U C L C a n c e r I n s t i t u t e

Statistical methods for the analysis

of Infinium DNA methylation data

Andrew Teschendorff

Statistical Genomics Group

UCL Cancer Institute

University College London

http://www.ucl.ac.uk/cancer/rescancerbiol/statisticalgenomics

U C L C a n c e r I n s t i t u t e

Outline

1. A beta mixture quantile dilation

normalisation method for 450k Illumina

Infinium data (type1/2 probe normalisation).

2. Confounding factors and Independent

Surrogate Variable Analysis (ISVA).

ISVA : Teschendorff et al Bioinformatics 2011

U C L C a n c e r I n s t i t u t e

The type1/2 design problem in

450k data

• Type2 density peaks

shifted towards centre.

• This could skew ranking

towards type1 probes.

• Ideally, approaches which

seek to find DMRs or

DVRs require proximal

probes to be comparable.

• Peak-Based Correction

(PBC) validated on cell-

lines.

Dedeurwaeder et al Epigenomics 2011.

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PBC method on tumour tissue

• PBC method is problematic

when methylated peaks not

well-defined.

• Presence of “Holes”: the

holes are created due to

constant scaling factors.

• Need method that works for

broad peaks and avoids (as

much as possible) holes.

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A Beta-mixture quantile (BMIQ)

dilation normalisation strategy Type1 fit:

prob(M)

beta(M)

Type2 fit:

Desirable properties:

1. Number of U, H, M probes in each

design is determined by the beta

mixture model and is unchanged

by transformation.

2. Monotonic transformation.

3. Matching of densities at U and M

ends.

Dilation

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Assessment of BMIQ: tumour tissue

PBC BMIQ

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Assessment of BMIQ: cell-lines

Error over replicates Agreement with BPS

450k Data from

Dedeurwaeder et al Epigenomics 2011.

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Relative ranking of type1 vs type2

8 Breast Cancer vs

8 Normal Tissue Cancer tissue:

phenotypes A (18) vs B (14)

• PBC overcorrects data leading to a

relative enrichment of type2 probes

(caused by “holes”).

• Clear skew towards type1.

• Removed by PBC/BMIQ.

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Relative ranking of type1 vs type2

GBM: 49 CIMP+ vs 32 CIMP-

• PBC overcorrects data leading to a

relative enrichment of type2 probes

(caused by “holes”).

• Using regularised t-statistics to

rank features causes less of a

problem…..

GBM 450k data from Turcan S et al Nature March 2012

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Conclusions (I)

• Type1/2 bias creates a problem mainly if probes are

ranked according to absolute differential methylation.

• No strong type1/2 bias if probes ranked according to

regularized t-statistics (logit transform scale). However,

this may depend on phenotype, cell type, signal-to-noise

ratio,…etc.

• BMIQ/PBC reduce bias of type2 probes, however, at the

expense of increased inter-sample variance may

compromise cross-validation accuracy of type2 probes

(specially true for PBC).

• BMIQ outperforms PBC.

BMIQ appropriate in studies where there is type1/2 bias,

for DMR strategies and classification tasks.

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2. Statistical confounding

• Confounding (batch effects) is widespread (e.g TCGA OvC) and may affect

up to 80 or 90% of features (Leek JT et al Nat Rev Genet 2010). More

serious for quantitative data e.g DNAm or mRNA expression.

• Not adjusting for confounders may seriously bias estimates of statistical

significance (correlated confounders => high FDR, orthogonal confounders

=> high FNR).

No enrichment of known

biological signature,

GSEA P-value>0.05

Enrichment of known biological

signature,

GSEA P-value < 1e-7.

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Statistical confounding

• Unsupervised inter-array normalisation strategies (e.g quantile

normalisation) do not remove all variation associated with confounders

(Teschendorff AE et al PLoS One 2009, Leek JT et al Nat Rev Genet

2010), or may mask biologically/clinically important global differences in

DNA methylation (Moore LE et al Lancet Onc 2008).

• Explicit adjustment (e.g Johnson et al Biostatistics 2007 –COMBAT

algorithm): but what if factors are unknown or subject to measurement

error/uncertainty?

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Surrogate Variable Analysis (SVA)

Leek J T , Storey J D PNAS 2008;105:18718-18723

EBF(Y)EBSX

Y: Phenotype of interest (POI)

Biological variation of interest

Surrogate variable space

Confounding variation

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Drawbacks of SVA

• Framework is not flexible: suppose some confounders are

biological and adjustment for these is not required.

• Model misspecification: what if F(Y) is a poor model and

residual variation contains variation associated with POI ?

• Identifiability of confounders

is important if adjustment

required on a surrogate

variable subspace.

Biological variation of interest

Residual biological

variation of interest

Confounding variation

Surrogate variable space

Problem: the PCA/SVD used in SVA is not optimal.

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Blind source separation

Given these four images can we

reconstruct the original faces.?

?

? ?

?

One image One sample profile

One pixel One Probe

Pixel intensity Probe beta-value

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Blind Source Separation

Given these four images can we

reconstruct the original faces ?

?

? ?

?

One image One sample profile

One pixel One Probe

Pixel intensity Probe beta-value

One face One source of

data variation

ICA

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Independent Surrogate Variable Analysis

(I-SVA)

Teschendorff et al Bioinformatics 2011

KV

CFPOIV

V

K

|| UG F(Y) X

:selection Feature )4

)}(R)(R:{v

:selection subspace ISV & ISVsConstruct 3)

εASR

:ICA )2

RBF(Y)X

:matrix residual of Estimation )1

v

v

22

1k

kk

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ISVA vs SVA: modelling beadchip effects

in Illumina Infinium DNAm data

• ISVA outperforms SVA in

modelling beadchip effects

• Driven by sparse

(leptokurtic) sources.

Teschendorff A E et al.

Bioinformatics 2011;27:1496-1505

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Improved robustness of ISVA

DNAmSet3 SVA SVA* ISVA

aDMCs 201 163 225

nPCGTs 15 13 29

P-value 0.01 0.007 3e-7

DNAmSet1 SVA SVA* ISVA

aDMCs 688 688 902

nPCGTs 110 110 148

P-value 7e-26 7e-26 2e-34

DNAmSet2 SVA SVA* ISVA

aDMCs 4 8 232

nPCGTs 1 1 59

P-value 0.27 0.4 2e-19

DNAmSet4 SVA SVA* ISVA

aDMCs 185 479 469

nPCGTs 19 53 64

P-value 0.01 3e-11 8e-16

• Only ISVA captures

the age-PCGT DNAm

signature in all data

sets.

• Age-DNAm signatures:

Maegawa et al, Rakyan

et al, Teschendorff et al,

Genome Res. 2010.

Koch et al Aging 2011,

Bocklandt S et al PLoS

One 2011

Teschendorff A E et al.

Bioinformatics 2011;27:1496-1505

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Dimensionality estimation

“Diagnostic” SVD heatmap Dimensionality estimation can be

done using

Random Matrix Theory (RMT)

(Plerou et al Phys Rev E 2002)

RMT provides an analytical

framework in which to compare

observed properties of a data

matrix to universal properties of

random matrices.

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ISVA on 450k data (32 cancers)

“Diagnostic” SVD heatmap

ISV heatmap

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Conclusions (II)

• Confounders are often unknown or only approximations

to the real confounders are known therefore it is

better to model the confounders from the data itself.

• SVA may break down inspection of the surrogate

variable subspace subspace selection PCA/SVD

used in SVA not optimal.

• ISVA improves identifiabilty of confounders and

statistical inference (validated on 27k data), through use

of blind source separation algorithms.

• ISVA can be applied to 450k data (tested ~ 50k probes).