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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Using limma for Differential Expression
James W. [email protected]
BioC 2010July 29, 2010
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Overview
Overall goal is to teach use of limma
Example analyses
colonCAestrogen
Statistical discussions
Linear modelsExperimental designDesign/contrast matricesMultiple comparisons
Visualization/output of results
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Why limma?
Fit nearly any model
Technical replicates
One/two color arrays
Increased power
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Why not limma?
Complexity
Reliance on normal theory
Can’t fit linear mixed models
Can’t handle multiple levels of technical replication
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Normal analysis workflow
Import data
Pre-process
Fit model(s)
Make comparisons
Filter data
Output results
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Load Data
Load data we will use today.
> x <- "http://www.umich.edu/~jmacdon/BioC2010.Rdata"
> con <- url(x)
> load(con)
> close(con)
If using thumb drive, start R in directorycontaining BioC2010.Rdata, then
> load("BioC2010.Rdata")
> ls()
[1] "colonCA" "estrogen"
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
colonCA
> library(Biobase)
> head(pData(colonCA))
expNr samp class
1 1 -1 t
2 2 1 n
3 3 -2 t
4 4 2 n
5 5 -3 t
6 6 3 n
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Simple t-test
Assume no pairingTwo common parameterizationsCell means modelBaseline modelThese parameterizations are equivalent
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
The t-statistic
General form of a t-statistic
t =β̂s√n
Numerator captures differences
Denominator acts as ’yardstick’ for numerator
We are testing β = 0
Compare to reference distribution to assess significance
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Inference for t-statistic
−10 0 10 20
0.0
0.1
0.2
0.3
t−distribution
Den
sity
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Inference for t-statistic
−10 0 10 20
0.0
0.1
0.2
0.3
t−distribution
Den
sity
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Inference for t-statistic
−10 0 10 20
0.0
0.1
0.2
0.3
t−distribution
Den
sity
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Cell Means Model
yij = µj + εij
or
ytumor1 = µtumor + εtumor1
ynormal1 = µnormal + εnormal1
or
yij = Iµtumor + Iµnormal + εij
I ∈ (0, 1)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Cell Means Design Matrix
> design <- model.matrix(~0+pData(colonCA)$class)
> colnames(design) <- c("Normal","Tumor")
> head(design)
Normal Tumor
1 0 1
2 1 0
3 0 1
4 1 0
5 0 1
6 1 0
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Cell Means Contrast Matrix
Recall t-statistic:
t =β̂s√n
> makeContrasts(Tumor - Normal, levels = design)
Contrasts
Levels Tumor - Normal
Normal -1
Tumor 1
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Fit Cell Means Model
> fit <- lmFit(colonCA, design)
> fit <- contrasts.fit(fit, contrast)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Baseline Model
yij = α + τj + εij
or
ynormal1 = α + εnormal1
ytumor1 = α + τ1 + εtumor1
or
yij = α + I τj + εij
I ∈ (0, 1)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Baseline Model Design Matrix
> tumorvnormal <- pData(colonCA)$class
> design <- model.matrix(~tumorvnormal)
> colnames(design) <- c("Intercept","Tumor-Normal")
> head(design)
Intercept Tumor-Normal
1 1 1
2 1 0
3 1 1
4 1 0
5 1 1
6 1 0
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Fit Baseline Model
> fit <- lmFit(colonCA, design)
Now what?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Sample size
The t-statistic (again)
t =β̂s√n
Denominator dependent on
Sample variability
Number of replicates
Sample variability dependent on
Number of replicates
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
eBayes
Fewer replicates increase variability:
Mathematically
By chance
eBayes step estimates ’average’ variability over all genes and
Adjusts high variability genes down
Adjusts low variability genes up
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Filter data
Things to consider:
eBayes needs all genes
Multiple comparisons problem
Statistical vs biological significance
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Selecting ’Top’ Genes
eBayes/topTable control output by
Coefficient of interestNumber of genesp-value (adjusted)Fold change
treat/topTreat control output by
All of the aboveIncorporates fold change into computation of p-value
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Output data
> fit2 <- eBayes(fit)
> output <- topTable(fit2, coef = 2)
> ## or
> fit2 <- treat(fit)
> output <- topTreat(fit2, coef = 2)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Output
How do the results for eBayes and treat differ?Check man pages for how to incorporate fold change.How do the results differ when adding a fold change criterion?How would one select genes with a FDR of 5%?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Paired Analysis
Colon cancer data are actually paired:
> head(pData(colonCA))
expNr samp class
1 1 -1 t
2 2 1 n
3 3 -2 t
4 4 2 n
5 5 -3 t
6 6 3 n
So how do we handle this aspect?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Paired data
●
●
●
●
●
1 2 3 4 5
45
67
89
1011
●
●
●
●
●
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Paired analysis ’by hand’
> ind <- pData(colonCA)$samp > 0
> dat <- exprs(colonCA)[,!ind] -
+ exprs(colonCA)[,ind]
> design <- rep(1, ncol(dat))
> fit <- lmFit(dat, design)
> fit.pair1 <- eBayes(fit)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Paired analysis using batch term
> pair <- factor(abs(pData(colonCA)$samp))
> design <- model.matrix(~tumorvnormal +
+ pair)
> colnames(design) <- c("Intercept", "Tumor-Normal",
+ paste("Pair", 2:22, sep=""))
> head(design)[,1:4]
Intercept Tumor-Normal Pair2
1 1 1 0
2 1 0 0
3 1 1 1
4 1 0 1
5 1 1 0
6 1 0 0
Pair3
1 0
2 0
3 0
4 0
5 1
6 1
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Paired analysis using batch term
●
●
●
●
●
1 2 3 4 5
45
67
89
1011
●
●
●
●
●
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
> fit <- lmFit(colonCA, design)
> fit.pair2 <- eBayes(fit)
> comp <- cbind(fit.pair1$coef, fit.pair2$coef[,2])
> colnames(comp) <- c("Direct","Batch")
> head(comp)
Direct Batch
Hsa.3004 0.25 0.25
Hsa.13491 0.14 0.14
Hsa.13491.1 0.22 0.22
Hsa.37254 0.13 0.13
Hsa.541 0.30 0.30
Hsa.20836 0.16 0.16
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Data
> pData(estrogen)
sample
high10-1.cel 1
high10-2.cel 2
high48-1.cel 3
high48-2.cel 4
low10-1.cel 5
low10-2.cel 6
low48-1.cel 7
low48-2.cel 8
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Comparisons
Comparisons of interest:
High vs low estrogen
10 vs 48 hour incubation
Interaction
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Design Matrix
What would a cell means design matrix look like?How would it be constructed?Hint: See ?formulaHow about the contrasts matrix?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Design Matrix I
> Level <- factor(rep(c("High","Low"), each=4))
> Time <- factor(rep(c("10","48"), each = 2,
+ times = 2))
> design <- model.matrix(~0+Level*Time)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Design Matrix
What would a baseline design matrix look like?How would it be constructed?How about the contrasts matrix?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Design Matrix II
> design <- model.matrix(~Level*Time)
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
Estrogen Differential Expression
> fit <- lmFit(estrogen, design)
> fit2 <- eBayes(fit)
But now what?
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
decideTests
topTable for multiple coefficientsVarious options to control multiplicity
separate
global
hierarchical
nestedF
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
decideTests
> rslt <- decideTests(fit2[,2:4])
> rslt[1:5,]
LevelLow Time48
1000_at 0 0
1001_at 0 0
1002_f_at 0 0
1003_s_at 0 0
1004_at 0 0
LevelLow:Time48
1000_at 0
1001_at 0
1002_f_at 0
1003_s_at 0
1004_at 0
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
vennDiagram
> vennDiagram(rslt)
LevelLow Time48
LevelLow:Time48 12166
0
133
0
287
0
39
0
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
GSEA
No significant genes in interaction.Does that mean we are done?Consider genes as a set instead of individually.
geneSetTest
Competitive analysisH0: Our set of genes no more differentiallyexpressed than the remainder of genes on the chip.
roast/romer
Self-contained analysisH0: Our set of genes is not differentially expressed.
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
geneSetTest
Two required arguments:
’Indicator’vector for genes of interest
Vector of statistics
> ind <- as.numeric(row.names(topTable(fit2,
+ coef = 4,
+ number = 100,
+ p.value = 0.2)))
> geneSetTest(ind, fit2$t[,4])
[1] 2.3e-14
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BioC2010
Introduction
Colon CancerData
Two-group
Filter/Output Data
Paired analysis
Estrogen Data
roast
Four required arguments:
’Indicator’ vector for genes of interest
Matrix of expression values
Design matrix
Contrast matrix
> roast(ind, exprs(estrogen), design, c(0,0,0,1))
Active.Prop P.Value
Mixed 1.00 0.003
Up 0.32 0.990
Down 0.68 0.011