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RNA-seq data analysis and differential expression
Michael Love Biostatistics Department
UNC Chapel Hill
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Outline
1. Example RNA-seq experiment
2. Statistical analysis of RNA-seq counts
3. Theory of shrinkage estimation
4. Testing steps & statistical power
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Our goal: what is airway transcriptome response to glucocorticoid hormone?
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four human donors
airway epithelial cells
control
treat with dexamethasone
extract mRNA
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Glucocorticoid mechanism of action
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(C) CSLS / University of Tokyo hBp://csls-‐text3.c.u-‐tokyo.ac.jp/
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Compare gene expression across treatment,
within cell line
ü Visualize differences between samples
ü Test for differences in gene expression, one gene at a time
ü Visualize differences across all genes
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control
treated with dexamethasone
cDNA libraries
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Compare gene expression across treatment,
within cell line
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control
treated with dex.
cDNA libraries PCA plot
MA plot
"counts plot"
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2. FPKM/TPM vs counts
• FPKM: fragments per kilobase per million mapped reads
• TPM: transcripts per million
• FPKM/TPM ∝ gene expression comparable across genes
• Counts have extra information: useful for statistical modeling
cummeRbund
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mRNAs to RNA-seq fragments
Kij = count of fragments aligned to gene i, sample j is proporQonal to: • expression of RNA • length of gene • sequencing depth • lib. prep. factors (PCR) • in silico factors (alignment) • ...
colors: different genes
mRNA transcript
SE reads or PE fragments
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Sequencing depth
sample 1 sample 2
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Variance of counts
Consider one gene:
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Variance of counts
Consider one gene: • Binomial sampling distribuQon
• With millions of reads & small proporQon for each gene −> Poisson sampling distribuQon
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Raw counts vs. normalized counts
Raw count with mean of 100 Poisson sampling, so SD=10
Raw count mean = 1000 Scaled by 1/10 SD = ?
Raw count mean = 10 Scaled by 10 SD = ?
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Raw counts vs normalized counts
Kij ⇠ L(µij = sijqij)
Kij
sij⇠ L(µij = qij)
raw count for gene i, sample j normalizaQon factor ∝ gene expression
some distribuQon
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staQsQcal inference "for free" edgeR, DESeq2
mean parameter
can be made to work with extra modeling e.g. limma-‐voom
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Biological replicates
If the proporQons of mRNA stays exactly constant ("technical replicate") we can expect Poisson dist.
But realisQcally, biological variaQon across sample units is expected
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Biological replicates
Biological variaQon for the abundance of a given gene produces "over-‐dispersion" relaQve to the Poisson dist.
NegaQve Binomial = Poisson with a varying mean
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Dispersion parameter
Var(Kij) = µij + ↵iµ2ij
Poisson part: sampling fragments
Extra variaQon due to biological variance
disp = 0.01 −> CV 10% disp = 0.25 −> CV 50%
for large counts: (coefficient of variaQon) p↵i ⇡
�
µ⌘ CV
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3. Shrinkage estimation distribuQon of 1000 darts players' ability: not observed
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"shrunken" esQmates less error overall than individual esQmates
observed distribuQon: averages of 3 throws from each of 1000 players
shrink the averages towards a center defined by the observed distribuQon
each throws 3 darts: sample variance of the average
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Shrinkage estimation
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populaQon distribuQon
sampling variance around true ability
empirical distribuQon
the center defines the prior mean
MLE maximum likelihood esQmates
shrunken esQmates or MAP maximum a posteriori
dashed = unobserved
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Shrinkage estimation
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✗ ✗
✓ ✓ ✗
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Shrinkage estimators in genomics
• Lönnstedt and Speed 2002: microarray
• Smyth 2004: limma for microarray
• Robinson and Smyth 2007: edgeR for SAGE and then applied to RNA-seq
• Many adaptations: DSS and DESeq2 are a similar approach, data-driven strength of shrinkage
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Shrinkage of dispersion for RNA-seq a subset of genes (Pickrell) all genes (Pasilla)
1. Gene es.mate = maximum likelihood esQmate (MLE) 2. Fi3ed dispersion trend = the mean of the prior 3. Final es.mate = maximum a posteriori (MAP)
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Shrinkage of fold changes for RNA-seq
noisy esQmates due to low counts large FDR from the staQsQcal model, but we shouldn't trust the esQmate itself
shrinkage is not equal. strong moderaQon for low informaQon genes: low counts
almost no shrinkage
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Why shrink fold changes?
Split a dataset into two equal parts, compare LFC
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Why shrink fold changes?
G. A. Moyerbrailean et al. "A high-‐throughput RNA-‐seq approach to profile transcripQonal responses" hBp://dx.doi.org/10.1101/018416
Comparison of log fold changes across two experiments. "A new two-‐step high-‐throughput approach: 1. gene expression screening of a large number of condiQons 2. deep sequencing of the most relevant condiQons"
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Two paths in RNA-seq analysis
Count matrix
DifferenQal expression
tesQng, p-‐values, FDR
DESeq()results()
glmLRT() topTags()
TransformaQons and Exploratory Data Analysis (EDA) clustering, heatmaps, sample-‐sample distances vst(), rlog(), plotPCA()
cpm(), plotMDS()
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DESeq2
edgeR
DESeq2
edgeR
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Regularized logarithm, "rlog"
similar idea as fold change shrinkage, now sample-‐to-‐sample fold changes
sample 1 sample 1
sample 2
sample 2
log2(x + 1) "rlog"
Poisson noise from low counts, when squared a big contribuQon to Euclidean distance between samples
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rlog stabilizes variance along the mean
log2(x + 1) "rlog"
improving distances, clustering, visualizaQons
corrects systema,c dependencies, doesn't force all variances equal.
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standard deviaQo
n
standard deviaQo
n
rank( mean ) rank( mean )
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Also in DESeq2: VST
• Variance stabilizing transformation: calculate the dependence of variance on the mean (using the dispersion trend)
• Closed-form expression f(x) for stabilizing
• vst() is a faster implementation
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4. Testing steps
1. size factors (sequencing depth) 2. dispersion (additional variance)
3. Wald test or likelihood ratio test
4. build a results table
count matrix (from featureCounts, summarizeOverlaps, htseq, tximport, etc.)
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Statistical power
• False positive rate (1 - specificity): under the null (no differences), how many called positives?
• Precision (1 - false discovery rate): of the positives (called DE), how many are true positives?
• Power (sensitivity): under the alternative to the null, how many called positive?
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Statistical power Why not use a simple t-‐test on log normalized counts?
t-‐test
DESeq2
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Factors influencing power
• Range of count – Sequencing depth
– Expression – Gene length
• Sample size
• Dispersion • True fold change
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Bioc pkg: RNASeqPower
varying the count varying the dispersion
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Power depends on range of counts
By excluding some tests, e.g. genes with mean normalized count < 5, we reduce the penalty on adjusted p-‐values from mulQple test correcQon.
mean normalized count mean normalized count
log fold change
raQo
of small p-‐value
s
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Power depends on range of counts
• Filter on a statistic which is: – independent of the test statistic under the null
– correlated under the alternate hypothesis
Bourgon, Gentleman and Huber, PNAS 2010.
quanQle of mean of normalized counts
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Independent Hypothesis Weighting
• Wolfgang will teach later this week...
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Testing against a threshold
null hypothesis: fold change = 1 null hypothesis: fold change is < 2 or > 1/2
using 'lfcThreshold' in results()
"For well-‐powered experiments, however, a staQsQcal test against the convenQonal null hypothesis of zero LFC may report genes with staQsQcally significant changes that are so weak in effect strength that they could be considered irrelevant or distrac.ng."
"We get too many DEGs..."
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Bioconductor help
• Vignettes:
> browseVignettes("DESeq2") > vignette("DESeq2")
• Type ? then the function name:
> ?results
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Bioconductor help results package:DESeq2 R Documentation
Extract results from a DESeq analysis
Description:
‘results’ extracts a result table from a DESeq analysis giving base means across samples, log2 fold changes, standard errors, test statistics, p-values and adjusted p-values; ‘resultsNames’ returns the names of the estimated effects (coefficents) of the model; ‘removeResults’ returns a ‘DESeqDataSet’ object with results columns removed.
Usage:
results(object, contrast, name, lfcThreshold = 0, altHypothesis = c("greaterAbs", "lessAbs", "greater", "less"), listValues = c(1, -1), cooksCutoff, independentFiltering = TRUE, alpha = 0.1, filter, theta, pAdjustMethod = "BH", format = c("DataFrame", "GRanges", "GRangesList"), test, addMLE = FALSE, tidy = FALSE, parallel = FALSE, BPPARAM = bpparam())
...
Arguments:
object: a DESeqDataSet, on which one of the following functions has already been called: ‘DESeq’, ‘nbinomWaldTest’, or ‘nbinomLRT’
contrast: this argument specifies what comparison to extract from the ‘object’ to build a results table. one of either:
• a character vector with exactly three elements: the name of a factor in the design formula, the name of the numerator level for the fold change, and the name of the denominator level for the fold change (simplest case)
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Bioconductor help
Value:
For ‘results’: a ‘DESeqResults’ object, which is a simple subclass of DataFrame. This object contains the results columns: ‘baseMean’, ‘log2FoldChange’, ‘lfcSE’, ‘stat’, ‘pvalue’ and ‘padj’, and also includes metadata columns of variable information....
...
References:
Richard Bourgon, Robert Gentleman, Wolfgang Huber: Independent filtering increases detection power for high-throughput experiments. PNAS (2010), <URL: http://dx.doi.org/10.1073/pnas.0914005107>
See Also:
‘DESeq’
Examples:
## Example 1: simple two-group comparison
dds <- makeExampleDESeqDataSet(m=4)
...
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Looking up help for objects
> class(dds)[1] "DESeqDataSet"attr(,"package")[1] "DESeq2"
> ?DESeqDataSet
> help(package="DESeq2", help_type="html")
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Bioconductor support site
• biological quesQon • all code, any errors/warnings • sessionInfo()
always provide:
All ques.ons about Bioconductor sooware post to: support.bioconductor.org
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