transporters (LI.M4.3)
myeloid cell enriched receptors and transporters (LI.M4.3)
DC surface signature (LI.S5)
DC surface signature (LI.S5)
DC surface signature (LI.S5)
enriched in monocytes (IV) (LI.M118.0)
enriched in monocytes (IV) (LI.M118.0)
enriched in monocytes (IV) (LI.M118.0)
complement activation (I) (LI.M112.0)
complement activation (I) (LI.M112.0)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
Monocyte surface signature (LI.S4)
Monocyte surface signature (LI.S4)
enriched in monocytes (II) (LI.M11.0)
enriched in monocytes (II) (LI.M11.0)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
immune activation − generic cluster (LI.M37.0)
immune activation − generic cluster (LI.M37.0)
enriched in neutrophils (I) (LI.M37.1)
enriched in neutrophils (I) (LI.M37.1)
enriched in neutrophils (I) (LI.M37.1)
enriched in activated dendritic cells (II) (LI.M165)
enriched in activated dendritic cells (II) (LI.M165)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
activated dendritic cells (LI.M67)
activated dendritic cells (LI.M67)
TLR and inflammatory signaling (LI.M16)
TLR and inflammatory signaling (LI.M16)
TLR and inflammatory signaling (LI.M16)
antiviral IFN signature (LI.M75)
antiviral IFN signature (LI.M75)
P value:
antiviral IFN signature (LI.M75)
P value:
0.01
0.001
10−4
10−5
10−6
Effect size:
P value:
0.01
0.001
10−4
10−5
10−6
Effect size:
0.68
0.98
0.01
0.001
10−4
10−5
10−6
Effect size:
0.68
0.98
0.68
Each mini-plot shows the effect size of the enrichment and the corresponding p-value,
as before. Additionally, the fraction of up-regulated and down-regulated genes is visualized by coloring a fraction of the area of the mini-plot red or blue, respectively2 .
The tmodPanelPlot function has several parameters, notably for filtering and labelling:
1
Searching for enrichment only in up- or only in down-regulated genes depends on how the gene list is
sorted; this is described in Section “Testing for up- or down-regulated genes separately”.
2
The colors can be modified by the parameter pie.colors
28
0.98
• Filtering:
– filter.empty.rows and filter.empty.cols remove, respectively, modules and result tables with no enrichment above pval.thr
– filter.rows.pval and filter.rows.auc removes rows that do not contain at least one p value or AUC above the specified threshold
– filter.by.id shows only a selected subset of modules
• Labelling:
– row.labels.auto: by default, the row labels of the panel plot are generated
automatically from the module descriptions. This option specifies how.
– row.labels: alternatively, labels for the modules shown can be provided
manually as a named vector
– col.labels: alternative labels for the columns (in order of appearance in
the results list)
– col.labels.style: where the column labels should be put (top, bo om,
both, none)
Internally, tmodPanelPlot is a convenient wrapper for the much more customizable
function pvalEffectPlot, operating directly on matrices of effect sizes and p values.
29
Chapter 5
Working with limma
5.1
Limma and tmod
Given the popularity of the limma package, tmod includes functions to easily integrate
with limma. In fact, if you fit a design / contrast with limma function lmFit and calculate
the p-values with eBayes(), you can directly use the resulting object in tmodLimmaTest
and tmodLimmaDecideTests1 .
res.l <- tmodLimmaTest(fit, Egambia$GENE_SYMBOL)
length(res.l)
## [1] 2
names(res.l)
## [1] "Intercept" "TB"
head(res.l$TB)
1
The function tmodLimmaDecideTests is described in the next section
30
##
ID
Title cerno
N1
AUC
## LI.M37.0
LI.M37.0 immune activation - generic cluster 414.3 100 0.726
## LI.M11.0
LI.M11.0
enriched in monocytes (II) 105.6
## LI.M112.0 LI.M112.0
## LI.S4
## LI.M75
## LI.M67
##
complement activation (I)
75.6
11 0.867
LI.S4
Monocyte surface signature
70.0
10 0.884
LI.M75
antiviral IFN signature
66.1
10 0.865
LI.M67
activated dendritic cells
50.4
6 0.971
cES
P.Value adj.P.Val
## LI.M37.0
2.07 4.57e-17
1.58e-14
## LI.M11.0
2.64 7.92e-08
9.67e-06
## LI.M112.0 3.44 8.39e-08
9.67e-06
## LI.S4
3.50 1.84e-07
1.59e-05
## LI.M75
3.31 7.78e-07
5.38e-05
## LI.M67
4.20 1.21e-06
6.97e-05
5.2
20 0.786
Minimum significant difference (MSD)
The tmodLimmaTest function uses coefficients and p-values from the limma object to order the genes. By default, the genes are ordered by MSD (Minimum Significant Difference), rather than p-value or log fold change.
The MSD is defined as follows:
MSD
=
CI.L
>0
−CI.R if logFC < 0
if logFC
Where logFC is the log fold change, CI.L is the left boundary of the 95% confidence
interval of logFC and CI.R is the right boundary. MSD is always greater than zero and
is equivalent to the absolute distance between the confidence interval and the x axis. For
example, if the logFC is 0.7 with 95% CI = [0.5, 0.9], then MSD=0.5; if logFC is -2.5 with
95% CI = [-3.0, -2.0], then MSD = 2.0.
The idea behind MSD is as follows. Ordering genes by decreasing absolute log fold
change will include on the top of the list some genes close to background, for which log
fold changes are grand, but so are the errors and confidence intervals, just because measuring genes with low expression is loaded with errors. Ordering genes by decreasing
absolute log fold change should be avoided.
31
On the other hand, in a list ordered by p-values, many of the genes on the top of the
list will have strong signals and high expression, which results in be er statistical power
and ultimately with lower p-values – even though the actual fold changes might not be
very impressive.
However, by using MSD and using the boundary of the confidence interval to order
the genes, the genes on the top of the list are those for which we can confidently that the
actual log fold change is large. That is because the 95% confidence intervals tells us that
in 95% cases, the real log fold change will be anywhere within that interval. Using its
bountary closer to the x-axis (zero log fold change), we say that in 95% of the cases the log
fold change will have this or larger magnitude (hence, “minimal significant difference”).
This can be visualized as follows, using the drop-in replacement for limma’s topTable
function, tmodLimmaTopTable, which calculates msd as well as confidence intervals. We
will consider only genes with positive log fold changes and we will show top 50 genes as
ordered by the three different measures:
plotCI <- function(x, ci.l, ci.r, title="") {
n <- length(x)
plot(x,
ylab="logFC", xlab="Index",
pch=19, ylim=c( min(x-ci.l), max(x+ci.r)),
main=title)
segments(1:n, ci.l, 1:n, ci.r, lwd=5, col="#33333333")
}
par(mfrow=c(1,3))
x <- tmodLimmaTopTable(fit, coef="TB")
print(head(x))
##
logFC.TB
t.TB msd.TB SE.TB
## 34
0.0282
0.0756 -0.728 0.373
0.0288 -0.728
0.784
0.9954
## 36
1.5242
3.8798
1.6398
0.728
2.320
0.0439
## 41
0.0789
0.1783 -0.817 0.442
0.0955 -0.817
0.975
0.9950
## 44
0.1532
0.3239 -0.806 0.473
0.1985 -0.806
1.112
0.9950
## 52
-0.2350 -0.6170 -0.537 0.381 -0.2451 -1.007
0.537
0.9950
## 62
-0.3195 -0.5585 -0.840 0.572 -0.5007 -1.479
0.840
0.9950
0.728 0.393
32
d.TB ciL.TB ciR.TB qval.TB
x <- x[ x$logFC.TB > 0, ] # only to simplify the output!
x2 <- x[ order(abs(x$logFC.TB), decreasing=T),][1:50,]
plotCI(x2$logFC.TB, x2$ciL.TB, x2$ciR.TB, "logFC")
x2 <- x[ order(x$qval.TB),][1:50,]
plotCI(x2$logFC.TB, x2$ciL.TB, x2$ciR.TB, "q-value")
x2 <- x[ order(x$msd.TB, decreasing=T),][1:50,]
plotCI(x2$logFC.TB, x2$ciL.TB, x2$ciR.TB, "MSD")
q−value
MSD
4
logFC
4
logFC
6
2
2
2
4
logFC
8
6
6
10
8
8
logFC
0
10
20
30
40
50
0
10
Index
20
30
Index
40
50
0
10
20
30
40
Index
Black dots are logFCs, and grey bars denote 95% confidence intervals. On the left panel,
the top 50 genes ordered by the fold change include several genes with broad confidence
intervals, which, despite having a large log fold change, are not significantly up- or downregulated.
On the middle panel the genes are ordered by p-value. It is clear that the log fold
changes of the genes vary considerably, and that the list includes genes which are more
and less strongly regulated in TB.
The third panel shows genes ordered by decreasing MSD. There is less variation in
the logFC than on the second panel, but at the same time the fallacy of the first panel
is avoided. MSD is a compromise between considering the effect size and the statistical
significance.
What about enrichments?
33
50
x <- tmodLimmaTopTable(fit, coef="TB", genelist=Egambia[,1:3])
x.lfc
<- x[ order(abs(x$logFC.TB), decreasing=T),]
x.qval <- x[ order(x$qval.TB),]
x.msd
<- x[ order(x$msd.TB, decreasing=T),]
comparison <- list(
lfc=tmodCERNOtest(x.lfc$GENE_SYMBOL),
qval=tmodCERNOtest(x.qval$GENE_SYMBOL),
msd=tmodCERNOtest(x.msd$GENE_SYMBOL))
tmodPanelPlot(comparison)
34
msd
qval
lfc
enriched in neutrophils (I) (LI.M37.1)
innate antiviral response (LI.M150)
chromosome Y linked (LI.M240)
enriched in monocytes (IV) (LI.M118.0)
myeloid cell enriched receptors and transporters (LI.M4.3)
AP−1 transcription factor network (LI.M20)
TLR and inflammatory signaling (LI.M16)
DC surface signature (LI.S5)
enriched in monocytes (II) (LI.M11.0)
enriched in activated dendritic cells (II) (LI.M165)
Monocyte surface signature (LI.S4)
activated dendritic cells (LI.M67)
antiviral IFN signature (LI.M75)
complement activation (I) (LI.M112.0)
immune activation − generic cluster (LI.M37.0)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.98
In this case, the results of p-value and msd-ordering are very similar.
While MSD is a general method, it relies on a construction of confidence intervals,
which might not be possible in some cases.
5.3
Comparing tests across experimental conditions
In the above example with the Gambian data set there were only two coefficients calculated in limma, the intercept and the TB. However, often there are several coefficients
35
or contrasts which are analysed simultaneously, for example different experimental conditions or different time points. tmod includes several functions which make it easy to
visualize such sets of enrichments.
The object res.l created above using the tmod function tmodLimmaTest is a list of tmod
results. Any such list can be directly passed on to functions tmodSummary and tmodPanelPlot, as long as each element of the list has been created with tmodCERNOtest or a
similar function. tmodSummary creates a table summarizing module information in each
of the comparisons made. The values for modules which are not found in a result object
(i.e., which were not found to be significantly enriched in a given comparison) are shown
as NA’s:
head(tmodSummary(res.l), 5)
##
ID
## LI.M11.0
Title AUC.Intercept
LI.M11.0
enriched in monocytes (II)
0.815
## LI.M112.0 LI.M112.0
complement activation (I)
NA
## LI.M118.0 LI.M118.0
enriched in monocytes (IV)
NA
## LI.M124
LI.M124 enriched in membrane proteins
0.881
## LI.M127
LI.M127
##
type I interferon response
q.Intercept AUC.TB
## LI.M11.0
## LI.M112.0
## LI.M118.0
q.TB
0.000114
0.786 9.67e-06
NA
0.867 9.67e-06
NA
0.838 2.85e-03
## LI.M124
0.011487
## LI.M127
NA
NA
NA
NA
0.945 1.04e-02
We can neatly visualize the above information on a heatmap-like representation:
tmodPanelPlot(res.l, text.cex=0.8)
36
TB
Intercept
enriched in neutrophils (I) (LI.M37.1)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
enriched in monocytes (IV) (LI.M118.0)
TLR and inflammatory signaling (LI.M16)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
antiviral IFN signature (LI.M75)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
innate antiviral response (LI.M150)
myeloid cell enriched receptors and transporters (LI.M4.3)
AP−1 transcription factor network (LI.M20)
DC surface signature (LI.S5)
P value:
0.01
0.001
10−4
10−5
10−6
Effect size:
0.5
0.97
The function tmodPanelPlot has many optional arguments for customization, including options for label sizes, p value thresholds and custom functions for plo ing the test
37
results instead of just red blobs.
It is often of interest to see which enriched modules go up, and which go down? Specifically, we would like to see, for each module, how many genes are up-, and how many
genes are down-regulated. tmodPanelPlot takes an optional argument, pie, which contains information on significantly regulated genes in modules. We can conveniently generate it from a limma linear fit object with the tmodLimmaDecideTests function:
pie <- tmodLimmaDecideTests(fit, genes=Egambia$GENE_SYMBOL)
head(pie$TB[ order( pie$TB[,"Up"], decreasing=T), ])
##
Down Zero Up
## DC.M3.4
0
11
9
## DC.M4.2
0
16
7
## LI.M11.0
0
16
4
## LI.M37.0
0
110
4
## LI.M112.0
0
9
4
## LI.M165
0
24
4
data(tmod)
tmod$MODULES["DC.M3.4",]
##
ID
Title Category Annotated
## DC.M3.4 DC.M3.4 Interferon
DC.M3
Yes
##
URL
## DC.M3.4 http://www.biir.net/public_wikis/module_annotation/V2_Trial_8_Modules_M3.4
##
Source SourceID original.ID
## DC.M3.4 http://www.biir.net/
DC
B
M3.4 53
The pie object is a list. Each element of the list corresponds to one coefficient and is a
data frame with the columns “Down”, “Zero” and “Up” (in that order). Importantly, all
names of the “res.l” list must correspond to an item in the pie list.
all(names(pie) %in% names(res.l))
## [1] TRUE
38
We can now use this information in tmodPanelPlot:
TB
Intercept
tmodPanelPlot(res.l, pie=pie, text.cex=0.8, grid="b")
enriched in neutrophils (I) (LI.M37.1)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
enriched in monocytes (IV) (LI.M118.0)
TLR and inflammatory signaling (LI.M16)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
antiviral IFN signature (LI.M75)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
innate antiviral response (LI.M150)
myeloid cell enriched receptors and transporters (LI.M4.3)
AP−1 transcription factor network (LI.M20)
DC surface signature (LI.S5)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.97
A pie-like plot can be also generated:
tmodPanelPlot(res.l,
pie=pie, pie.style="pie")
39
TB
Intercept
enriched in neutrophils (I) (LI.M37.1)
enriched in monocytes (II) (LI.M11.0)
immune activation − generic cluster (LI.M37.0)
enriched in monocytes (IV) (LI.M118.0)
TLR and inflammatory signaling (LI.M16)
complement activation (I) (LI.M112.0)
Monocyte surface signature (LI.S4)
antiviral IFN signature (LI.M75)
enriched in activated dendritic cells (II) (LI.M165)
activated dendritic cells (LI.M67)
innate antiviral response (LI.M150)
myeloid cell enriched receptors and transporters (LI.M4.3)
AP−1 transcription factor network (LI.M20)
DC surface signature (LI.S5)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.97
There is also a more general function, tmodDecideTests that also produces a
tmodPanelPlot-compatible object, a list of data frames with gene counts. However,
instead of taking a limma object, it requires (i) a gene name, (ii) a vector or a matrix of
log fold changes, and (iii) a vector or a matrix of p-values. We can replicate the result of
tmodLimmaDecideTests above with the following commands:
tt.I = 5 & ll <= 250 ]
ll <- lengths(m2g_g)
m2g_g <- m2g_g[ ll >= 5 & ll <= 250 ]
m_r <- data.frame(ID=names(m2g_r), Title=names(m2g_r))
m_g <- data.frame(ID=names(m2g_g),
Title=bm$name_1006[ match(names(m2g_g), bm$go_id)])
ensemblR
<- makeTmod(modules=m_r, modules2genes=m2g_r)
ensemblGO <- makeTmod(modules=m_g, modules2genes=m2g_g)
## these objects are no longer necessary
rm(bm, m_g, m_r, m2g_r, m2g_g)
7.3.3
Gene ontologies (GO)
GO terms are perhaps the most frequently used type of gene sets in GSEA, in particular
because they are available for a much larger number of organisms than other gene sets
(like KEGG pathways).
There are many sources to obtain GO definitions. As described in the previous sections, GO’s can be also obtained from ENSEMBL via biomaRt and from MSigDB. In fact,
MSigDB may be the easiest way.
However, GO annotations can also be obtained from AnnotationDBI Bioconductor
packages as shown below. Note that the Entrez gene IDs are in the EG column of the
70
Egambia object.
library(org.Hs.eg.db)
mtab <- toTable(org.Hs.egGO)
There are over 15,000 GO terms and 250,000 genes in the mtab mapping; however,
many of them map to either a very small or a very large number of genes. At this stage,
it could also be useful to remove any genes not present in our particular data set, but that
would make the resulting tmod object less flexible. However, we may be interested only
in the “biological process” ontology for now.
mtab <- mtab[ mtab$Ontology == "BP", ]
m2g <- split(mtab$gene_id, mtab$go_id)
## remove the rather large object
rm(mtab)
ll <- lengths(m2g)
m2g <- m2g[ ll >= 10 & ll <= 100 ]
length(m2g)
## [1] 2224
Using the mapping and the GO.db it is easy to create a module set suitable for tmod:
library(GO.db)
gt <- toTable(GOTERM)
m <- data.frame(ID=names(m2g))
m$Title <- gt$Term[ match(m$ID, gt$go_id) ]
goset <- makeTmod(modules=m, modules2genes=m2g)
rm(gt, m2g, m)
This approach allows an offline mapping to GO terms, assuming the necessary DBI
is installed. Using AnnotationDBI databases such as org.Hs.eg.db has, however, also
two major disadvantages: firstly, the annotations are available for a small number of organisms. Secondly, the annotations in ENSEMBL may be more up to date.
71
We can now compare the results of the analysis with MSigDB. There is one hitch,
though. The authors of MSigDB decided to use their own identifiers instead of GO identifiers. The GO identifiers can still be extracted from MSigDB, but can only be found in the
field EXTERNAL_DETAILS_URL. Below, the function renameMods is used to replace the
MSigDB identifiers with GO identifiers.
msig.bp <- msig[ msig$MODULES$Subcategory == "BP" ]
go_ids <- gsub(".*/", "", msig.bp$MODULES$EXTERNAL_DETAILS_URL)
names(go_ids) <- msig.bp$MODULES$ID
msig.bp <- renameMods(msig.bp, go_ids)
Now we can run the enrichment on tt with both data sets and compare the results.
Note, however, that while systematic gene names are used in MSigDB, the object goset
was created from org.Hs.eg.db and uses Entrez identifiers. Also, we will make both
sets directly comparable by filtering for the common genes, and we will request a result
for all modules, even if they are not significant.
both <- intersect(msig.bp$MODULES$ID, goset$MODULES$ID)
msig.bp <- msig.bp[both]
goset.both <- goset[both]
rescomp <- list()
rescomp$orghs
<-
tmodCERNOtest(tt$EG, mset=goset.both, qval=Inf, order.by="n")
rescomp$msigdb
<-
tmodCERNOtest(tt$GENE_SYMBOL, mset=msig.bp, qval=Inf, order.by="n")
all(rownames(rescomp$msigdb) == rownames(rescomp$orghs))
## [1] TRUE
plot(rescomp$msigdb$P.Value, rescomp$orghs$P.Value, log="xy",
xlab="MSigDB GO", ylab="org.Hs.eg.db GO", bty="n")
abline(0, 1, col="grey")
72
1e−04 1e−03 1e−02 1e−01 1e+00
org.Hs.eg.db GO
1e−15
1e−11
1e−07
1e−03
MSigDB GO
The differences are quite apparent, and most likely due to the differences in the versions of the GO database.
7.3.4
KEGG pathways
One way to obtain KEGG pathway gene sets is to use the MSigDB as described above.
However, alternatively and for other organisms it is possible to directly obtain the pathway definitions from KEGG. The code below might take a lot of time on a slow connection.
library(KEGGREST)
pathways <- keggLink("pathway", "hsa")
## get pathway Names in addition to IDs
paths
<- sapply(unique(pathways), function(p) keggGet(p)[[1]]$NAME)
m <- data.frame(ID=unique(pathways), Title=paths)
73
## m2g is the mapping from modules (pathways) to genes
m2g <- split(names(pathways), pathways)
## kegg object can now be used with tmod
kegg <- makeTmod(modules=m, modules2genes=m2g)
Note that KEGG uses a slightly modified version of Entrez identifiers – each numeric
identifier is preceded by a three le er species code (e.g. “hsa” for humans) followed by a
colon:
eg <- paste0("hsa:", tt$EG)
tmodCERNOtest(eg, mset="kegg")
Again, the most important part is to ensure that the gene identifiers in the tmod object
(kegg in this case) correspond to the gene identifiers in in the ordered list.
7.3.5
Manual creation of tmod module objects: MSigDB
For the purposes of an example, the code below shows how to parse the XML MSigDB
file using the R package XML. Essentially, this is the same code that tmodImportMsigDB
is using:
library(XML)
foo
<- xmlParse( "msigdb_v6.1.xml" )
foo2 <- xmlToList(foo)
There are over 10,000 “gene sets” (equivalent to modules in tmod) defined. Each member of foo2 is a named character vector:
path1 <- foo2[[1]]
class(path1)
## [1] "character"
74
names(path1)
##
[1] "STANDARD_NAME"
"SYSTEMATIC_NAME"
"HISTORICAL_NAMES"
##
[4] "ORGANISM"
"PMID"
"AUTHORS"
##
[7] "GEOID"
"EXACT_SOURCE"
"GENESET_LISTING_URL"
## [10] "EXTERNAL_DETAILS_URL" "CHIP"
"CATEGORY_CODE"
## [13] "SUB_CATEGORY_CODE"
"CONTRIBUTOR"
"CONTRIBUTOR_ORG"
## [16] "DESCRIPTION_BRIEF"
"DESCRIPTION_FULL"
"TAGS"
## [19] "MEMBERS"
"MEMBERS_SYMBOLIZED"
"MEMBERS_EZID"
## [22] "MEMBERS_MAPPING"
"FOUNDER_NAMES"
"REFINEMENT_DATASETS"
## [25] "VALIDATION_DATASETS"
For our example analysis, we will use only human gene sets. We further need to make
sure there are no NULLs in the list.
orgs <- sapply(foo2, function(x) x["ORGANISM"])
unique(orgs)
## [1] "Homo sapiens"
"Mus musculus"
"Rattus norvegicus"
## [4] "Danio rerio"
"Macaca mulatta"
NA
foo3 <- foo2[ orgs == "Homo sapiens" ]
foo3 <- foo3[ ! sapply(foo3, is.null) ]
Next, construct the MODULES data frame. We will use four named fields for each
vector, which contain the ID (systematic name), description, category and subcategory:
modules <- t(sapply(foo3,
function(x)
x[ c("SYSTEMATIC_NAME", "STANDARD_NAME", "CATEGORY_CODE", "SUBCATEGORY_CODE") ]))
colnames(modules) <- c( "ID", "Title", "Category", "Subcategory" )
modules <- data.frame(modules, stringsAsFactors=FALSE)
Then, we create the modules to genes mapping and the GENES data frame. For this,
we use the MEMBERS_SYMBOLIZED field, which is a comma separated list of gene symbols
belonging to a particular module:
75
m2g <- lapply(foo3,
function(x) strsplit( x["MEMBERS_SYMBOLIZED"], "," )[[1]])
names(m2g) <- modules$ID
mymsig <- makeTmod(modules=modules, modules2genes=m2g)
mymsig
## An object of class "tmod"
##
14645 modules, 32403 genes
From now on, you can use the object mymsig with tmod enrichment tests.
Note that it is not necessary to create the members GENES and GENES2MODULES
manually. The reverse mapping from genes to modules, GENES2MODULES, will be automatically inferred from MODULES2GENES. If no meta-information on genes is provided
in GENES, then a minimal data frame will be created with one column only (ID).
76
Chapter 8
Case studies
8.1
Metabolic profiling of TB patients
8.1.1
Introduction
One of the main objectives in writing tmod was the ability to analyse metabolic profiling data and other uncommon data sets. In 2012, we have analysed metabolic profiles
of serum collected from patients suffering from tuberculosis (TB) and healthy controls
(Weiner 3rd et al. 2012). It turned out that there are huge differences between these two
groups of individuals, involving amino acid metabolism, lipid metabolism and many others. In the course of the analysis, we found correlations between the metabolites which are
not explained fully by the metabolic pathways. For example, cortisol is correlated with
kynurenine due to the immunoactive function of these molecules indicating an activation
of the immune system, and not because these two molecules are linked by a synthesis process. Vice versa, kynurenine and tryptophan were not directly correlated, even though
these molecules are clearly linked by a metabolic process, because tryptophan is not an
immune signalling molecule, while kynurenine is.
The tmod package includes both, the data set used in the Weiner et al. paper and
the cluster definitions (modules) published therein. In the following, we will use these
modules to analyse the metabolic profiles1 .
1
Formally, this is not correct, as the modules were derived from the data set that we are going to analyse,
however it serves for demonstration purposes
77
First, we load the data modules and the data set to analyse.
data(modmetabo) ## modules
data(tbmprof)
ids <- rownames(tbmprof)
tb <- factor(gsub("\\..*", "", ids))
sex <- factor( gsub( ".*\\.([MF])\\..*", "\\1", ids))
table(tb, sex)
##
sex
## tb
F
M
##
HEALTHY 58 34
##
TB
8.1.2
25 19
Differential analysis
The metabolic profiling data has not exactly a normal distribution, but that varies from
one compound to another. It is possible to normalize it by ranking, but we can simply use
the wilcoxon test to see differences between males and females as well as TB patients and
healthy individuals.
wcx.tb <- apply(tbmprof, 2, function(x) wilcox.test(x ~ tb, conf.int=T))
wcx.tb <- t(sapply(wcx.tb, function(x) c(x$estimate, x$p.value)))
wcx.sex <- apply(tbmprof, 2, function(x) wilcox.test(x ~ sex, conf.int=T))
wcx.sex <- t(sapply(wcx.sex, function(x) c(x$estimate, x$p.value)))
wcx <- data.frame(ID=colnames(tbmprof),
E.tb=wcx.tb[,1], pval.tb=wcx.tb[,2],
E.sex=wcx.sex[,1], pval.sex=wcx.sex[,2],
row.names=colnames(tbmprof))
The data frame contains the results of all tests. We can now test both the healthy/tb
comparison and the male/female comparison for enrichment in metabolic profiling modules. Instead ordering the feature identifiers, we use the option “input.order” to determine the sorting.
78
ids <- wcx$ID
res <- list()
res$tb <- tmodCERNOtest(ids[order(wcx$pval.tb)], mset=modmetabo)
res$tb
ID
Title cerno N1
## ME.107 ME.107
##
Amino acids cluster 104.6 18
## ME.37
ME.37 Kynurenines, taurocholates and cortisol cluster 116.9 25
## MP.2
MP.2
##
AUC
Amino Acid
cES
99.2 28
P.Value adj.P.Val
## ME.107 0.882 2.91 1.28e-08
5.39e-07
## ME.37
0.884 2.34 2.82e-07
5.91e-06
## MP.2
0.706 1.77 3.36e-04
4.70e-03
res$sex <- tmodCERNOtest(ids[order(wcx$pval.sex)], mset=modmetabo)
res$sex
##
ID
Title cerno N1
## ME.26 ME.26
AUC
cES
P.Value adj.P.Val
Hormones cluster
62.5 10 0.920 3.12 2.92e-06
0.000123
Steroid
61.0 11 0.873 2.77 1.59e-05
0.000335
## ME.69 ME.69 Cholesterol cluster
45.1 11 0.819 2.05 2.55e-03
0.035649
## MS.1
MS.1
Both these result tables are concordant with previous findings. The enriched modules
in male vs female comparison are what one would expect. In TB, a cluster consisting of
kynurenine, bile acids and cortisol is up-regulated, while amino acids go down. We can
take a closer look at it using the evidencePlot function.
Why is there a module called “Amino acid cluster” and another one called “Amino
acid”? The “cluster” in the name of the module indicates that it has been build by clustering of the profiles, while the other module has been based on the biochemical classification
of the molecules. This information is contained in the Category column of the MODULES
data frame:
modmetabo$MODULES[ c("ME.107", "MP.2"), ]
##
ID
Title Category
## ME.107 ME.107 Amino acids cluster
Cluster
## MP.2
Pathway
MP.2
Amino Acid
79
To get an overview for both of these comparisons at the same time, we can use the
tmodPanelPlot function. The size of the blobs below corresponds to the AUC values from
the tables above.
tb
sex
tmodPanelPlot(res)
Amino Acid (MP.2)
Amino acids cluster (ME.107)
Kynurenines, taurocholates and cortisol cluster (ME.37)
Hormones cluster (ME.26)
Steroid (MS.1)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.92
This, unfortunately, does not tell us in which group the metabolites from a given modules are higher. For this, we can use the “estimate” from the wilcox.test above and a
parameter for tmodPanelPlot called “pie”. To create the value for this parameter – a list
that describes, for each condition and for each module, how many metabolites change in
one direction, and how many change in the other.
pie.data <- wcx[,c("E.sex", "E.tb")]
colnames(pie.data) <- c("sex", "tb")
pie <- tmodDecideTests(wcx$ID, lfc=pie.data, lfc.thr=0.2, mset=modmetabo)
tmodPanelPlot(res, pie=pie, pie.style="rug", grid="between")
80
sex
tb
Amino Acid (MP.2)
Amino acids cluster (ME.107)
Kynurenines, taurocholates and cortisol cluster (ME.37)
Hormones cluster (ME.26)
Steroid (MS.1)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.92
We see now that the cortisol cluster is higher in TB, while amino acids are found at
lower concentration in the patients. Also, we see that most of the steroids found (cluster
ME.26 and module MS.1) are lower in females. The la er is not surprising if we inspect it
closely.
wcx <- wcx[order(wcx$pval.sex),]
showModule(wcx[,c("E.sex", "pval.sex")], wcx$ID, "MS.1", mset=modmetabo)
##
E.sex pval.sex
ID
## HMDB00493
-0.87 3.04e-06
HMDB00493
## HMDB00365
-0.64 4.03e-05
HMDB00365
## HMDB02759
-0.62 1.07e-04
HMDB02759
## M.37186
-0.50 1.49e-04
M.37186
## HMDB03818.1 -0.39 1.54e-04 HMDB03818.1
## M.32619
-0.36 3.42e-04
M.32619
## HMDB03818
-0.46 4.35e-03
HMDB03818
## HMDB01032
-0.27 5.28e-03
HMDB01032
## HMDB02802
-0.10 8.85e-02
HMDB02802
## HMDB00063
-0.12 1.55e-01
HMDB00063
## HMDB04026
-0.08 3.35e-01
HMDB04026
##
## HMDB00493
Name Pathway
5alpha-androstan-3beta,17beta-diol disulfate
81
Lipid
## HMDB00365
epiandrosterone sulfate
## HMDB02759
Lipid
androsterone sulfate
Lipid
5alpha-androstan-3alpha,17beta-diol monosulfate (1)
Lipid
4-androsten-3beta,17beta-diol disulfate (2)
Lipid
pregn steroid monosulfate*
Lipid
## HMDB03818
4-androsten-3beta,17beta-diol disulfate (1)
Lipid
## HMDB01032
dehydroisoandrosterone sulfate (DHEA-S)
Lipid
## HMDB02802
cortisone
Lipid
## M.37186
## HMDB03818.1
## M.32619
## HMDB00063
cortisol
Lipid
## HMDB04026
21-hydroxypregnenolone disulfate
Lipid
##
Subpathway
HMDB
KEGG MetabolonID
## HMDB00493
Steroid HMDB00493 C12525
M.37190
## HMDB00365
Steroid HMDB00365 C07635
M.33973
## HMDB02759
Steroid HMDB02759
M.31591
## M.37186
Steroid
M.37186
## HMDB03818.1
Steroid HMDB03818 C04295
M.37203
## M.32619
Steroid
M.32619
## HMDB03818
Steroid HMDB03818 C04295
M.37202
## HMDB01032
Steroid HMDB01032 C04555
M.32425
## HMDB02802
Steroid HMDB02802 C00762
M.1769
## HMDB00063
Steroid HMDB00063 C00735
M.1712
## HMDB04026
Steroid HMDB04026 C05485
M.46115
i <- "HMDB00493" # what is it?
modmetabo$GENES[i,]
##
ID
Name Pathway
## HMDB00493 HMDB00493 5alpha-androstan-3beta,17beta-diol disulfate
##
Subpathway
## HMDB00493
HMDB
KEGG MetabolonID
Steroid HMDB00493 C12525
M.37190
par(mfrow=c(1,2))
showGene(tbmprof[,i], sex, main=modmetabo$GENES[i, "Name"],
ylab="Relative abundance")
## now for cortisol cluster
i <- "HMDB00063"
82
Lipid
wcx <- wcx[order(wcx$pval.tb),]
showModule(wcx[,c("E.tb", "pval.tb")], wcx$ID, "ME.37",
mset=modmetabo)[1:10,] # only first 10!
##
E.tb
pval.tb
ID
Name
## M.47908
-7.00e-01 2.67e-14
M.47908
Unknown
## M.32599
-8.00e-01 2.32e-10
M.32599 glycocholenate sulfate*
## HMDB00169 -6.30e-01 5.12e-09 HMDB00169
## Mx.22110
-6.45e-05 1.38e-08
mannose
Mx.22110
3-hydroxykynurenine
## HMDB00063 -5.40e-01 1.99e-08 HMDB00063
cortisol
## HMDB00159 -2.90e-01 2.49e-08 HMDB00159
phenylalanine
## M.32807
-1.22e+00 3.58e-08
M.32807
taurocholenate sulfate
## M.46637
-1.03e+00 6.66e-08
M.46637
Unknown
## M.46652
-8.40e-01 1.42e-07
M.46652
Unknown
## HMDB00684 -3.10e-01 1.79e-07 HMDB00684
kynurenine
##
Pathway
Subpathway
Lipid
Secondary Bile Acid Metabolism
## M.47908
## M.32599
## HMDB00169 Carbohydrate Fructose, Mannose and Galactose Metabolism
## Mx.22110
Amino acid
Tryptophan Metabolism
## HMDB00063
Lipid
Steroid
## HMDB00159
Amino Acid
Phenylalanine and Tyrosine Metabolism
Lipid
Secondary Bile Acid Metabolism
Amino Acid
Tryptophan Metabolism
## M.32807
## M.46637
## M.46652
## HMDB00684
##
HMDB
KEGG MetabolonID
## M.47908
M.47908
## M.32599
M.32599
## HMDB00169 HMDB00169 C00159
## Mx.22110
M.584
C02794
Mx.22110
## HMDB00063 HMDB00063 C00735
M.1712
## HMDB00159 HMDB00159 C00079
M.64
## M.32807
M.32807
## M.46637
M.46637
## M.46652
M.46652
## HMDB00684 HMDB00684 C00328
M.15140
83
showGene(tbmprof[,i], tb, main=modmetabo$GENES[i, "Name"],
ylab="Relative abundance")
5alpha−androstan−3beta,17beta−diol disulfate
cortisol
3.0
15
Relative abundance
Relative abundance
2.5
10
5
2.0
1.5
1.0
0.5
8.1.3
TB
HEALTHY
M
F
0
Functional multivariate analysis
We can practically circumvent a gene-by-gene analysis. In fact, we are rarely interested in
the p-values associated with single genes or metabolites. There is too many of them, and
the statistical power is limited by the sheer number of tests and the requirement of correction for multiple testing. In case you have not read the part on FMA above, “Functional
multivariate analysis”, in its simplest form, is simply combining a principal component
analysis (PCA) with enrichment analysis. PCA lets us explore where the variance in the
data is; enrichment analysis allows us to interprete the principal components in functional
terms.
In tmod, it can be done in a few lines of code:
pca <- prcomp(tbmprof, scale.=T)
ret <- tmodPCA(pca, genes=colnames(tbmprof), mset=modmetabo,
plot.params=list(group=tb))
84
20
15
10
5
0
−10
−5
PC 2
Polyunsaturated Fatty
Acid (n3 and n6)
Lipid
Long chain fatty
acid cluster
Long Chain
Fatty Acid
Kynurenines, taurocholates
and cortisol cluster
Secondary Bile
Acid Metabolism
−10
−5
0
5
10
15
Medium Chain
Fatty Acid
Lysolipid
Long
PC 1Chain
Fatty Acid
Lipid
Medium−chain fatty
Polyunsaturated Fatty
acids cluster
Acid (n3 and n6)
Long chain fatty
acid cluster
Amino acids
cluster
The ret object now contains the results of enrichments (in the ret$enrichments member) and we can directly throw it on a panel plot:
tmodPanelPlot(ret$enrichments)
85
Component2
Component1
Kynurenines, taurocholates and cortisol cluster (ME.37)
Lysolipid (MS.47)
Medium−chain fatty acids cluster (ME.6)
Amino acids cluster (ME.107)
Medium Chain Fatty Acid (MS.37)
Polyunsaturated Fatty Acid (n3 and n6) (MS.40)
Long Chain Fatty Acid (MS.36)
Long chain fatty acid cluster (ME.2)
Lipid (MP.1)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.95
OK, but which of the terms are characteristic for TB patients? Which for the healthy
controls? In the above, the enrichments were based on a list sorted by the absolute PCA
weights. However, we can split it into a list ordered by signed weights ordered once from
small to large values, and once from large to small values.
pca <- prcomp(tbmprof, scale.=T)
ret <- tmodPCA(pca, genes=colnames(tbmprof), mset=modmetabo,
plot.params=list(group=tb),
mode="cross")
86
Long Chain Secondary Bile
Fatty Acid Acid Metabolism
Kynurenines, taurocholates
and cortisol cluster
Lipid
Polyunsaturated Fatty
Acid (n3 and n6)
15
20
Long chain fatty
acid cluster
10
Long Chain
Fatty Acid
5
Polyunsaturated Fatty
Acid (n3 and n6)
Medium Chain
Fatty Acid
Medium−chain fatty Lipid
acids cluster
Lysolipid
−10
−5
Kynurenines, taurocholates
and cortisol cluster
Putative
hypoxia−related cluster
Pyrophosphates
cluster
Peptide
Amino acids Long chain fatty
cluster
acid cluster
0
PC 2
Carbohydrate
Secondary Bile
Acid Metabolism
−10
−5
0
5
Nicotine
PC 1
metabolites cluster
10
15
Hippurate
cluster
Urea cycle; Arginine
and Proline Metabolism
Amino acids
cluster
Amino
Acid
In essence, reading this plot is simple. First, note that this time the tag clouds on the
top and the bo om correspond to the two ends of the vertical, y axis (second component);
and the tag clouds at the left and right correspond to the two ends of the horizontal, x axis
(first PCA component).
Now, take the amino acid cluster (bo om of the plot): it is enriched at the lower end of
the y axis, which means, that features in that cluster are higher in the yellow points which
are at the bo om of the plot (lower end of the y). In other words, amino acids are higher
in healthy persons – a finding which corroborates the differential analysis above.
Similarly, “kynurenines” are at the left, lower side of the x axis, which means, that
features from this cluster are at higher levels in TB patients.
What about the male-female differences? They probably can be found in other, less
important2 components. We could look for them manually, but we can also search which
2
That is, components which include a smaller fraction of the total variance in the data set
87
of the responses (turned to orthogonal PCA components) is best predicted by the sex
factor.
foo <- summary(lm(pca$x ~ sex))
foo <- t(sapply(foo,
function(x) c(r=x$r.squared, pval=x$coefficients[2,4])))
head(foo[ order(foo[,2]), ])
##
r
pval
## Response PC5
0.2457 8.49e-10
## Response PC10
0.2146 1.36e-08
## Response PC7
0.0328 3.48e-02
## Response PC8
0.0221 8.39e-02
## Response PC107 0.0199 1.02e-01
## Response PC6
0.0192 1.08e-01
We can use the components 1 (which corresponds to TB/healthy) and components 5,
which corresponds to male/female differences, as suggested by the above calculations.
ret <- tmodPCA(pca, genes=colnames(tbmprof), mset=modmetabo,
plot.params=list(group=paste(sex, tb)),
components=c(2,5))
88
10
5
0
−5
PC 5
Steroid
Lysophosphatidylcholines
and bilirubines cluster
−10
Lysolipid
Hormones
cluster
Long Chain
Fatty Acid
Lipid
−10
−5
0
5
10
15
20
Long Chain Long chain
PC
2
fatty
Fatty Acid
acid cluster
Kynurenines, taurocholates Secondary Bile
and cortisol cluster
Polyunsaturated Fatty
Acid (n3 and n6)
Lipid
Acid Metabolism
Orange circles and blue triangles are females, located mostly in Q1 and Q2 (top half);
this corresponds to differences on the y axis and the tagcloud next to it (hormone cluster,
steroids etc.). On the other hand, TB patients (blue triangles and yellow circles) are in Q1
and Q4 (right-hand side), which corresponds to the TB-specific tag cloud below the y axis.
8.2
Case study: RNASeq
The example below has been extended from the edgeR package users manual.
The code below loads the data and, using org.Hs.eg.db, adds Entrez IDs and HGNC
symbols.
89
library(edgeR)
rawdata <- read.csv("rnaseq_example.csv", stringsAsFactors=FALSE)
y <- DGEList(counts=rawdata[,4:9], genes=rawdata[,1:3])
map <- toTable(org.Hs.egREFSEQ2EG)
y$genes$EG <- map$gene_id[ match(y$genes$idRefSeq, map$accession) ]
map <- toTable(org.Hs.egSYMBOL)
y$genes$Symbol <- map$symbol[ match(y$genes$EG, map$gene_id) ]
Next, we perform differential gene expression to test for the difference between normal
tissue (N) and tumor (T).
Patient <- paste0("P.", rep(c(8, 33, 51), each=2))
Tissue
<- rep(c("N", "T"), 3)
design <- model.matrix(~Patient+Tissue)
y <- calcNormFactors(y)
design <- model.matrix(~Patient+Tissue)
y <- estimateDisp(y, design, robust=TRUE)
fit <- glmQLFit(y, design)
## calculate the results for coefficient of interest
lrt <- glmQLFTest(fit, coef="TissueT")
Since there are no confidence intervals for log fold changes in edgeR, we cannot compute MSD, and therefore we will use the p-values to order the genes in the following code:
ord <- order(lrt$table$PValue)
res.rnaseq <- list()
res.rnaseq$tmod <- tmodCERNOtest(lrt$genes$Symbol[ord])
res.rnaseq$goset <- tmodCERNOtest(lrt$genes$EG[ord], mset=goset)
So far, so good. However, an alternative to using MSD is test the log fold change of
the selected contrast not against 0, but against a pre-selected threshold using the TREAT
method (McCarthy and Smyth 2009), implemented in edgeR in the function glmTreat:
90
lrt.treat <- glmTreat(fit, coef="TissueT", lfc=log2(2))
ord <- order(lrt.treat$table$PValue)
res.rnaseq$treat.tmod <- tmodCERNOtest(lrt$genes$Symbol[ord])
res.rnaseq$treat.goset <- tmodCERNOtest(lrt$genes$EG[ord], mset=goset)
res.rnaseq <- res.rnaseq[c(1,3,2,4)]
treat.goset
goset
treat.tmod
tmod
tmodPanelPlot(res.rnaseq, filter.rows.pval=1e-3)
cell adhesion (LI.M51)
enriched for cell migration (LI.M122)
extracellular matrix, collagen (LI.M210)
cell cycle and transcription (LI.M4.0)
cytoskeleton/actin (SRF transcription targets) (LI.M145.1)
immune activation − generic cluster (LI.M37.0)
B cell surface signature (LI.S2)
complement activation (I) (LI.M112.0)
complement activation (II) (LI.M112.1)
enriched in monocytes (II) (LI.M11.0)
enriched in myeloid cells and monocytes (LI.M81)
platelet degranulation (GO:0002576)
muscle filament sliding (GO:0030049)
cardiac muscle contraction (GO:0060048)
skeletal muscle contraction (GO:0003009)
sarcomere organization (GO:0045214)
muscle organ development (GO:0007517)
epidermis development (GO:0008544)
peptide cross−linking (GO:0018149)
P value:
0.01
10−4
0.001
10−5
10−6
Effect size:
0.5
0.93
The results are very similar, but the p-values are lower.
91
References
Banchereau, Romain, Alejandro Jordan-Villegas, Monica Ardura, Asuncion Mejias,
Nicole Baldwin, Hui Xu, Elizabeth Saye, et al. 2012. “Host Immune Transcriptional
Profiles Reflect the Variability in Clinical Disease Manifestations in Patients with
Staphylococcus Aureus Infections.” PLoS One 7 (4). Public Library of Science: e34390.
Chaussabel, Damien, Charles Quinn, Jing Shen, Pinakeen Patel, Casey Glaser, Nicole
Baldwin, Dorothee Stichweh, et al. 2008. “A Modular Analysis Framework for Blood
Genomics Studies: Application to Systemic Lupus Erythematosus.” Immunity 29 (1). Elsevier: 150–64.
Damian, Doris, and Malka Gorfine. 2004. “Statistical Concerns About the GSEA Procedure.” Nature Genetics 36 (7). Nature Publishing Group: 663–63.
Li, Shuzhao, Nadine Rouphael, Sai Duraisingham, Sandra Romero-Steiner, Sco Presnell, Carl Davis, Daniel S Schmidt, et al. 2014. “Molecular Signatures of Antibody Responses Derived from a Systems Biology Study of Five Human Vaccines.” Nature Immunology 15 (2). Nature Publishing Group: 195–204.
Maer dorf, Jeroen, Martin Ota, Dirk Repsilber, Hans J Mollenkopf, January Weiner,
Philip C Hill, and Stefan HE Kaufmann. 2011. “Functional Correlations of PathogenesisDriven Gene Expression Signatures in Tuberculosis.” PloS One 6 (10). Public Library of
Science: e26938.
McCarthy, Davis J, and Gordon K Smyth. 2009. “Testing Significance Relative to a
Fold-Change Threshold Is a TREAT.” Bioinformatics 25 (6). Oxford University Press: 765–
71.
Smyth, Gordon K. 2005. “Limma: Linear Models for Microarray Data.” In Bioinformatics and Computational Biology Solutions Using R and Bioconductor, edited by R. Gentleman,
92
V. Carey, S. Dudoit, R. Irizarry, and W. Huber, 397–420. New York: Springer.
Subramanian, Aravind, Pablo Tamayo, Vamsi K Mootha, Sayan Mukherjee, Benjamin
L Ebert, Michael A Gille e, Amanda Paulovich, et al. 2005. “Gene Set Enrichment Analysis: A Knowledge-Based Approach for Interpreting Genome-Wide Expression Profiles.”
Proceedings of the National Academy of Sciences of the United States of America 102 (43). National Acad Sciences: 15545–50.
Tomfohr, John, Jun Lu, and Thomas B Kepler. 2005. “Pathway Level Analysis of Gene
Expression Using Singular Value Decomposition.” BMC Bioinformatics 6 (1). BioMed Central: 225.
Weiner 3rd, January, and Teresa Domaszewska. 2016. “Tmod: An R Package for General and Multivariate Enrichment Analysis.” PeerJ Preprints 2016 (09). PeerJ, Inc.
Weiner 3rd, January, Shreemanta K Parida, Jeroen Maer dorf, Gillian F Black, Dirk
Repsilber, Anna Telaar, Robert P Mohney, et al. 2012. “Biomarkers of Inflammation, Immunosuppression and Stress with Active Disease Are Revealed by Metabolomic Profiling
of Tuberculosis Patients.” PloS One 7 (7). Public Library of Science: e40221.
Weiner, January. 2013. Pca3d: Three Dimensional PCA Plots.
———. 2014. Tagcloud: Tag Clouds.
Wendt, Hans W. 1972. “Dealing with a Common Problem in Social Science: A Simplified Rank-Biserial Coefficient of Correlation Based on the U Statistic.” European Journal of
Social Psychology 2 (4). Wiley Online Library: 463–65.
Yamaguchi, Ken D, Daniel L Ruderman, Ed Croze, T Charis Wagner, Sharlene
Velichko, Anthony T Reder, and Hugh Salamon. 2008. “IFN-β -Regulated Genes Show
Abnormal Expression in Therapy-Naïve Relapsing–remi ing MS Mononuclear Cells:
Gene Expression Analysis Employing All Reported Protein–protein Interactions.” Journal
of Neuroimmunology 195 (1). Elsevier: 116–20.
93
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