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Linear models and Limma

Københavns Universitet,19 August 2009

Mark D. RobinsonBioinformatics, Walter+Eliza Hall InstituteEpigenetics Laboratory, Garvan Institute

(with many slides taken from Gordon Smyth)

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Limma = linear models formicroarray data

o Morning Theory! Introduction

! Background correction

! Moderated t-tests

! Simple linear models

o Morning Practical! Demonstration of smoothing

! Limma objects (beta7)

! Background correction andnormalization (beta7)

! Simple experimental designs

! 2-colour example (beta7)

! Affymetrix example (cancer)

o Afternoon Theory

! More advanced designs /linear modeling

! Moderated F-tests

! Gene set tests

! Other analyses limma can do

o Afternoon practical

! Factorial design (estrogen)

! Gene set testing (cancer)

! Time course experiment(SAHA/depsipeptide)

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Expression measures

Two-colour

Affymetrix

Illumina

log-intensity(summarizedover probes)

log-intensity(summarizedover beads)

probe or gene

array

yga = log2(R/G)

yga =

yga =

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Questions of Interest

o What genes have changed in expression? (e.g.between disease/normal, affected by treatment)Gene discovery, differential expression

o Is a specified group of genes all up-regulated in aparticular condition?Gene set differential expression

o Can the expression profile predict outcome?Class prediction, classification

o Are there tumour sub-types not previouslyidentified? Do my genes group into previouslyundiscovered pathways?Class discovery, clustering

Today will cover first two questions - differential expression

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MicroarrayDifferential Expression Studies

o 103 – 106 genes/probes/exons on a chip orglass slide

o Inputs to limma: log-intensities (1-colour data)or log(R/G) log-ratios (for 2-colour data)

o Several steps to go from raw data to table of“expression”: background correction,normalization

o Idea: Fit a linear model to the expression datafor each gene

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Two colourmicroarrays

http://en.wikipedia.org/wiki/DNA_microarray

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Two-colour data: Log-Intensities

*

2log ( )f bR R R= !

*

2log ( )f bG G G= !

For each probe:

Various ways to calculate background.

Will often modify to ensure:

Rf – Rb >0 and Gf – Gb > 0.

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Two-colour data: Means andDifferences

M R G= !

( ) / 2A R G= +

For each probe:

“minus”

“add”

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Data Summaries

G1 R1 G2 R2 G3 R3 G4 R4

A1M1 A2M2 A3M3 A4M4

For each gene

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MA Plot

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Log-Ratios orSingle Channel Intensities?

o Tradition analysis, treats log-ratios M=log(R/G) asthe primary data, i.e., gene expression measurementsare relative

o Alternative approach treats individual channelintensities R and G as primary data, i.e., geneexpression measures are absolute (Wolfinger,Churchill, Kerr)

o Single channel approach makes new analyses possiblebut- make stronger assumptions- requires more complex models (mixed models in place of

ordinary linear models) to accommodate correlationbetween R and G on same spot

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BG correction affects DE results

o Importance of careful pre-processing and qualitycontrol cannot be over-emphasized for microarraydata

o Can have dramatic effect on differential expressionresults

o Consider here the normexp method of adaptivebackground correction- background correction step of the RMA algorithm

- Can also be applied to two colour data

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Additive + multiplicative errormodel

Observe intensity for one probe on one array

additiveerrors

multiplicativeerrors

Intensity = background + signal

This idea underlies variance stabilizing transformationsvsn (two colour data) and vst (for Illumina data)

I = B + S

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normexp convolution model

Intensity = Background + Signal

N(!,!2) Exponential(")

+=

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Conditional expectation undernormexp model

Then

with

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normexp background correction

o Estimate the three parameters

o Replace I with E(S|I)

o For Affymetrix data, I is the “Perfect Match” dataintensity

o For two-colour data, I=Rf-Rb or I=Gf-Gb

o In the RMA algorithm, parameter estimation uses anad hoc density kernel method

o In limma (two colour), parameter estimationmaximises the saddlepoint approximation to thelikelihood

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PM data on log2 scale: raw and fitted model

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Background corrected intensity

= E(Signal | Observed Intensity)

Observed Intensity

E(

Sign

al | Inte

nsi

ty)

Adaptivebackgroundcorrectionproducespositive signal

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Offsets to stabilise the variance

Offset reduces variability at low intensities

Log-ratios

Background correction

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Why do offsets stabilize thevariance?

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Why do offsets stabilize thevariance?

o log2( 800/100 ) = log2 ( 8/1 ) = 3 (8-fold)

o Additive noise affects small numbers more

o Offsets introduce bias:

o log2[(80+10)/(10+10)] = 2.17

o But the tradeoff (drop in variance for increasein bias) is usually worth it

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A self-self experiment:two background methods

553 spots not plotted

First statistical point – choose background correction to stabilise the variance as a

function of intensity

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Comparison of 2-colour BG correctionmethods

Fals

e dis

cove

ries

(lim

ma)

Genes selectedRitchie et al. 2007

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References

o Silver et al. (2009). Microarray backgroundcorrection: maximum likelihood estimation for thenormal-exponential convolution. Biostatistics. [completemathematical development of the saddle point approximation]

o Ritchie et al. (2007). A comparison of backgroundcorrection methods for two-colour microarrays.Bioinformatics. [shows “normexp” performs best for 2-colour data]

o Irizarry et al. (2003). Exploration, normalization andsummaries of high density oligonucleotide arrayprobe level data. Biostatistics. [Describes RMA BG correction,but doesn't give much detail of the normexp convolution model.]

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Normalization

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Normalization

Two-colour

BG correction andnormalization areclosely connected

Even after BGcorrection, someeffects remain.

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Normalization

One-colour

Similarly for singlechannel data,adjustments needto be made for allsamples to becomparable.

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Moderated t-tests

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Borrowing information acrossgenes

o Small data sets: few arrays, inference forindividual genes is uncertain

o Curse of dimensionality: many tests,need to adjust for multiple testing, loss ofpower

o Benefit of parallelism: same model isfitted for every gene. Can borrow informationfrom one gene to another

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Hard and soft shrinkage

o Hard: simplest way to borrow information isto assume that one or more parameters areconstant across genes

o Soft: smooth genewise parameters towards acommon value in a graduated way, e.g., Bayes,empirical Bayes, Stein shrinkage …

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A very common experiment

Wild-type mouse x 2 Mutant mouse x 2

Which genes are differentially expressed?

n1 = n2 = 2 Affymetrix arrays

25,000 probe-sets

Gene X

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Ordinary t-tests

give very high false discovery rates

Residual df = 2

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Another very commonexperiment

Which genes are differentially expressed?

n = 2 two-colour arrays

30,000 probes

Wild-type mouse 1 Mutant mouse 1

Wild-type mouse 2 Mutant mouse 2

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Ordinary t-tests

give very high false discovery rates

Residual df = 1

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Small sample size, many tests

o These experiments would be under-poweredeven with just one gene

o Yet we want to test differential expression foreach of 50k genes, hence lots of multipletesting and further loss of power

The problem:

The solution:

The same statistical model is being fitted for everygene in parallel. Can borrow strength from othergenes.

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t-tests with common variance

across genes

with residual standard deviation pooled

More stable, but ignores gene-specific variability

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A better compromise

Moderated t-statistics

Shrink standard deviations towards common value

= degrees offreedom

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Gs%

0s

1s%

1s

2s%

2s

L

Gs

,pooledgt

gt%

gt

d

0d

Shrinkage of standard deviations

L

The data decides whethergt% should be closer to

,pooledgt or to

gt

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Why does it work?

o We learn what is the typical variability level bylooking at all genes, but allow some flexibilityfrom this for individual genes

o Adaptive

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Hierarchical model for variances

Data

Prior

Posterior

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Posterior Statistics

Moderated t-statistics

Posterior variance estimators

Baldi & Long 2001, Wright & Simon 2003, Smyth 2004

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Exact distribution for moderatedt

0 ggddtt +%:

An unexpected piece of mathematics shows that, underthe null hypothesis,

The degrees of freedom add!

The Bayes prior in effect adds d0 extra arrays forestimating the variance.

Wright and Simon 2003, Smyth 2004

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More on empirical Bayes statistics

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Hierarchical model for means

Data

Prior

Lönnstedt and Speed 2002, Smyth 2004

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Posterior Odds

Posterior odds of differential expression

Lönnstedt and Speed 2002, Smyth 2004

Monotonic function of t%

Hence t% gives the best possible ranking of genes

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Estimating Hyper-Parameters

Closed form estimators with good propertiesare available:

for c0 in terms of quantiles of the | |gt%

for s0 and d0 in terms of the first twomoments of log s2

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Marginal Distributions

0

00

with prob 1-

1 / with prob

d d

g

d d

t pt

c c t p

+

+

!"#

+"$

%

Under the hierarchical model, sg is independent ofthe moderated t-statistics instead

Under usual likelihood model, sg is independent of theestimated coefficients.

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Moment estimators for s0 and d0

Marginal moments of log s2 lead to estimators ofs0 and d0:

Estimate d0 by solving

where

Finally

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Quantile Estimation of c0

Let r be rank of | |gt% in descending order, and let F(;)

be the distribution function of the t-distribution. Canestimate c0 by equating empirical to theoretical quantiles:

Get overall estimator of c0 by averaging the individualestimators from the top p/2 proportion of the | |

gt%

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Short note on multiple testing

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Multiple testing and adjusted p-values

o Traditional method in statistics is to control familywise error rate, e.g., by Bonferroni.

o Holm’s method is improved (step-down)modification of Bonferroni.

o Controlling the false discovery rate (FDR) is moreappropriate in microarray studies

o Benjamini and Hochberg method controls expectedFDR for independent or weakly dependent teststatistics. Simulation studies support use formicroarray data.

o All methods can be implemented in terms ofadjusted p-values.

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End of morning theory - Summary

o Background correction, normalization areimportant considerations -- normexp, offsets

o Moderation will generally always help --moderation of variances is very effective

o Convenient model gives known nulldistribution

o Multiple testing

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Linear models

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More complex experiments

o More complex microarray experiments can berepresented by linear models

o For one-channel platforms, the linear modelcan be set up using the usual univariate linearmodel formulae

o For two-colour platforms, the linear modelshave some special properties

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Linear Models

o In general, need to specify:

- Dependent variable

- Explanatory variables (experimental design,covariates, etc.)

o More generally:

vector ofobserveddata

designmatrix

Vector ofparameters toestimate

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Linear Models for microarrays

o Analyse all arrays together combininginformation in optimal way

o Combined estimation of precision

o Extensible to arbitrarily complicatedexperiments

o Design matrix: specifies RNA targets usedon arrays

o Contrast matrix: specifies whichcomparisons are of interest

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Design # Linear models

Wild-type mouse x 2 Mutant mouse x 2

$1 = wt log-expression

$2 = mutant % wt

Design matrices for 1-colour arrays are easier to specify!

E[y1]=E[y2]=$1 E[y3]=E[y4]= $1+ $2

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Designs # Linear Models

A B1

2

1

1

y

y!

" # " #=$ % $ %&' (' (

Ref

A

B

B A! " #

1

1

2

2

3

1 0

1 0

1 1

y

y

y

!

!

" # " #" #$ % $ %= & $ %$ % $ %' ($ % $ %

' ( ' (

A B2log ( / )y R G B A= ! "

1

2

RefA

B A

!

!

" #

" #

A B

C

1

1

2

2

3

1 0

1 1

0 1

y

y

y

!

!

" # " #" #$ % $ %= & $ %$ % $ %' ($ % $ %&' ( ' (

1

2

B A

C A

!

!

" #

" #

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Matrix Multiplication

A B1

2

1

1

y

y

!!

!

" # " # " #= =$ % $ % $ %& &' ( ' (' (

Ref

A

B

1 1

1

2 1

2

3 1 2

1 0

1 0

1 1

y

y

y

!!

!!

! !

" # " # " #" #$ % $ % $ %= & = &$ %$ % $ % $ %' ($ % $ % $ %+' ( ' ( ' (

A B

C

1 1

1

2 1 2

2

3 2

1 0

1 1

0 1

y

y

y

!!

! !!

!

" # " # " #" #$ % $ % $ %= & = & +$ %$ % $ % $ %' ($ % $ % $ %& &' ( ' ( ' (

1

23

1

2

RefA

B A

!

!

" #

" #

1

2

B A

C A

!

!

" #

" #

B A! " #

Contrast:

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Linear Model Estimates

Obtain a linear model for each gene g

Estimate models to get

coefficients

standard deviations

standard errors

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Contrasts

A contrast is any linear combination of the coefficients"j which we want to test equal to zero.

Define contrasts

Want to test

vs

were C is the contrast matrix.

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Pax5: example of saturateddesign

Pax5-/-Wt

IL-7 removed Rag1-/-

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2

7

5

11

1

12

4

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8

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Robust design – can tolerate failure of some of the arrays

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Regression Analysis

Choose 3 comparisons between the 4 RNAsources to be the coefficients of the linearmodel, e.g.,- PW: Pax5-/- vs Wt

- RW: Rag1-/- vs Wt

- IW: IL-7 withdrawn vs Wt

For each gene, fit a linear model with acoefficient for each contrast

Any other comparisons of interest can beextracted from the linear model as contrasts

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!!!

"

#

$$$

%

&

•

!!!!!!!!!!!!!!!!!

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RW

PW

m

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110

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010

010

011

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101

101

100

100

001

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12

11

10

9

8

7

6

5

4

3

2

1 Exercise: Fill in the designmatrix.

Can be fitted using robust regression, but problems with se’s, as Patty Solomon has

observed

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!!!!!!

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(

)

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11100

10010

00010

01100

01001

00001

00100

WT.P11 µ + a1

MT.P21µ + (a1+a2) + b + (a1+a2)b

MT.P11µ +a1+b+a1.b

WT.P21µ + a1 + a2

WT.P1

µ

MT.P1 µ + b

1

2

3

4

5

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Example of factorial design

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Moderated F-statistics

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Moderated F-Statistic

Moderated F-statistic

MST=Mean Sum of squares between Treatments

The idea of shrinking the variance extendsimmediately to multiple contrasts

Wright & Simon 2003, Smyth 2004

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Doubly shrunk F statistic

The moderated F is not a monotonically function ofthe posterior odds

A doubly shrunk F statistic can be shown have tothe desired relationship to the posterior odds

Tai and Speed 2006, 2007

Improves further the gene ranking

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Single or double shrinkage

o Shrinking the variances only is enough whencomparing two groups

o When comparing 3 or more groups, furthergain can be had by shrinking the $ also (recall

Stein estimator needs at least 3 means)

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Functional category analysis

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Functional category analysis

o Used on a set of genes deemed to bedifferentially expressed

o Asks the question: is my set of genes enrichedfor a particular molecular function?

o Useful for establishing what pathways / typesof genes are affected

o Nowadays largely superceded by gene settests

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Overlap statistics

o Question: Say you have a set of 85 genes (ofa total 20000 genes) known to be associatedwith function X. Calculate the probability ofrandomly selecting 40 or more of those genesin a list of 100 DE genes.

o Answer: ?

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Overlap statistics

o Question: Say you have a set of 85 genes (of a total 20000genes) known to be associated with some function. Calculatethe probability of randomly selecting 40 or more of thosegenes in a list of 100 DE genes.

o Answer: Hypergeometric (i.e. the “urn”problem).

N=19915 “white”m=85 black

n=100k=40

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Gene set tests

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Gene sets

o Test significance of a (apriori specified) groupof genes

o The genes might belong to a known pathwayor might be the top genes from a relatedexperiment

o The set might be significant even if individualgenes are not

o Gene set enrichment analysis (GSEA)originated by Mootha et al PNAS 2003 andSubramanian et al PNAS 2005

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Available gene set methods

o GSEA: gene set enrichment analysis. Complexmethod using Kolmogorov-Smirnov type tests andsample permutation. Needs two-groups, manyarrays, many genes and many sets.

o GSA: gene set analysis. Uses combination ofpermutation of samples and standardization acrossgenes. More powerful. Still needs two-groups, manygenes and many sets.

o GST: gene set tests using Wilcoxon test. Userandomization over genes. Applicable to linearmodels and small samples, but can be over-optimisticif the genes in the set are highly correlated.

o Now, rotation-based gene set tests.

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Gene set tests

All microarray probes,ranked by a test statisticof interest

t1t2t3t4:

A priori subsetof genes

X1, X2, X3 … Xn

Look for ranks for set genes amongst test statistics

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Viewing gene sets

Cell adhesion genes

Genes regulated by MYB

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What’s the hypothesis?

o Two major types of gene set tests:competitive or self-contained

o Competitive:Genes in the set tend to be more strongly DE thanrandomly chosen genes

o Self-contained:At least some genes in the set are truly DE

Goeman & Bühlmann, Bioinformatics 2007

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Permutation

o Competitive gene set tests are usually testedby permuting genes, but this ignores inter-gene correlations

o Self-contained gene set tests are usually testedby permuting arrays, but this is limited to two-group comparisons with large numbers

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Rotation gene set tests (ROAST)

o Self-contained hypothesis

o The first test suitable for small samples whichcorrectly accounts for inter-gene correlation

o Can handle complex linear model designs,including array weights, random effects etc

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Two steps: projection androtation

o Project data onto space orthogonal tonuisance parameters in the linear model

o Random rotation of the orthogonal residualsprovides fractional permutation, avoidsgranularity of p-values

o Assumes multivariate normality, but proves tobe highly robust against deviations fromnormality

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Set summary statistics

o Compute empirical Bayes t-statistics for each gene inset

o Convert to z-statistics

o Mean of z2:– good power, even when only a subset of genes respond

– not robust against non-normality

o Mean50: mean of top half of |z|:– good power

– robust

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References

o Subramanian et al (2005). A knowledge-basedapproach for interpreting genome-wideexpression profiles. PNAS 102, 15545-15550.

o Efron and Tibshirani (2007). On testing thesignificance of sets of genes. Ann Appl Stat 1,107-129.http://www-stat.stanford.edu/~tibs/GSA/

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Multi-level models I:duplicate spots

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Hard shrinking: examples

o Common correlation model for within-arrayduplicates spotsSmyth et al (2005). The use of within-array replicate spots for assessingdifferential expression in microarray experiments. Bioinformatics 21, 2067-2075.

o Common correlation models for singlechannel analysis of two-color microarray dataSmyth, G. K. (2005). Individual channel analysis of two-colour microarraydata. 55th Session of the International Statistics Institute, 5-12 April 2005,Sydney, Australia.

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Common correlation model

Given a blocking factor with variance component !b2,

focus on within-block correlations

Common correlation model assumes

Has proved effective for technical blocking factorsfor which correlations are high

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Duplicate Spots

o If the clone library is not too large, it is oftenpossible to print each gene more than onceon an array

o Duplicates are always side-by-side or a fixeddistance apart

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Genes printed induplicate pairs

One pair

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Duplicate spots are correlated

o Duplicate spots are a form of technicalreplication, share lots of common causes

o Cannot be treated as replicates on separatearrays, log-ratios from duplicate spots arecorrelated

o How best to use duplicate spots? Usualapproach is simply to average them

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Common Correlation Model

o Assume the between-duplicate correlation isthe same for every gene

o Justified by the belief that the correlationsprings mainly from spatial proximity

o Improves estimation of variances

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Consequences for individual genes

o If the number of genes is large, then theestimator of " is very accurate, so " may betreated as known as far as inference for eachindividual gene is concerned

o This doesn’t change estimation of !g butgreatly changes estimation of #g

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Validation with Spike-In Data

o Does the idea of using common correlationswork in practice?

o Check the ability of the common-correlationt-statistic to distinguish calibration from ratiospike-in spots

o Scorecard system includes calibrationcontrols, 3-fold up and down ratio controls,and 10-fold up and down ratio controls

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Multilevel models II:Separate channel analysis

of two-colour data

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Separate channel analysis of two-colour microarray data

G1 R1 G2 R2 G3 R3 G4 R4

Each spot is a block of size 2

The two channels give correlated pair of values

Common correlation model sets intra-spotcorrelation equal across genes

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Why Use Means and Differences?

cor( , ) 0M A =

An old idea dating back to Tukey, Altman & Bland

Ifvar( ) var( )R G=

then

regardless of the correlation between R andG.

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Common Reference Experiment

Ref B

Ref C

Ref B

Ref C

RefM

Bµ = !}

}Ref

MCµ = !

( Ref)/2A

Bµ = +

( Ref)/2A

Cµ = +

Why not use the A-values as well as M-values?

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A simple normal model

g! is the intra-spot correlation

Gene g, array i

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Models in terms of M and A

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M and A parameters

Mgi Rgi Ggiµ µ µ= !

( ) / 2Agi Rgi Ggi

µ µ µ= +

2 22 (1 )Mgi g g

! ! "= #

2 2 (1 ) / 2Agi g g

! ! "= +

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Correlation

2

1

2

41tanh log

2

Ag

g

Mg

!"

!

#=

M and A are independent but have differentvariances.

Have converted a correlated problem into aheteroscedastic problem

Can estimate correlation by estimatingvariances:

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Common correlation model

o Assume the intra-spot correlation is constantacross genes

o Justified by (i) variance components areobserved to be positively correlated and (ii)standard errors for coefficients are notsensitive to correlation value

o Common correlation can then be assumed toknown at individual gene level

o Converts a mixed model into a weightedregression

lmscFit() in limma

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ApoAI Experiment

8 wild type arrays and 8 ApoAI-/- arrays, all relativeto a common reference

Median intraspot correlation is estimated as

ˆ 0.85! =

The efficiency gain from using A-values is

ˆ10.08

ˆ1

!

!

"=

+

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Individual Channel Normalization

Using A-values in the analysis requires that theybe normalized to have comparable valuesbetween arrays: “single channel normalization”

For the ApoAI data:

Within-array loess normalization only

A-quantile normalization

Quantile normalization

ˆ 0.85! =

ˆ 0.89! =

ˆ 0.84! =

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Ignoring the Reference

Why not ignore the common reference channel? If weuse only the red channel in the common referenceexperiment,

2

1 2

1 1var( )

C BR R

n n!

" #$ = +% &

' (

var( ) 1

var( ) 2(1 )

C B

C B

R R

M M !

"=

" "

so

so adjusting for a common reference is worthwhile

whenever " > 0.5

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Disconnected Design

B C

D E

A-values make no contribution to estimating BvsCcomparison (direct)

M-values make no contribution to estimating BvsDcomparison (indirect)

Relative efficiency of indirect comparison comparedto direct is 1 !"

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Observed false discovery rates

0 1000 2000 3000 4000

01

00

20

03

00

40

0

Tests Rejected

Know

n F

als

e P

ositiv

es

Mixed modelIgnore CorSpotCor

Data from Holloway et al (2006) BMC Bioinformatics 7, Article 511.

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Why common correlation iseffective

o Bias introduced into the variance estimationseems to be offset by increase in precision

o Great simplification of mathematical model

o Penalizes genes with large within-blockvariances

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A Shrinkage Hierarchy

o Fold changes – shrinkage may not be required(unless more than 2 groups)

o Genewise variances – soft smoothing givesspectacular improvement

o Technical replicate correlations – hardsmoothing has proved successful

As we move from parameters of interest to higherorder nuisance parameters, bias decreases inimportance relative to noise

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Other bits and pieces

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Some other common variations

o Technical replicates

o Paired samples

o Array weights

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Summary

o Borrowing strength is essential in small-scalemicroarray experiments

o Information can be shared across genes oracross arrays

o Parameters may be set common betweengenes (correlations) or shrunk in a graduatedway (standard errors)

o Power can be increased by testing hypothesesfor sets of genes

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Acknowledgements

WEHI Bioinformatics

o Gordon Smyth

o Matt Ritchie

o Alicia Oshlack

o Terry Speed

Garvan Epigenetics

o Susan Clark

o Aaron Statham

o Marcel Coolen

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Computer Laboratories

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Proposed schedule

a.m.

o ModerationDemo.R

o LimmaObjects.R

o BGNormalization.R

o SimpleExperiments.R

p.m.

o FactorialDesign.R

o GeneSetAnalysis.R

o TimeCourse.R

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Getting started

o Grab the files from the ‘KU-August2009-LIMMA’directory (or archive) and copy/move to aconvenient location on your computer

o Set the variable ‘rootDir’ to that directory. Forexample:

rootDir <- “~/Desktop/KU-August2009-LIMMA/data”

o Make rootDir the working directory of your Rsession

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limma package documentation

o Function help pages?lmFit, ?eBayes

o Class help pages?"RGList-class"?"MArrayLM-class"

o Group help pageshelp("06.LinearModels")

o User’s Guide

limmaUsersGuide()

o The R html help system is a good top view

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Moderation Demo

o Illustration of sampling from the model

o Reduction in false discoveries

o Empirical Bayes differential expression

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Limma Objects

o RGList

o MAList

o MArrayLM

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BG correction / normalization demo

o Various procedures for BG correction,normalization

o Jurkat data:

same vs. same

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Simple Experiment 1:Integrin beta7+ vs beta7–

beta7- beta7+

o Reading two-color data

o Control spots

o Background correction

o Dye-swaps

o Empirical Bayes differential expression

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Simple Experiment 2: Cancer cellsversus normal cells

Normalcell line

Cancercell line

o Reading Affymetrix data

o Simple design versus contrasts

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Factorial Experiment: Estrogen

10 hours 48 hours

Absent

Estrogen

Present

o Reading Affymetrix data

o Factorial designs, contrasts

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Gene set analysis

o Convenient “functional category analysis”

o Newer, flexible set-based testing

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Targets of SAHA and depsipeptideA time course experiment

o Study effects of SAHA and depsipeptide onthe acute T-cell leukemia cell line CEM

o SAHA and depsipeptide are structurallydifferent but have similar biological effects(induce death through intrinsic apoptoticpathway)

o Prising out subtle differences is of greatinterest

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SAHA/depsipeptide:Experimental design

SAHA Vehicle only depsipeptide

0hr 0hr 0hr

1hr 1hr 1hr

2hr 2hr 2hr

4hr 4hr 4hr

8hr 8hr 8hr

16hr 16hr 16hr

Time courses of 6 arrays were done at each time.

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Aims of experiment

o Identify common responders: genes whichrespond similarly to SAHA and depsipeptide

o Identify specific responders: genes whichrespond to one of SAHA or depsipeptide, butnot to the other

o Different responders, genes which respond toboth SAHA and depsipeptide but differently,are of lesser interest

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Linear model analysis

o Fit genewise linear models to all the arrayssimultaneously

o Include effects for drug x time

o Allow for probe-specific dye-effects

o Treat each time series of 6 arrays as arandomized block, i.e., allow arrays hybridizedtogether to be correlated

2nd statistical point – analyse all arrays together