The second-simplest cDNA microarray data analysis problem

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The second-simplest cDNA microarray data
analysis problem

• Terry Speed, UC Berkeley
• Bioinformatic Strategies For Application of
  Genomic Tools to Environmental Health Research,
  March 5, 2001
• NIEHS National Center for Toxicogenomics NCSU
  Bioinformatics Research Center

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Biological question Differentially expressed
genes Sample class prediction etc.
Experimental design
Microarray experiment
16-bit TIFF files
Image analysis
(Rfg, Rbg), (Gfg, Gbg)
Normalization
R, G
Estimation
Testing
Clustering
Discrimination
Biological verification and interpretation
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Some motherhood statements

• Important aspects of a statistical analysis
  include
• Tentatively separating systematic from random
  sources of variation
• Removing the former and quantifying the latter,
  when the system is in control
• Identifying and dealing with the most relevant
  source of variation in subsequent analyses
• Only if this is done can we hope to make more or
  less valid probability statements

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The simplest cDNA microarray data analysis
problem is identifying differentially expressed
genes using one slide

• This is a common enough hope
• Efforts are frequently successful
• It is not hard to do by eye
• The problem is probably beyond formal statistical
  inference (valid p-values, etc)
• for the foreseeable future, and heres why

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An M vs. A plot
M log2(R / G) A log2(RG) / 2
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Background matters
From Spot
From GenePix
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No background correction
With background correction
From the NCI60 data set (Stanford web site)
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An experiment having within-slide replicates
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Background makes a difference
Background method Segmentation method Exp1
Exp2 S.nbg 6 6 Gp.nbg 7 6 SA.nbg 6
6 No background QA.fix.nbg 7 6 QA.hist.nbg
7 6 QA.adp.nbg 14 14 S.valley 17 21 GP
11 11 Local surrounding SA 12 14 QA.fix
18 23 QA.hist 9 8 QA.adp 27 26 Others
S.morph 9 9 S.const 14 14
Medians of the SD of log2(R/G) for 8 replicated
spots multiplied by 100 and rounded to the
nearest integer.
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Normalisation - lowess

• Global lowess (Matt Callows data, LNBL)
• Assumption changes roughly symmetric at all
  intensities.

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From the NCI60 data set (Stanford web site)
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Ngai lab, UCB
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Tiagos data from the Goodman lab, UCB
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From the Ernest Gallo Clinic Research Center
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From Peter McCallum Cancer Research Institute,
Australia
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Normalisation - print tip
Assumption For every print group, changes
roughly symmetric at all intensities.
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M vs A after print-tip normalisation
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Normalization (ctd) Another data set
Log-ratios
Print-tip groups

• After within slide global lowess normalization.
• Likely to be a spatial effect.

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Taking scale into account

• Assumption
• All print-tip-groups have the same spread
  in M
• True log ratio is mij where i represents
  different print-tip-groups and j
  represents different spots.
• Observed is Mij, where
• Mij ai mij
• Robust estimate of ai is
• MADi medianj yij - median(yij)

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Normalization (ctd) That same data set
Log-ratios
Print-tip groups

• After print-tip location and scale normalization.
• Incorporate quality measures.

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Matt Callows Srb1 dataset (5). Newtons and
Chens single slide method
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Matt Callows Srb1
dataset (8). Newtons, Sapir Churchills and
Chens single slide method
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The approach of Roberts et al (Rosetta)
Genomic DNA vs. Genomic DNA
Data from Bing Ren
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The second simplest cDNA microarray data analysis
problem is identifying differentially expressed
genes using replicated slides

• There are a number of different aspects
• First, between-slide normalization then
• What should we look at averages, SDs
  t-statistics, other summaries?
• How should we look at them?
• Can we make valid probability statements?
• A report on work in progress

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Normalization (ctd) Yet another data set

• Between slides this time (10 here)
• Only small differences in spread apparent
• We often see much greater differences

Log-ratios
Slides
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The NCI 60 experiments (no bg)
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Taking scale into account

• Assumption All slides have the same spread
  in M
• True log ratio is mij where i represents
  different slides and j represents different
  spots.
• Observed is Mij, where
• Mij ai mij
• Robust estimate of ai is
• MADi medianj yij - median(yij)

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Which genes are (relatively) up/down regulated?

• Two samples.
• e.g. KO vs. WT or mutant vs. WT

? n
T
C
? n
For each gene form the t statistic
average of n trt Ms sqrt(1/n (SD of n trt
Ms)2)
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Which genes are (relatively) up/down regulated?

• Two samples with a reference (e.g. pooled control)

? n
T
C
? n
C
C

• For each gene form the t statistic
  
• average of n trt Ms - average of n ctl Ms
• sqrt(1/n (SD of n trt Ms)2 (SD of n ctl Ms)2)

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One factor more than 2 samples
T2
T3
T4
T1
x 2
x 2
x 2
x 2
C

• Samples Liver tissue from mice treated by
  cholesterol modifying drugs.
• Question 1 Find genes that respond differently
  between the treatment and the control.
• Question 2 Find genes that respond similarly
  across two or more treatments relative to control.

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One factor more than 2 samples
T6
T1
T5
T2
T4
T3

• Samples tissues from different regions of the
  mouse olfactory bulb.
• Question 1 differences between different
  regions.
• Question 2 identify genes with a pre-specified
  patterns across regions.

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Two or more factors

• 6 different experiments at each time point.
• Dyeswaps.
• 4 time points (30 minutes, 1 hour, 4 hours, 24
  hours)
• 2 x 2 x 4 factorial experiment.

ctl
OSM
? 4 times
OSM EGF
EGF
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Which genes have changed?When permutation
testing possible

• 1. For each gene and each hybridisation (8 ko 8
  ctl), use Mlog2(R/G).
• 2. For each gene form the t statistic
• average of 8 ko Ms - average of 8 ctl Ms
• sqrt(1/8 (SD of 8 ko Ms)2 (SD of 8 ctl Ms)2)
• 3. Form a histogram of 6,000 t values.
• 4. Do a normal Q-Q plot look for values off the
  line.
• 5. Permutation testing.
• 6. Adjust for multiple testing.

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Histogram qq plot
ApoA1
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Apo A1 Adjusted and Unadjusted p-values for the
50 genes with the largest absolute t-statistics.
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Which genes have changed?Permutation testing not
possible

• Our current approach is to use averages, SDs,
  t-statistics and a new statistic we call B,
  inspired by empirical Bayes.
• We hope in due course to calibrate B and use that
  as our main tool.
• We begin with the motivation, using data from a
  study in which each slide was replicated four
  times.

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Results from 4 replicates
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BLOR compared
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• M
• t
• t ?M

Results from the Apo AI ko experiment
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• M
• t
• t ?M

Results from the Apo AI ko experiment
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Empirical Bayes log posterior odds ratio
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• M
• B
• t
• M ? B
• t ?B
• t ? M ?B

Results from SR-BI transgenic experiment
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• M
• B
• t
• M ? B
• t ?B
• t ? M ?B

Results from SR-BI transgenic experiment
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Extensions include dealing with

• Replicates within and between slides
• Several effects use a linear model
• ANOVA are the effects equal?
• Time series selecting genes for trends

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Rosetta once more In vivo Binding Sites of
Gal4p in Galactose
P lt0.001
Un-enriched DNA (Cy3)
antibody-enriched DNA (Cy5)
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Summary (for the second simplest problem)

• Microarray experiments typically have thousands
  of genes, but only few (1-10) replicates for each
  gene.
• Averages can be driven by outliers.
• Ts can be driven by tiny variances.
• B LOR will, we hope
• use information from all the genes
• combine the best of M. and T
• avoid the problems of M. and T

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Acknowledgments

• UCB/WEHI
• Yee Hwa Yang
• Sandrine Dudoit
• Ingrid Lönnstedt
• Natalie Thorne
• David Freedman
• CSIRO Image Analysis Group
• Michael Buckley
• Ryan Lagerstorm

• Ngai lab, UCB
• Goodman lab, UCB
• Peter Mac CI, Melb.
• Ernest Gallo CRC
• Brown-Botstein lab
• Matt Callow (LBNL)
• Bing Ren (WI)

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• Some web sites
• Technical reports, talks, software etc.
• http//www.stat.berkeley.edu/users/terry/zarray/Ht
  ml/
• Statistical software R GNUs S
  http//lib.stat.cmu.edu/R/CRAN/
• Packages within R environment
• -- Spot http//www.cmis.csiro.au/iap/spot.htm
• -- SMA (statistics for microarray analysis)
  http//www.stat.berkeley.edu/users/terry/zarray/So
  ftware /smacode.html

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Factorial Design
Age Effect
2
A1
P01
4
Zone Effect
1
3
5
P04
A 4
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Factorial design
m
ma
Different ways of estimating parameters. e.g. Z
effect. 1 (m z) - (m) z 2 - 5 ((m
a) - (m)) -((m a)-(m z)) (a) - (a z)
z 4 3 - 5 z
2
A1
P01
4
1
3
5
P04
A 4
mz
mzaza
How do we combine the information?
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Regression analysis
Define a matrix X so that E(M)X? Use least
squares estimate for z, a, za
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Looking at effect of Z log(zone 4 / zone1)
gene A
gene B
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Estimate
Z effect

• ?
• t ? / SE
• ? ? t

Log2(SE)
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Zone Age Zone ? Age
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Top 50 genes from each effect
Zone . Age interaction
Age
19
0
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2
0
19
Zone
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• T
• B
• t ? M ?B
• t ?B

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(No Transcript)
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• M
• t
• t ?M

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• M
• B
• t
• M ? B
• t ?B
• t ? M?B

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Some statistical questions

• Image analysis addressing, segmenting,
  quantifying
• Normalisation within and between slides
• Quality of images, of spots, of (log) ratios
• Which genes are (relatively) up/down regulated?
• Assigning p-values to tests/confidence to
  results.

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Some statistical questions, ctd

• Planning of experiments design, sample size
• Discrimination and allocation of samples
• Clustering, classification of samples, of genes
• Selection of genes relevant to any given analysis
• Analysis of time course, factorial and other
  special experiments... much more

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The NCI 60 experiments (bg)