Statistical Analyses of Microarray Data

Rafael A. Irizarry

Department of Biostatisticsrafa@jhu.edu

http://biosun01.biostat.jhsph.edu/~ririzarr

Outline

• Scientific questions

• Review of technology

• Role of statistics

• Two case studies

Scientific Questions

• Expression

• Differential expression

• Expression patterns

“To understand gene function, it is helpful to know when and where it is expressed and…”

“…under what circumstances the expression level is affected.”

“… questions concerning functional pathways and how cellular components work together to regulate and carry out cellular

processes.”

Lipshutz et al. (1999) Nature genetics, 21, pp. 20-21

What do Microarrays do?Interrogate labeled nucleic acid samples

model systems, microdissections, cell lines, human tissue bank

kanRUPTAG DOWNTAG

• RNA samples

• Oligonucleotide barcodes

How do they do it?

Probes

Labeled targets

cDNA clones(probes)

PCR product amplificationpurification

printing

microarray

Hybridize target to microarray

mRNA target

excitation

laser 1laser 2

emission

scanning

analysis

0.1nl/spot

overlay image and normalize

cDNA Arrays

High Density Oligonucleotide Arrays

24µm24µm

Millions of copies of a specificMillions of copies of a specificoligonucleotide probeoligonucleotide probe

Image of Hybridized Probe ArrayImage of Hybridized Probe Array

>200,000 different>200,000 differentcomplementary probes complementary probes

Single stranded, Single stranded, labeled RNA targetlabeled RNA target

Oligonucleotide probeOligonucleotide probe

**

**

*

1.28cm1.28cm

GeneChipGeneChip Probe ArrayProbe ArrayHybridized Probe CellHybridized Probe Cell

Compliments of D. Gerhold

Role of Statistics

Biological questionDifferentially expressed genesSample class prediction etc.

Testing

Biological verification and interpretation

Microarray experiment

Estimation

Experimental design

Image analysis

Normalization

Clustering Discrimination

Quantify Expression

Part of the image of one channel false-coloured on a white (v. high) red (high) through yellow and green (medium) to blue (low) and black scale

Does one size fit all?

Segmentation: limitation of the fixed circle method

SRG Fixed Circle

Inside the boundary is spot (fg), outside is not.

Some local backgrounds

We use something different again: a smaller, less variable value.

Single channelgrey scale

Quantification of Expression

For each spot on the slide we calculateRed intensity = Rfg – Rbg

fg = foreground, bg = background, andGreen intensity = Gfg – Gbg

and combine them in the log (base 2) ratioLog2( Red intensity / Green intensity)

we now have one differential expression for each gene for each array

Top 2.5%of ratios red, bottom 2.5% of ratios green

The red-green ratios can be spatially biased

Another example

Oligo Array Image Analysis

• About 100 pixels per probe cell

• These intensities are combined to form one number representing expression for the probe cell oligo

Normalization at Probe Level

Normalization at Probe Level

Dilution Experiment Data

Dilution Experiment Data

PM MM

Default until 2002

• GeneChip® software uses Avg.diff

with A a set of “suitable” pairs chosen by software.• Log ratio version is also used.• For differential expression Avg.diffs are compared

between chips.

j

jj MMPMdiffAvg )(1

.

What is the evidence? Lockhart et. al. Nature Biotechnology 14 (1996)

Two case studies

Spike-In Experiments

• Add concentrations (0.5pM – 100 pM) of 11 foreign species cRNAs to hybridization mixture

• Set A: 11 control cRNAs were spiked in, all at the same concentration, which varied across chips.

• Set B: 11 control cRNAs were spiked in, all at different concentrations, which varied across chips. The concentrations were arranged in 12x12 cyclic Latin square (with 3 replicates)

Set A: Probe Level Data (12 chips)

Spike-In BProbe Set Conc 1 Conc 2 Rank

BioB-5 100 0.5 1

BioB-3 0.5 25.0 2

BioC-5 2.0 75.0 3

BioB-M 1.0 35.7 4

BioDn-3 1.5 50.0 5

DapX-3 35.7 3.0 6

CreX-3 50.0 5.0 7

CreX-5 12.5 2.0 8

BioC-3 25.0 100 9

DapX-5 5.0 1.5 10

DapX-M 3.0 1.0 11

Later we consider 23 different combinations of concentrations

Observed RanksGene AvDiff MAS 5.0 Li&Wong AvLog(PM-BG)

BioB-5 6 2 77 1

BioB-3 16 1 33 2

BioC-5 74 6 22 5

BioB-M 30 3 6 3

BioDn-3 44 5 27 4

DapX-3 239 24 796 7

CreX-3 333 73 386 11

CreX-5 3276 33 43 9

BioC-3 2709 8572 12 10300

DapX-5 2709 102 59 17

DapX-M 165 19 30 6

kanRA

Transformation into deletion pool

Select for Ura+ transformantsGenomic DNA preparation

Circular pRS416

PCRCy5 labeled PCR products Cy3 labeled PCR products

Oligonucleotide array hybridization

B

EcoRI linearized PRS416

NHEJ Defective

MCS

CEN/ARS

URA3 ttaaaatt

CEN/ARS

URA3

UPTAG DOWNTAG

• .

Y K U 7 0 N E J 1 Y K U 8 0

Y K U 7 0 N E J 1 Y K U 8 0

Average Red and Green Scatter Plot

Average Red and Green MVA plot

Histograms

QQ-Plot

Z-Scores

Average Red and Green MVA Plot

Average Red and Green Scatter Plot

Summary

• Simple data exploration useful tool for quality assessment

• Statistical thinking helpful for interpretation

• Statistical models may help find signals in noise

Acknowledgements

UC Berkeley StatBen BolstadSandrine DudoitTerry SpeedJean Yang

MBG (SOM)Jef BoekeSiew-Loon OoiMarina LeeForrest Spencer

BiostatisticsKarl BromanLeslie CopeCarlo CoulantoniGiovanni ParmigianiScott Zeger

Gene LogicFrancois Colin Uwe Scherf’s Group

PGATom Cappola Skip GarciaJoshua Hare

WEHIBridget HobbsNatalie Thorne