case study i: two-sample analysis

Case Study I: Two-Sample Analysis

Ru-Fang Yeh

October 23, 2004 Genentech Hall Auditorium, Mission Bay, UCSF

Microarrays: Case Studies and Advanced Analysis

Biological verification and interpretation

TestingEstimation Discrimination

Analysis

Clustering

Microarray experiment

Experimental design

Image analysis

Normalization

Biological question

Quality Measurement

Failed

Pass

Preprocessing

Sample/ConditionGene 1 2 3 4 … 1 0.46 0.30 0.80 1.51 … 2 -0.10 0.49 0.24 0.06 … 3 0.15 0.74 0.04 0.10 … : …

Annotation


Short-oligonucleotide chip data:• quality assessment,• background correction, • probe-level normalization,• probe set summary

Two-color spotted array data:• quality assessment; diagnostic plots,• background correction, • array normalization.

CEL, CDF files gpr, gal files

probes by sample matrix of log-ratios or log-intensities

Analysis of expression data:• Identify D.E. genes, estimation and testing,• clustering, • discrimination, and etc.

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g Array CGH data:•quality assessment; diagnostic plots,•, background correction • clones summary; • array normalization.

UCSF spot file

Imag

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Biological Question: Molecular Phenotypic Difference in Rat Alveolar

Type I and Type II Cells

From “Freshly-isolated Rat Alveolar Type I Cells, Type II Cells, and Cultured Type II Cells Have Distinct Molecular

Phenotypes.” (To appear, A J Phys) By Robert Gonzalez, Yee Hwa Yang, Chandi Griffin, Lennell

Allen, Zachary Tigue, and Leland Dobbs.


Pulmonary Alveolar Epithelium

Type I Cells

Type II Cells


Type I Cells Type II Cells% Lung cells ~8% ~15%% Lung internal surface area ~98% ~2%Volume / cell ~2000 µm3 ~400 µm3

Surface / area ~5300 µm2 ~100 µm2

Stone, AJRCMB 1992

• Morphologic characteristics conserved across the entire range of mammals.

Known/Possible - water and ion transport - surfactant metabolismFunctions - host defense (oxidants - ion transport

& microorganisms - produce immune

- tumor suppression effector molecules

- matrix preservation - Progenitor cells for TI cells after oxidant

injury (and in lung

development)

Alveolar Epithelial Type I and Type II Cells


Type II cell

Proliferation

Type I cell

TransdifferentiationThe process by which one “stable” (differentiated) cellular phenotype changes into a different “stable” cellular phenotype.

Evans, 1975Adamson, 1975

Alveolar Epithelial Cell Lineage Following Lung Injury


Study Objectives

Long term goals: Increase understanding of• alveolar epithelial cell lineages. • the mechanisms that regulate alveolar epithelial development and

differentiation.

Use microarrays to establish molecular profiles of TI and TII cells:• Identification of differences in expression of single genes to

- provide additional marker genes- develop new hypotheses about cellular functions of each cell type

• To determine changing patterns of expression of groups of genes- to understand processes of (trans)-differentiation in vivo and in vitro- to identify candidate factors (transcription cascades) important in

regulating differentiation

Gene Expression Experiment

TII Cells Cultured TII Cells

TI Cells


Freshly Isolated TI and TII Cells

TII CELLS TI CELLS

TI cell fragment

TII cell


• Matrix (EHS, contracted collagen gels)• Soluble factors (ex: KGF)• Apical surface exposed to air• Mechanical contraction

• Matrix (TCP, fibronectin)

• Apical surface covered by liquid• Mechanical distention

Type II Cells in vitro


Experimental design

• Probe: Affymetrix Rat U34 chip A, with 8799 probe sets.

• Target: 4 biological replicates of each cell type: - TID0: freshly isolated TI cells- TIID0: freshly isolated TII cells- TIID7: cultured TII cells (for 7 days)

[traditionally used as a model for TI day 0 cells]

Cell purity criterion: < 2% cross-contamination


Preparing mRNA samples:

Dissection of tissue

RNA Isolation

Amplification

Probelabelling

Hybridization




RNA Isolation

Amplification

Probelabelling

Hybridization

Biological Replicate




RNA Isolation

Amplification

Probelabelling

Hybridization

Technical replicate


Analysis Aims

Main Questions: Establish molecular profiles of TI and TII cells:

1. Identification of differences in expression of single genes to:- provide additional marker genes

- develop new hypotheses about cellular functions of each cell type.

2. To understand the process of (trans)-differentiation in vivo and in vitro

3. To identify candidate factors (transcription cascades) important in regulating differentiation.

Approaches:

1. Identify differentially expressed (DE) genes between TID0 and TII D0.

2. Comparing TID0 and TIID7; are they similar?

3. Finding common regulatory element (transcription factor binding site) in groups of candidate co-regulated genes.




Analysis

Clustering


Experimental design

Image analysis

Normalization

Biological question

Quality Measurement

Failed

Pass

Preprocessing


Annotation

Preprocessing

• Quality Assessment.• Background subtraction.• Normalization.• Summarization of probe sets value.


High Density Oligonucleotide Arrays (Affymetrix)

24µm24µm

Millions of copies of a specificMillions of copies of a specificoligonucleotide probe per probe celloligonucleotide probe per probe cell

Image of Hybridized Probe ArrayImage of Hybridized Probe Array

~500,000 probe cells on each ~500,000 probe cells on each chipchip

Single stranded, Single stranded, labeled RNA labeled RNA targettarget

Oligonucleotide Oligonucleotide probeprobe

**

**

*

GeneChipGeneChip Probe ArrayProbe Array

Hybridized Hybridized Probe CellProbe Cell

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

1.28cm1.28cm


How Affymetrix Arrays Are Made



Figure from Lipshutz et al. Nat. Gen. 1999.


5’ 3’

mRNA reference sequence

…TCGTCTGTATCACAGACACAAAGTTGACTG…PM: CAGACATAGTGTCTGTGTTTCAACTMM: CAGACATAGTGTGTGTGTTTCAACT

MMFluorescent probe intensity

For one gene (probe set): 16 probes/gene for Rat U34

PM


DAT FileHybridization+ Scanning

Image analysis

CEL File

CHP FileIntensity value

Absent / Present call

CDF File+

Text FileProbe ID +

Log2 (Intensity)

Excel File

RMAGCRMA

MASGCOS

dChip

Report File, quality

Preprocessing0. Quality Assessment.1. Background subtraction

(B).2. Normalization (N).3. Summarization of

probe sets values (S).


Quantile NormalizationBolstad et al (2003)

• Quantile normalization is a method to make the distribution of probe intensities the same for every chip.

• The normalization distribution is chosen by averaging each quantile across chips.


Probe Set Summarization:Robust Multi-array Average -- Irizarry et al (2003)

• The RMA model assumes that each probe cell is made up of

Log2 Normalized (Observed Intensity – Background) =

Chip effect + Probe-specific effect + error

• The expression level is estimated using a robust procedure (such as median polish or IRLS) to fit the above linear model.

PM

RMA values: log2 Expression for chip i


Summarization Method Comparison: AffyComp http://affycomp.biostat.jhsph.edu/

Median SD across replicates

average false positivesif we use fold-change > 2 as a cut-off

http://affycomp.biostat.jhsph.edu/










Software

• Affymetrix: MAS v5.1 or GCOS v1.0

• RMA (Robust Multi-array Average) / GCRMA / PLM: - Bioconductor http://www.bioconductor.org

- affylmGUI http://bioinf.wehi.edu.au/affylmGUI/

- RMAExpress http://stat.www.berkeley.edu/~bolstad/RMAExpress/RMAExpress.html

- Axon: Acuity (RMA only, commercial)- GeneTraffic (RMA only, commercial)

• Li & Wong’s MBEI (Multiplicative Model-Based Expression Index):- dChip http://www.dchip.org/

http://www.bioconductor.org/

http://bioinf.wehi.edu.au/affylmGUI/

http://stat.www.berkeley.edu/~bolstad/RMAExpress/RMAExpress.html

http://www.dchip.org/


Qualitative Quality Assessment Using PLM

Weights Residuals

More QC Examples:http://stat-www.berkeley.edu/users/bolstad/PLMImageGallery/index.html

http://stat-www.berkeley.edu/users/bolstad/PLMImageGallery/index.html


QC with affyPLM


QC with boxplots


RMAExpress






affylmGUI








Analysis

Clustering


Experimental design

Image analysis

Normalization

Biological question

Quality Measurement

Failed

Pass

Preprocessing


Annotation

Analysis


2. Compare TID0 and TIID7.3. Beyond expression.


~ 8800 probe sets

50 + 131 > 4x (M>2)163 + 401 > 2x

Simple fold-change rules give no assessment of statistical significance

Need to construct test statistics incorporating variability estimates (from replicates).

DE by Average Fold-Change (M): Freshly Isolated TI vs TII Cells

TI

TII

4x2x

2x4x

M:

A:


Two-sample t-statistic & p-value

• The two-sample t-statistic

is used to test equality of the group

means 1, 2

• The p-value p* is the probability

that, under the null hypothesis (H0:

1=2), the test statistic is at least

as extreme as the observed value

t*.

€

T =X 1 − X 2

s 1n1

+ 1n2

t*-t*

p*/2p*/2


More Two-Sample Statistics

Perform statistical tests on normalized, log-transformed data:

• Standard t-test: assumes normally distributed data in each class

(!), equal variances within classes

• Welch t-test: as above, but allows unequal variances

• Wilcoxon test: non-parametric, rank-based

• permutation test: estimate

the distribution of the test

statistic under the null

hypothesis by permutations

of the sample labels


When there are few replicates…

• (Fold-change) Averages can be driven by outliers.

• T-statistics can be driven by tiny variances.

Solution: “robust” version of t-statistic

- Replace mean by median

- Replace standard deviation by median absolute deviation

€

M

€

M

se(M )


1. Penalized-t

Trying to find a compromise between solely using t and solely using mean. There are several similar solutions of the following form:

where s = standard deviation.

Question: how to estimate a? - 90th percentile of standard deviations (s values). Efron et al (2000).

- minimizes the coefficient of variation(cv) of the absolute t-values (SAM). Tusher et al (2001)

€

t* =M

(s + a) / n

Alternative Test Statistics


2. Moderated t-statistics (G Smyth 2004, Limma):

where is the shrinkage estimate of standard deviation

Other Statistics (cont.)

€

t* =M

˜ s / n

€

˜ s 2 =s2d + s0

2d0

d + d0

Pooled sd from all genes

sd for gene i

Estimation is done using an extension to the empirical Bayes method in Lonnstadt &Speed (2002)


3. B-statistic: log posterior odds ratios

log Pr(gene i IS DE) / Pr(gene i IS NOT DE)

Equivalent to moderated-t in terms of ranking genes.

4. Single-channel methods modeling absolute gene-expression levels:- Newton et al 2001: log-intensities ~ Gamma - Wolfinger et al 2001: linear mixed model on log-intensities

5. Composite methods: Differential Expressed genes via Distance Synthesis (Yang et al 2004) to choose genes that are extreme on all measures by defining a “distance” statistic based on measures of choice.

Other Statistics (cont.)


DE by Fold Changes, (limma) Moderated-t, B (lods)


Assessing Significance I: Diagnostic Plots


Univariate hypothesis testing: For single gene, test the null hypothesis

H0 : the gene is NOT differentially expressed.

And p-value can be generated via theory or permutation tests.

Is this p-value correct?

• Yes if only looking at ONE gene…

• Will expect 10000*0.01 = 100 genes with p-value < 0.01 in 10,000 non-DE genes!

-- clearly we can’t just use standard p-value thresholds (.05, .01)!

• Need to adjust p-values for meaningful interpretation!

Assessing Significance II: Testing


(Unadjusted) p-values of moderated-t


Multiple Hypothesis Testing

H0

Ha


Type I Error Rates (False Positives)

• Family-Wise Error Rate (FWER)

Pr(V > 0) = Pr( At least one false positive )

• False Discovery Rate (FDR) -- The FDR (Benjamini & Hochberg 1995) is the expected proportion of type I errors among the rejected hypotheses.

FDR = E(Q),

With Q = V/R, if R > 0

0, if R = 0


Multiple Testing: Controlling a Type I Error Rate

AIM:

For a given type I error rate , use a procedure to select a set of “significant” genes that guarantee a type I error rate .


Adjusted p-values: Controlling the FWER

• The Bonferroni correction: m pg ; most conservative adjustment.

assume independence among genes.

• Sidák: 1-(1-pg)m

• minP (Westfall & Young):

estimated through permutation; allow dependency between genes.

• maxT: replace pg by test statistics Tg, min by max. Less computationally intensive than minP.

• Step-down• Step-up

Choosing all genes with adjusted p-value controls the FWER at level

€

˜ p g ≤ α

€

˜ p g = Pr( mink=1,...,m

Pk ≤ pg | H0)


Controlling the FDR (Benjamini/Hochberg)

• Order unadjusted p-values:

• To control FDR = E(V/R) at level , reject the hypothesis

• Adjusted p-values:

• Interpretation: expect 5% false positives among genes with < 0.05 FDR-adjusted p-values.


Adjusted p-values

p=0.01


Adjusted p-values

p=0.01p=0.01


Identify DE Genes: TI vs TII Cells

1. Select a statistic which will rank the genes in order of strength of the evidence for differential expression, from strongest to weakest.

2. Choose a critical value for the ranking of statistics above which any value is considered to be significant.

• Number of estimated DE genes

B-statistics

> 0

Bonferroni-Adj. p-value

< 0.01

Median

Fold- change

> 4x

Median

Fold- change

> 2x

TIID0 vs TID0 1500 538 138 + 68 =206 415 + 193 =608

TIID7 vs TID0 1411 295 80 + 83 =163 528 + 210 =738


FWER or FDR?

• Choose FWER if high confidence in ALL selected genes is desired (for example, selecting candidate genes for RT-PCR validation). Loss of power due to strong control of type-I error.

• Use more flexible FDR procedures if certain proportions of false positives are tolerable (e.g. gene discovery, selecting candidate co-regulated gene sets for GO/pathway analysis).

Analysis


2. Comparing TID0 and TIID7.3. Beyond differential expression…




Analysis

Clustering


Experimental design

Image analysis

Normalization

Biological question

Quality Measurement

Failed

Pass

Preprocessing


Annotation


What is next ?

• Further experiments: RT-PCR, immunohistochemistry, ELISA…

• Annotation

• Functional categories of DE genes between TID0 and TIID0. - Gene Ontology [http://www.geneontology.org]- GenMapp [http://www.genmapp.org/]- GOStats [http://gostat.wehi.edu.au/]- Bioconductor: GOStats and goTools

• Finding upstream regulatory element with our current experiments alone? - Experimental and methodological challenges.


RT-PCR Verification


Annotation

Affy ID

L26913_at

GenBank Accession/Refseq

NM_053828

NP_446280

Locuslink

116553

Biochemical pathways

(KEGG)

Nucleotide SequenceGACAAGCCAGCAGCCTAGGCCAGCCCACAGTTCTACAGCTCCCTGGTTCTCTCACTGGCTCTGGGCTTCATGGCGCTCTGGGTGACTGCAGTCCTGGCTCTTGCTTGCCTTGGTGGTCTCGCCGCCCCAGGGCCGGTGCCAAGATCTGTGTCTCTCCCTCTGACCCTTAAGGAGCTTATTGAGGAGCTGAGCAACATCACACAAGACCAGACTCCCCTGTGCAACGGCAGCATGGTATGG

UniGene

Rn.9921

RGD

Il13 Name

Interleukin 13

Gene Symbol

IL13

Swiss-Prot

P42203

GOGO:0005144 [interleukin-13

receptor binding]

GO:0005576 extracellular

GO:0006955 [immune response]

Map PositionChromosome:10q22

39.1 Mb

PubMed 121624387916615

…

Literature


GO Functional Category Enrichment


Can we find common transcriptional regulatory elements/motifs in the co-expressed genes?

List of Affy IDs (DE genes) (co-expression co-regulation)

ComputationalMethods

Candidate transcription factor binding sites/motifs

Upstream sequences of co-expressed genes+ additional data

Genome ResourceGenbankEnsembl

UCSC Genome Browser

Biological VerificationChromatin immunoprecipitation…

Hypotheses of Gene modules, network…

EZRetrieve, SOURCE…

TRANSFACExpression

Other genomes


Transcriptional Regulation


Challenges for higher eukaryotes

• Getting the right sequences is hard- (now minor): Transcription start sites (TSS) could be very far from

translation start sites (ATG). Typically undetermined and low prediction accuracy unless full-length cDNAs or 5’EST are available

- Regulatory motifs could be anywhere: promoter (TSS proximity), very far 5’ upstream (a few to hundreds kb), introns, even 3’downstream.

• High signal to noise ratio- motifs are weak and short: 6-12 bp with 8-9 bits of information (~4

conserved bases)

- Large target regions yield high false positives


Computational Motif Finding in Co-expressed Genes1. Supervise approach: mapping known motif sites

68 TI/138 TII Affy IDs marker genes (DE > 4x)

Score matches

Candidate regulator (TF) withbinding sites in DE genes

23 /70 Refseqs: retrieve peptides +repeat masked (-2000,-1)bp

from annotated TSS

Genome ResourceEnsembl/EnsMart www.ensembl.org

Biological VerificationChromatin immunoprecipitation…


TRANSFACwww.gene-regulation.com

0/7 DE TFs6 w/ binding site info

TFblast

#matches > #expected?

200 non-DE genes

Yes*

http://www.ensembl.org/

http://www.gene-regulation.com/


Mapping Known DE TF Motifs to DE Genes

TF Type-I Type-II

ATF 17 (13) / 14 58 (37) / 44

V-Jun 0 (0) / 0 6 (3) / (<1)

IRF-1 4 (4) / 0 7 (6) / 4

EGR-1/EGR-2 0 (0) / 1 2 (2) / 4

#matches (#genes) / #expected matches

QuickTime™ and aTIFF (LZW) decompressor









Motif Finding in Co-expressed Genes2. De novo Stochastic Algorithms

68 TI/138 TII Affy IDs marker genes (DE > 4x)

Gibbs SamplerAlignACE

MEME

Candidate sequence motifs and sites in DE genes

23 /70 Refseqs: retrieve repeat masked (-2000,-1)bp from TSS

Genome ResourceEnsembl/EnsMart www.ensembl.org

Biological Verification


TRANSFACwww.gene-regulation.com

Computational Verification:Match known TFBS?

http://www.ensembl.org/

http://www.gene-regulation.com/


Top 12 motifs by AlignACE (default parameters, background %GC =50)

Type-I Type-II


Motif Finding in Co-expressed Genes

1. Mapping known motif sites.Input : Subsets of sequences + known binding sites.

Limited by known sites & lots of false positives.

2. De novo motif finding algorithm.Input : Subsets of Sequences.

Need a good filter to reach at a good subset of sequences. Mostly stochastic so harder to translate results.

3. Regression methods on expression data (REDUCE: Bussemaker et al 2001)

Input : Expression Data + corresponding upstream sequences.

Usually Y ~ X where Y: expression data and X: words/motifs.

4. Phylogenetic Footprinting/Shadowing (Vista: Loots et al 2002)

Input : Subset of upstream sequences of orthologous genes.

Can’t find organism specific sites (estimated 32-40% human sites are not functional in mouse), but could be compensated by using various species for resolution.


Biological Verification & Interpretation: TI TII (D0 or D7), candidate regulator…

Adjust p-values for multiple testing

Ranking genes for DE: fold-change, moderated-t, lods


Experimental design: Affy arrays

Quantile Normalization

RMA Summarization

Biological Question: Alveolar TI vs TII Cells

Quality Measurement

Failed

Pass

Preprocessing


Finding TFBS for co-expressed genes

Conclusion

case study i: two-sample analysis

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