Analyzing Cross-Plattform Consistency Using Tests Against ...bioinf.boku.ac.at/CAMDA2008/05.12.2008/klinglm_talk.pdfIntroduction Material and Methods Experimental Design Methods Exploratory
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Analyzing Cross-Plattform Consistency UsingTests Against Ordered Alternatives
CAMDA Emerald Competition
Florian Klinglmueller1 Thomas Tuechler2
1Core Unit for Medical Statistics and InformaticsMedical University of Vienna
florian.klinglmueller@meduniwien.ac.at2WWTF Chair for Bioinformatics
BOKU Universitythomas.tuechler@boku.ac.at
05.12.2008 / CAMDA@Boku University
Introduction
Material and MethodsExperimental DesignMethods
Exploratory Data AnalysisTotal-RNA to Messenger-RNASaturation
ResultsMonotone GenesAcross PlatformNormalization Effect
Discussion - OutlookSummary and Discussion
Titration
4:0 ...L
0:4 ...K
1:3 ...M2
3:1 ...M1
Liver
Kidney
Total – RNA Mixtures:
Design Hierarchy
Affymetrix
Illumina
Agilent
3 Platforms
Experimental Design:
Design Hierarchy
Affymetrix
...
...
...
...
Rat 2
Rat 1Illumina
Agilent
3 Platforms
6 Rats
Experimental Design:
Design Hierarchy
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
Experimental Design:
Design Hierarchy
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 Replicates
Experimental Design:
Main Questions
I Do the measured intensities reflect the titration?
I Agreement across platforms.
I Influence of normalization.
Tests Against Order-Restricted Alternatives
I Dose-response studiesI 70’s and 80’s literature:
I Barlow [1]I Robertson et al. [3]
I Microarray Application: Lin et al. [2]
I 5 Statistics: Marcus, Wilson, E2, M, ModifiedM
I E2 most powerful ⇒ we use E2
TestNull Hypothesis
We test the null hypothesis of equal means
H0,g : µL,g = µM1,g = µM2,g = µK ,g , (1)
against the ordered alternatives
Hup1,g : µL,g ≤ µM1,g ≤ µM2,g ≤ µK ,g , (2)
Hdown1,g : µL,g ≥ µM1,g ≥ µM2,g ≥ µK ,g , (3)
with at least one strict inequality.
I Main Principle: Isotonic Regression
Isotonic RegressionFitting Monotone Functions
Isotonic Regression: Formulation
Isotonic Function I Set T := {t1, ..., tn} with order relationI m(ti ) is called isotonic if
ti ≤ tj ⇒ m(ti ) ≤ m(tj)I F(T ): all isotonic functions on TI Direction has to be specified
Isotonic Regression I yi = m(ti ) + εi , m ∈ F(T )I Least-squares fit:
m̂ = argminm∈F(T )
∑ni=1(yi −m(ti ))2.
Isotonic RegressionExample
I T = {L ≤ M1 ≤ M2 ≤ K}I yg (ti ) = mup(ti ) + εiI Some gene expressions:
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1.0
2.0
3.0
4.0
Mixtures
Exp
ress
ion
L M1 M2 K
unrestrictedisotonic
Isotonic RegressionUpwards Trend
I T = {L ≤ M1 ≤ M2 ≤ K}I yg (ti ) = mup(ti ) + εiI Isotonic Regression for upwards trend:
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1.0
2.0
3.0
4.0
Mixtures
Exp
ress
ion
L M1 M2 K
●
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unrestrictedisotonic
Isotonic RegressionDownwards Trend
I T = {L ≥ M1 ≥ M2 ≥ K}I yg (ti ) = mdown(ti ) + εiI Isotonic Regression for downwards trend:
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1.0
2.0
3.0
4.0
Mixtures
Exp
ress
ion
L M1 M2 K
● ● ● ●
unrestrictedisotonic
StatisticDefinition of E2 Statistic
E2 (Barlow [1],Robertson et al. [3]):
E2up01 = 1−
∑kj(ykj − m̂up(ti ))2∑
kj(ykj − y)2, (4)
I Likelihood-ratio:
E2up01 = 1− ESS
TSS
p-Value CombinationCapturing the Hierarchical Variance Structure
I Revisit the design hierarchyI Now we add a new level: Normalization
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
NormalizationsBaseline vs. Quantile Normalization
I Both widely used
Baseline NormalizationAlign per array medians
1. From each array remove array-wise median
2. To each array add overall median
Removes systematic location shifts
Quantile NormalizationAlign order statistics
1. Per array - reduce expressions to ranks
2. Per array - reassign ranks to quantiles from mean distribution(means of order statistics)
Removes any systematic disturbance that keeps the order
NormalizationsBaseline vs. Quantile Normalization
I Both widely used
Baseline NormalizationAlign per array medians
1. From each array remove array-wise median
2. To each array add overall median
Removes systematic location shifts
Quantile NormalizationAlign order statistics
1. Per array - reduce expressions to ranks
2. Per array - reassign ranks to quantiles from mean distribution(means of order statistics)
Removes any systematic disturbance that keeps the order
NormalizationsBaseline vs. Quantile Normalization
I Both widely used
Baseline NormalizationAlign per array medians
1. From each array remove array-wise median
2. To each array add overall median
Removes systematic location shifts
Quantile NormalizationAlign order statistics
1. Per array - reduce expressions to ranks
2. Per array - reassign ranks to quantiles from mean distribution(means of order statistics)
Removes any systematic disturbance that keeps the order
p-Value CombinationCapturing the Hierarchical Variance Structure
I Revisit the design hierarchyI We want p
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
p-Value CombinationInverse Normal Method
I Combine one-sided p-values:
pC ,upg = 1− Φ(
1√N
∑i
Φ−1(1− pupig )), (5)
I pC ,downg analogue
I uniformly distritibuted conservative one-sided p-values
I Bonferroni correct directional decision:pCg = 2min(pC ,up
g , pC ,downg ).
p-Value CombinationPer Animal p-Values
I 6 Animals × 3 Platforms × 2 Normalizations → 36 timespupNorm,Plat,ig , pdown
Norm,Plat,ig , pNorm,Plat,ig
I Combine the 6 × 6 pupNorm,Plat,ig , pdown
Norm,Plat,ig to get get 6:
pCPlat ,upNorm,g , pCPlat ,down
Norm,g , and pCPlat
Norm,g
I Combine the 3 pCPlat ,upNorm,g , pCPlat ,down
Norm,g to get 2:
pCNorm,upg , pCNorm,down
g
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
p-Value CombinationPer Animal p-Values
I 6 Animals × 3 Platforms × 2 Normalizations → 36 timespupNorm,Plat,ig , pdown
Norm,Plat,ig , pNorm,Plat,ig
I Combine the 6 × 6 pupNorm,Plat,ig , pdown
Norm,Plat,ig to get get 6:
pCPlat ,upNorm,g , pCPlat ,down
Norm,g , and pCPlat
Norm,g
I Combine the 3 pCPlat ,upNorm,g , pCPlat ,down
Norm,g to get 2:
pCNorm,upg , pCNorm,down
g
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
p-Value CombinationPer Animal p-Values
I 6 Animals × 3 Platforms × 2 Normalizations → 36 timespupNorm,Plat,ig , pdown
Norm,Plat,ig , pNorm,Plat,ig
I Combine the 6 × 6 pupNorm,Plat,ig , pdown
Norm,Plat,ig to get get 6:
pCPlat ,upNorm,g , pCPlat ,down
Norm,g , and pCPlat
Norm,g
I Combine the 3 pCPlat ,upNorm,g , pCPlat ,down
Norm,g to get 2:
pCNorm,upg , pCNorm,down
g
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
p-Value CombinationPer Animal p-Values
I 6 Animals × 3 Platforms × 2 Normalizations → 36 timespupNorm,Plat,ig , pdown
Norm,Plat,ig , pNorm,Plat,ig
I Combine the 6 × 6 pupNorm,Plat,ig , pdown
Norm,Plat,ig to get get 6:
pCPlat ,upNorm,g , pCPlat ,down
Norm,g , and pCPlat
Norm,g
I Combine the 3 pCPlat ,upNorm,g , pCPlat ,down
Norm,g to get 2:
pCNorm,upg , pCNorm,down
g
Affymetrix
...
...
...
...
Rat 2
Rat 1
4:0 ...L
3:1 ...M1
1:3 ...M2
0:4 ...K
Rep 1
Rep 2
Rep 3
Illumina
Agilent
3 Platforms
6 Rats
4 Mixtures
3 ReplicatesAffymetrix
Agilent
2 Normalizations
p-Value CombinationSummary
I Comptute one sided permutation test p-values for eachanimal, on each platform seperately with Quantile - andBaseline - normalized data.
I Combine per animal tests from each plaform.
I Combine per platform tests from each normalization.
Results
Finally!
Exploratory AnalysisDistribution of Group Means on Raw Data
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2 K
0
5
10
15
20
Illumina
I Location-shift
I Higher messenger-RNA content in kidney?
I Both normalization methods remove anyvisible trends in location
I Baseline
I Quantile - also in scale
Exploratory AnalysisDistribution of Group Means on Raw Data
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10
15
20
Affymetrix
LM
1M
2 K
0
5
10
15
20
Agilent
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LM
1M
2 K
0
5
10
15
20
Illumina
I Location-shift
I Higher messenger-RNA content in kidney?
I Both normalization methods remove anyvisible trends in location
I Baseline
I Quantile - also in scale
Exploratory AnalysisDistribution of Group Means on Raw Data
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LM
1M
2 K
0
5
10
15
20
Affymetrix
LM
1M
2 K
0
5
10
15
20
Agilent
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LM
1M
2 K
0
5
10
15
20
Illumina
I Location-shift
I Higher messenger-RNA content in kidney?
I Both normalization methods remove anyvisible trends in location
I Baseline
I Quantile - also in scale
Exploration of TrendRelationship between Increases
M1
L
KM
2
L M1 M2 K
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
0 2 4 6
−6
−4
−2
0
M1−L
K−
M2
Illumina
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
0 5 10
−6
−4
−2
0
M1−L
K−
M2
Agilent
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
0 2 4 6
−6
−5
−4
−3
−2
−1
0
M1−L
K−
M2
Affymetrix
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
●
● ● ●
05
1015
20
Mixture
Mea
n E
xpre
ssio
n
L M1 M2 K
NM_052802
Maximum Mean Expression
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
0 2 4 6
−6
−5
−4
−3
−2
−1
0
M1−L
K−
M2
Affymetrix
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
● ● ●
●
05
1015
20
Mixture
Mea
n E
xpre
ssio
n
L M1 M2 K
NM_022519
Maximum Mean Expression
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Exploration of TrendRelationship between Increases
0 2 4 6
−6
−5
−4
−3
−2
−1
0
M1−L
K−
M2
Affymetrix
I Relationship betweenfirst/second increase
I Scatterplot - Illumina:Trends not linear;When first increaselarge then lastincrease small andvice versa
I Scatterplot - Agilent
I Scatterplot -Affymetrix
I Rightmost point
I Lowest point
I Saturation?
Test Setup
Settings
I R package IsoGene provided by Lin et al.
I 20000 permutations (1 week on Cluster)
I 2 Normalization Methods × 3 Platforms × 6 Animals
I 6111 well annotated genes available on all platforms
I remove one animal from Illumina data
I Family Wise Error: Bonferoni-Holm
Proportions of Significant GenesGeneral Overview
updownnone
updownnone
updownnone
0 20 40 60 80 100
IlluminaAgilentAffymetrix
I Baseline
I Quantile
Proportions of Significant GenesGeneral Overview
updownnone
updownnone
updownnone
0 20 40 60 80 100
IlluminaAgilentAffymetrix
I Baseline
I Quantile
Agreement Between PlatformsNumber of Genes
Affy−AgilAffy−IlluAgil−Illu
All
Affy−AgilAffy−IlluAgil−Illu
All
0 20 40 60 80 100
BaselineQuantile
I Fleiss’ κ-coefficient - agreement across platforms using FWRadjusted combined p-Vaues
I Quantile Normalisation: .52
I Baseline Normalisation: .37
Agreement Between NormalizationsNumber of Genes significant
Quantile Baseline
711
1070520 3810
Fleiss κ-coefficient: .57
I around 2 times moresignificant genesexclusive to baselinethan to quantilenormalized data
I more than 97% ofgenes exclusive tobaseline normalizeddata are upregulated
I up-down in quantileexclusive genes 40:60
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
SummaryResults
Data
I Substantial number of genes show significant monotonicity
I Across platform agreement exceeds chance levels
I Agreement on baseline normalized data is worse
I Baseline noramlized data shows more upward trends -incomplete removal of total/messenger-RNA effect
I Genes exclusively significant in baseline data are mostlyupward trends
Methods
I Isotonic regression as a means to detect monotonic trends
I p-Value combination as a means to compare results fromdiffernt platforms.
Thanks
I MSI - Martin Posch
I Statistic - Univie: Cluster
References
[1] Richard E. Barlow. Statistical Inference Under OrderRestrictions. John Wiley and Sons Ltd, 1972.
[2] D. Lin, Z. Shkedy, D. Yekutieli, T Burzykowski, H. Gaehlmann,A. Bondt, T. Perera, T. Geerts, and L. Bijnens. Testing fortrends in dose-response microarray experiments: a comparisonof several testing procedures, multiplicity and resampling-basedinference. Statistical Applications in Genetics and MolecularBiology, 2007.
[3] Tim Robertson, F. T. Wright, and R. L. Dykstra. OrderRestricted Statistical Inference. John Wiley & Sons Inc, 1988.
Thank you for your attention
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