carlo colantuoni carlo@illuminatobiotech

Summer Inst. Of Epidemiology and Biostatistics, 2010:

Gene Expression Data Analysis

1:30pm – 5:00pm in Room W2015

Carlo [email protected]

http://www.illuminatobiotech.com/GEA2010/GEA2010.htm

Class Outline• Basic Biology & Gene Expression Analysis Technology

• Data Preprocessing, Normalization, & QC

• Measures of Differential Expression

• Multiple Comparison Problem

• Clustering and Classification

• The R Statistical Language and Bioconductor

• GRADES – independent project with Affymetrix data.

http://www.illuminatobiotech.com/GEA2010/GEA2010.htm

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• Basic Biology & Gene Expression Analysis Technology– The Biology of Our Genome & Transcriptome– Genome and Transcriptome Structure & Databases– Gene Expression & Microarray Technology

• Data Preprocessing, Normalization, & QC– Intensity Comparison & Ratio vs. Intensity Plots (log transformation)– Background correction (PM-MM, RMA, GCRMA)– Global Mean Normalization– Loess Normalization– Quantile Normalization (RMA & GCRMA)– Quality Control: Batches, plates, pins, hybs, washes, and other artifacts– Quality Control: PCA and MDS for dimension reduction– SVA: Surrogate Variable Analysis

• Measures of Differential Expression– Basic Statistical Concepts– T-tests and Associated Problems– Significance analysis in microarrays (SAM) [ & Empirical Bayes]– Complex ANOVA’s (limma package in R)

• Multiple Comparison Problem– Bonferroni– False Discovery Rate Analysis (FDR)

• Differential Expression of Functional Gene Groups– Functional Annotation of the Genome– Hypergeometric test?, Χ2, KS, pDens, Wilcoxon Rank Sum– Gene Set Enrichment Analysis (GSEA)– Parametric Analysis of Gene Set Enrichment (PAGE)– geneSetTest– Notes on Experimental Design

• Clustering and Classification– Hierarchical clustering– K-means– Classification

• LDA (PAM), kNN, Random Forests• Cross-Validation

• Additional Topics• eQTL (expression + SNPs)• Next-Gen Sequencing data: RNAseq, ChIPseq• Epigenetics?– The R Statistical Language: http://www.r-project.org/– Bioconductor : http://www.bioconductor.org/docs/install/– Affymetrix data processing example

DAY #2:

•Intensity Comparison & Ratio vs. Intensity Plots

•Log transformation

•Background correction (Affymetrix, 2-color, other)

•Normalization: global and local mean centering

•Normalization: quantile normalization

•Batches, plates, pins, hybs, washes, and other artifacts

•QC: PCA and MDS for dimension reduction

•SVA: Surrogate Variable Analysis

Log Intensity

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Microarray Data Quantification

Log Intensity

Lo

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Logarithmic Transformation:

if : logz(x)=y then : zy=x

Logarithm math refresher:

log(x) + log(y) = log( x * y )

log(x) - log(y) = log( x / y )

Intensity vs. Intensity: LINEAR

Intensity Distribution: LINEAR

Intensity vs. Intensity: LOG

Intensity Distribution:LOG

Intensity vs. Intensity: LINEAR

Intensity vs. Intensity: LOG

Int vs. Int:LINEAR

Int vs. Int:LOG

Ratio vs. Int: LOG


Background Subtraction

Before Hybridization

Array 1 Array 2

Sample 1 Sample 2

After Hybridization

Array 1 Array 2

More Realistic - Before

Array 1 Array 2

Sample 1 Sample 2

Array 1 Array 2

More Realistic - After

poly CNo label

Intensity distributions for theno-label and Yeast DNA

The presence of background noise is clear from the fact that the minimum PM intensity is not 0 and that the geometric mean of the probesets with no spike-in is around 200 units.

Why Adjust for Background?

Hs RNA on Hs chip(w/ spike-ins)

PM intensities

Why Adjust for Background?

Local slope decreases as nominal concentration

decreases!

(E1 + B) / (E2 + B) ≈ 1

(E1 + B) / (E2 + B) ≈ E1 / E2

(E1 + B) ≈ B or …

(E1 + B) ≈ E1 or …

By using the log-scale transformation before analyzing microarray data, investigators have, implicitly or explicitly, assumed a multiplicative measurement error model (Dudoit et al., 2002; Newton et al., 2001; Kerr et al., 200; Wolfinger et al., 2001). The fact, seen in Figure 2, that observed intensity increase linearly with concentration in the original scale but not in the log-scale suggests that background noise is additive with non-zero mean. Durbin et al. (2002), Huber et al. (2002), Cui, Kerr, and Churchill (2003), and Irizarry et al. (2003a) have proposed additive-background-multiplicative-measurement-error models for intensities read from microarray scanners.

PM intensities

Affymetrix GeneChip Design

5’ 3’

Reference sequence

…TGTGATGGTGCATGATGGGTCAGAAGGCCTCCGATGCGCCGATTGAGAAT…GTACTACCCAGTCTTCCGGAGGCTAGTACTACCCAGTGTTCCGGAGGCTA

Perfectmatch (PM)Mismatch (MM)

NSB & SB

NSB

Motivation: PM - MM

PM = B + S MM = B

PM – MM = S

The hope is that:

But this is not correct!

MM is too much:

S=signal;B=background

At low S (A), S-B≈0 so:

S1-B1 / S2-B2 (M) is highly unstable.

Why not subtract MM?

Background: Solutions

Simulation

• We create some feature level data for two replicate arrays

• Then compute Y=log(PM-kMM) for each array

• We make an MA using the Ys for each array

• We make a observed concentration versus known concentration plot

• We do this for various values of k. The following “movie” shows k moving from 0 to 1.

k=0

Known level (log2)

Obs

erve

d le

vel (

log2

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Log2(Intensity)

Log2

(Rat

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k=1/4

Known level (log2)

Obs

erve

d le

vel (

log2

)

Log2(Intensity)

Log2

(Rat

io)

k=1/2

Known level (log2)

Obs

erve

d le

vel (

log2

)

Log2(Intensity)

Log2

(Rat

io)

k=3/4

Known level (log2)

Obs

erve

d le

vel (

log2

)

Log2(Intensity)

Log2

(Rat

io)

k=1

Known level (log2)

Obs

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d le

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log2

)

Log2(Intensity)

Log2

(Rat

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Real Data

MAS 5.0 RMA

RMA: The Basic Idea

PM=B+S

Observed: PMOf interest: S

Pose a statistical model and use it to predict S from the observed PM

The Basic Idea

PM=B+S

• A mathematically convenient, useful model

– B ~ Normal (,) S ~ Exponential ()

– No MM– Borrowing strength across probes

ˆ S E[S | PM]

Notice improved precision but worse accuracy

Problem

• Global background correction ignores probe-specific NSB

• MM have problems

• Another possibility: Use probe sequence

Probe-specific Background

G-C content effect in PM’s

Boxplots of log intensities from the array hybridized to Yeast DNA for strata of probes defined by their G-C content. Probes with 6 or less G-C are grouped together. Probes with 20 or more are grouped together as well. Smooth density plots are shown for the strata with G-C contents of 6,10,14, and 18.

Any given probe will have some propensity to non-specific binding. As described in Section 2.3 and demonstrated in Figure 3, this tends to be directly related to its G-C content. We propose a statistical model that describes the relationship between the PM, MM, and probes of the same G-C content.

General Model (GCRMA)

NSB SB

PMgij OiPM exp(hi( j

PM ) bgjPM gij

PM ) exp( f i( j ) gi gij )

MMgij OiMM exp(hi( j

MM ) bgjMM gij

MM )

We can calculate:

E[gi PMgij , MMgij ]Due to the associated variance with the measured MM intensities we argue that one data point is not enough to obtain a useful adjustment. In this paper we propose using probe sequence information to select other probes that can serve the same purpose as the MM pair. We do this by defining subsets of the existing MM probes with similar hybridization properties. We therefore propose to use subsets of probes with the same G-C content as a population of MM probes that can be considered pseudo-MM for all PM with the same G-C content.

The MA plot shows log fold change as a function of mean log expression level. A set of 14 arrays representing a single experiment from the Affymetrix spike-in data are used for this plot. A total of 13 sets of fold changes are generated by comparing the first array in the set to each of the others. Genes are symbolized by numbers representing the nominal log2 fold change for the gene. Non-differentially expressed genes with observed fold changes larger than 2 are plotted in red. All other probesets are represented with black dots. The smooth lines are 3SDs away with SD depending on log expression.

Naef & Magnasco (2003),PHYSICAL REVIEW E 68, 011906, 2003

Another sequence effect in PM’s and MM’s

Another sequence effect in PM’s and MM’s

We show in Fig. 2 joint probability distributions of PMs and MMs, obtained from all probe pairs in a large set of experiments. Actually, two separate probability distributions are superimposed: in red, the distribution for all probe pairs whose 13th letter is a purine, and in cyan those whose 13th letter is a pyrimidine. The plot clearly shows two distinct branches in two colors, corresponding to the basic distinction between the shapes of the bases: purines are large, double ringed nucleotides while pyrimidines have smaller single rings. This underscores that by replacing the middle letter of the PM with its complementary base, the situation on the MM probe is that the middle letter always faces itself, leading to two quite distinct outcomes according to the size of the nucleotide. If the letter is a purine, there is no room within an undistorted backbone for two large bases, so this mismatch distorts the geometry of the double helix, incurring a large steric and stacking cost. But if the letter is a pyrimidine, there is room to spare, and the bases just dangle. The only energy lost is that of the hydrogen bonds.

Naef & Magnasco (2003),PHYSICAL REVIEW E 68, 011906, 2003

C and T are pyrimidines.

(small)

A and G are purines.(large)

Another sequence effect in PM’s

Naef & Magnasco (2003), PHYSICAL REVIEW E 68, 011906, 2003

The asymmetry of (A,T) and (G,C) affinities in Fig. 3 can be explained because only A-U and G-C bonds carry labels (purines U and C on the mRNA are labeled). Carrying labels inside the proberegion is unfavorable because labels interfere with binding. (Remember also that G-C pairs have 3 and A-T pairs have 2 hydrogen bonds!).

C G T A

CG’s have 3 H bonds

U and C on the mRNA are labeled (A and G in

probe), and this label can interfere with binding.

Both these effects are greater when at the center

of the hybrid.

Two color platforms (Agilent, cDNA)

• Common to have just one feature per gene

• 60 vs. 25 NT?

• Optical noise still a concern

• After spots are identified, a measure of local background is obtained from area around spot

(this is also applicable to some spotted one-channel data)

Local background

---- GenePix

---- QuantArray

---- ScanAnalyze

Two color feature level data

• Red and Green foreground and background obtained from each feature

• We have Rfgij, Gfgij, Rbgij, Gbgij (g is gene, i is array and j is replicate)

• A default summary statistic is the log-ratio:

log2 [(Rf - Rb) / (Gf - Gb)]

Background subtractionNo background

subtraction

Diagnostics: images of Rb, Gb, scatterplot of log2 (Rf/Gf) vs. log2(Rb/Gb)

Correlation may be spatially dependent

Two color platforms

• Again, we can assess the tradeoff of accuracy and precision via simulation

• Simulation uses a self versus self (SVS) hybridization experiment -- no differential expression should occur.

• Mean squared error (MSE) = bias^2 + variance.

Lower MSE with NBS if correlation < 0.2

• A procedure that subtracts local background as a function of the correlation of fg and bg ratios may be a nice compromise between background subtraction and no background subtraction.

• For references, see background subtraction paper by C. Kooperberg J Computational Biol 2002.

• Limma package in R has many useful functions for background subtraction.

• Following the decision to background subtract, we need to consider a normalization algorithm.

Background Subtraction: Conclusions

Normalization

Normalization

• Normalization is needed to ensure that differences in intensities are indeed due to differential expression, and not some printing, hybridization, or scanning artifact.

• Normalization is necessary before any analysis which involves within or between slides comparisons of intensities, e.g., clustering, testing.

• Somewhat different approaches are used in two-color and one-color technologies

Varying distributions of intensities from each microarray.

Distributions of intensities after global mean normalization.

What does this normalization mean in Int vs. Int, or Ratio vs. Int space?

Distributions of intensities after global mean normalization – global mean

normalization is not enough …

Possible solutions:

Local Mean Normalization

Quantile Normalization

Local Mean Normalization

(loess):

Adjusts for intensity-dependent bias in

ratios.

Requires Comparison!

Quantile Normalization

Quantile normalization

• Quantiles is commonly used because its fast and conceptually simple

• Basic idea: – order values in each array– take average across probes– Substitute probe intensity with average– Put in original order

Example of quantile normalization

2 4 4

5 4 14

4 6 8

3 5 8

3 3 9

2 3 4

3 4 8

3 4 8

4 5 9

5 6 14

3 3 3

5 5 5

5 5 5

6 6 6

8 8 8

3 5 3

8 5 8

6 8 5

5 6 5

5 3 6

Original Ordered Averaged Re-ordered

Before Quantile Normalization

After Quantile Normalization

A worry is that it over corrects

Print-tip Effect

Print-tip Loess

Plate effect

Bad Plate Effect

Print Order Effect

Microarray Pseudo Images: Intensity

Microarray Pseudo Images: Ratios

Images of probe level data

This is the raw data

Images of probe level data

Residuals (or weights) from probe level model fits show problem clearly

Hybridization Artifacts

PCA, MDS, and Clustering:

Dimension Reduction to Detect Experimental

Artifacts and Biological Effects

Principle Components Analysis (PCA)

and

Multi-Dimensional Scaling (MDS)

Uncorrected Intensities: MDS Colored by Batch

Removing The Batch Effect

Much LikeRed:Green Analysis

Uncorrected Intensities: MDS Colored by Batch

Batch Subtracted Measures: MDS Colored by Batch

MDS of All Array Experiments: Subject Replicates

AGE

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AGE

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Surrogate Variable Analysis:

Removing Unwanted/Unknown

Effects


Requires the definition of the effect you are interested in (Exp. Vs. Con., or age, etc.).

Removes “unexplained” variance in gene expression data.

PCA-based (no missing data).

Quite a “strong” data clean up method.

Leek JT, Storey JD. Capturing heterogeneity in gene expression studies by surrogate variable analysis. PLoS Genet. 2007 Sep;3(9):1724-35.


Take residuals from model defining effect of interest.

PCA (SVD) on residual matrix.

Use top ? PC’s and determine genes associated with these PC’s. Each PC will be used to generate a SV.

Generate SV’s using data from these genes in original data matrix (not the residual matrix).

Incorporate SV’s in all subsequent analysis, e.g. as covariates in regression analysis.

BEFORE CORRECTION

AFTER CORRECTION

Biological Effects:

Tissue Types and Growth Factor

TreatmentsMake sure your normalization and QC methods 1] preserve what you are looking for, 2] remove what

you don’t want, and 3] don’t introduce artifacts.

Illumina 24K

carlo colantuoni carlo@illuminatobiotech

Documents

gene expression data

minimum pm intensity

affymetrix data

log x y intensity

data processing exampleday

linearintensity distribution

qcintensity comparison

y logx logy