1

Methodologies for Pre-processing Microarray Data

Ben Bolstad

bmb@bmbolstad.comhttp://bmbolstad.com

Mar 31, 2006

2

Outline• Introduction• Affymetrix GeneChips (a popular single channel

array)• Pre-processing using the RMA framework and

extensions

3

Biological Question

Experimental Design

Microarray Experiment

Pre-processingLow-level analysis

Image Quantification

Normalization

Summarization

Background Adjustment

Quality Assessment

High-level analysisEstimation Testing Annotation ….. Clustering Discrimination

Biological verification and interpretation

Images

Expression ValuesArray 1 Array 2 Array 3

Gene 1 10.05 9.58 9.76

Gene 2 4.12 4.16 4.05

Gene 3 6.05 6.04 6.08

Workflow for a typical microarrayexperiment

4

Introduction to preprocessing• Pre-processing typically constitutes the initial (and

possibly most important) step in the analysis of data from any microarray experiment

• Often ignored or treated like a black box (but it shouldn’t be)

• Consists of:Data explorationBackground correction, normalization, summarizationQuality Assessment

• These are interlinked steps

5

Background Correction/Signal Adjustment

• A method which does some or all of the following:Corrects for background noise, processing effects on the arrayAdjusts for cross hybridization (non-specific binding)Adjust estimated expression values to fall across an appropriate range

6

Normalization“Non-biological factors can contribute to the variability of data ...

In order to reliably compare data from multiple probe arrays, differences of non-biological origin must be minimized.“1

• Normalization is the process of reducing unwanted variation either within or between arrays. It may use information from multiple chips.

• Typical assumptions of most major normalization methods are (one or both of the following):

Only a minority of genes are expected to be differentially expressed between conditions Any differential expression is as likely to be up-regulation as down-regulation (ie about as many genes going up in expression as are going down between conditions)

1 GeneChip 3.1 Expression Analysis Algorithm Tutorial, Affymetrix technical support

7

Summarization• Reducing multiple measurements on the same

gene down to a single measurement by combining in some manner.

8

Quality Assessment• Need to be able to differentiate between good and

bad data. • Bad data could be caused by poor hybridization,

artifacts on the arrays, inconsistent sample handling, …..

• An admirable goal would be to reduce systematic differences with data analysis techniques.

• Sometimes there is no option but to completely discard an array from further analysis. How to decide …..

9

Affymetrix GeneChip• Commericial mass produced high

density oligonucleotide array technology developed by Affymetrix http://www.affymetrix.com

• Single channel microarray• Todays talk relates to arrays

designed for expression analysis

Image courtesy of Affymetrix Press Website.

10

Probes and Probesets

Typically 11 probe(pairs) in a probesetLatest GeneChips have as many as:54,000 probesets

1.3 Million probesCounts for HG-U133A plus 2.0 arrays

11

Two Probe Types

TAGGTCTGTATGACAGACACAAAGAAGATG

CAGACATAGTGTCTGTGTTTCTTCT

CAGACATAGTGTGTGTGTTTCTTCT

PM: the Perfect Match

MM: the Mismatch

Reference Sequence

Note that about 30% of MM probe intensities are brighter than corresponding PM probe intensities.

12

Hybridization to the ChipSample of Fragmented Labeled RNA

Labeling molecule that fluoresces

13

The Chip is Scanned

14

Image Analysis

15

Chip dat file – checkered board – close up pixel selection

16

Chip cel file – checkered board

Courtesy: F. Colin

17

Boxplot raw intensities

Array 1 Array 2 Array 3 Array 4

18

Density plots

19

Comparing arraysArray2

vs

Array 1

Bad

20

Comparing arraysLog2 Array2 vsLog2 Array 1

Better

21

Comparing arraysM = log2(Array2/Array1)

Vs

A = ½ log2(Array2*Array1)

Best

M= MinusA=Average

22

Typical MA-plot

Loess smoother

23

Pairwise MA plotsArray 1

Array 2

Array 3

Array 4

M=log2arrayi/arrayjA=1/2*log2(arrayi*arrayj)

24

Boxplots comparing M

Array 1 Array 2 Array 3 Array 4

M

25

RMA Background Approach• Convolution Model

= +

ObservedPM

SignalS

NoiseN

( )Exp α ( )2,N μ σ

( )

2

E

,

1

a pm ab bS PM pm a b

a pm ab

a o bb

μ σ α

φ

σ

φ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

−−= = +

−

= − −

+Φ −

=

Φ

26

GCRMA Background Approach

• PM=Opm+Npm+S• MM=Omm+Nmm

• O – Optical noise• N – non-specific binding• S – Signal

• Assume O is distributed Normal • log(Npm )and log(Nmm ) are assumed bi-variate

normal with correlation 0.7 • log(S) assumed exponential(1)

27

GCRMA continued• An experiment was carried out where yeast RNA was

hybridized to human chips, so all binding expected to be non specific.

• Fitted a model to predict log intensity from sequence composition gives base and position effects

• Uses these effects to predict an affinity for any given sequence call this A. The means of the distributions for the Npm, Nmm terms are functions of the affinities.

28

Non-Biological variability is a problem for single channel

arrays

5 scanners for 6 dilution groups

Log2

PM

inte

nsity

29

Normalization• In case of single channel microarray data this is

carried out only across arrays.• Could generalize methods we applied to two color

arrays, but several problems:Typically several orders of magnitude more probes on an Affymetrix array then spots on a two channel arrayWith single channel arrays we are dealing with absolute intensities rather than relative intensities.

• Need something fast

30

Quantile Normalization• Normalize so that the quantiles of each chip are

equal. Simple and fast algorithm. Goal is to give same distribution to each chip.

Target Distribution

Original Distribution

31

32

It works!!Unnormalized Scaling

Quantile Normalization

33

It Reduces VariabilityFold change forNon differential genes

Expression Values

Also no serious bias effects. For more see Bolstad et al (2003)

Unnormalized Quantile Scaling

Unnormalized Quantile Scaling

Varia

nce

Log2

Fol

d C

hang

e

34

Summarization• Problem: Calculating gene expression values.• How do we reduce the 11-20 probe intensities for each

probeset on to a gene expression value?• Our Approach

RMA – a robust multi-chip linear model fit on the log scale• Some Other Approaches

Single chipAvDiff (Affymetrix) – no longer recommended for use due to many flawsMas 5.0 (Affymetrix) – use a 1 step Tukey-biweight to combine the probe intensities in log scale

Multiple ChipMBEI (Li-Wong dChip) – a multiplicative model on natural scale

35

General Probe Level Model

• Where f(X) is function of factor (and possibly covariate) variables (our interest will be in linear functions)

• is a pre-processed probe intensity (usually log scale)

• Assume that

f( )kij kijy ε= +X

E 0kijε⎡ ⎤ =⎣ ⎦2Var kij kε σ⎡ ⎤ =⎣ ⎦

kijy

36

Parallel Behavior Suggests Multi-chip Model

Array Array

PM

pro

be in

tens

ity

PM

pro

be in

tens

ity

Differentially expressing Non Differential

37

Probe Pattern Suggests Including Probe-Effect

PM

pro

be in

tens

ity

PM

pro

be in

tens

ity

Differentially expressing Non Differential

Probe Number Probe Number

38

Also Want Robustness

PM

pro

be in

tens

ity

Non Differential

PM

pro

be in

tens

ity

PM

pro

be in

tens

ity

Differentially expressing

PM

pro

be in

tens

ity

Differentially expressing Non Differential

39

The RMA model

whereis a probe-effect i= 1,…,Iis chip-effect ( is log2 gene expression on array j) j=1,…,Jk=1,…,K is the number of probesets

( )( )2log N Bkij kijy PM=

kij k ki kj kijy m α β ε= + + +

kiα

kjβ k kjm β+

40

Median Polish Algorithm

11 1

1

0

00 0 0

J

I IJ

y y

y y

L

M O M M

L

L11 1 1

1

1

ˆ ˆ ˆ

ˆ ˆ ˆˆ ˆ ˆ

J

I IJ I

J m

ε ε α

ε ε α

β β

L

M O M M

L

L

Iterate

Sweep Rows

Sweep Columns

median median 0i jα β= =

median median 0i ij j ijε ε= =

ImposesConstraints

41

RMA mostly does well in practice

Detecting Differential Expression Not noisy in low intensities

RMA

MAS 5.0

42

One DrawbackRMA MAS 5.0

Linearity across concentration. GCRMA fixes this problemConcentration Concentration

log2

Exp

ress

ion

Val

ue

log2

Exp

ress

ion

Val

ue

43

GCRMA improve linearity

44

An Alternative Method for Fitting a PLM

• Robust regression using M-estimation• In this talk, we will use Huber’s influence function.

The software handles many more.• Fitting algorithm is IRLS with weights dependent on

current residuals ( )kij

kij

rr

ψ

45

Variance Covariance Estimates

• Suppose model is • Huber (1981) gives three forms for estimating variance

covariance matrix

Y X β ε= +

( ) ( ) ( )2 1 11 1/ Ti

i

n p r W X X Wψκ

− −− ∑

( ) ( )

( )( )

2

122

1/

1/

iTi

ii

n p rX X

n r

ψκ

ψ

−−

⎡ ⎤′⎢ ⎥⎣ ⎦

∑

∑

( )

( )

2

11/( )

1/

ii

ii

n p rW

n r

ψκ

ψ−

−

′

∑∑

We will use this form'TW X X= Ψ

46

We Will Focus on the Summarization PLM

• Array effect model

With constraint

kij ki kj kijy α β ε= + +

10

I

kiiα

=

=∑Probe Effect

Array Effect

Pre-processedLog PM intensity

47

Quality Assessment• Problem: Judge quality of chip data

• Question: Can we do this with the output of the Probe Level Modeling procedures?

• Answer: Yes. Use weights, residuals, standard errors and expression values.

48

Chip pseudo-images

49

An Image Gallery

http://PLMImageGallery.bmbolstad.com

“Tricolor”

“Crop Circles”

“Ring of Fire”

50

NUSE PlotsNormalizedUnscaledStandardErrors

( )( )

( ( ))kj

kjj kj

SENUSE

med SEβ

ββ

=

51

RLE Plots

RelativeLogExpression

( ) ( )kj kj kjRLE medβ β β= −

52

Acknowledgements• Terry Speed• Rafael Irizarry• Julia Brettschneider • Francois Colin• Zhijin (Jean) Wu

• Any one else …

53

References• Bolstad, B. M., Irizarry, R. A., Astrand, M., and Speed, T. P., A comparison of

normalization methods for high density oligonucleotide array data based on variance and bias, Bioinformatics, 19, 185 (2003).

• Irizarry RA, Bolstad BM, Collin F, Cope LM, Hobbs B, and Speed TP. Summaries of Affymetrix GeneChip Probe Level Data. Nucleic Acids Research, 31(4):e15, 2003.

• Bolstad BM, Collin F, Brettschneider J, Simpson K, Cope L, Irizarry RA, and Speed TP. (2005) Quality Assessment of Affymetrix GeneChip Data inBioinformatics and Computational Biology Solutions Using R and Bioconductor. Gentleman R, Carey V, Huber W, Irizarry R, and Dudoit S. (Eds.), Springer

• Wu, Z., Irizarry, R., Gentleman, R., Martinez Murillo, F. Spencer, F. A Model Based Background Adjustment for Oligonucleotide Expression Arrays. Journal of American Statistical Association 99, 909-917 (2004)