24/07/2007ISMB/ECCB 2007 24/07/2007ISMB/ECCB 2007

Bayesian association of haplotypes and non-genetic factors to

regulatory and phenotypic variation in human populations

Anitha Kannan and John Winn

Jim Huang*

Probabilistic and Statistical Inference Group, Edward S. Rogers Department of Electrical and Computer Engineering University of Toronto Toronto, ON, Canada

Microsoft Research Cambridge Machine Learning and Perception Group Cambridge, UK

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Outline

• Main contributions:

• Joint Bayesian modelling of genetic variation data and quantitative trait measurements

• Rich probabilistic model for genotype data• State-of-the-art results on predicting missing

genotypes

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OutlineGenotype: Unordered pair of SNPs along both chromosomes

Haplotype: Ordered set of SNPs along a chromosome

Presence of recombination hotspots partitions haplotypes into blocks [Daly, 2001]

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Part I: Learning haplotype block structure

• Our model for genotype data should:– Account for phase & parent-child information– Account for uncertainty in ancestral

haplotypes– Account for uncertainty in block structure– Account for population-specific haplotype

block statistics– Allow for prior knowledge of haplotype block

structure

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Previous models for genotype data

• Previous methods learn a low-dimensional representation of the genotype data:

• HAPLOBLOCK (Greenspan, G. and Geiger, D. RECOMB 2003)– Hard partitioning of data into set of haplotype blocks using low-

dimensional “ancestral” haplotypes

• fastPHASE (Scheet P. and Stephens, M. Am J Hum Genet 2006)– Learn ancestral haplotypes from high-dimensional genotype data

while accounting for uncertainty in haplotype blocks

• Jojic, N., Jojic, V. and Heckerman, D. UAI 2004.

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Low-dimensional latent representation

Probabilistic generative model for genotype data

High-dimensional data

Unsupervised learning via maximum likelihood

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Predicting missing genotype data

• Have we learned a good density model for genotype data?

• Gains from– Accounting for uncertainty in haplotype block structure– Accounting for uncertainty in ancestral haplotypes– Accounting for parental relationships

• Assess model using cross-validation/test prediction error

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Predicting missing genotype data

• Crohn’s/5q31 data set (Daly et al., 2001)– Crohn’s disease data from Chromosome 5q31 containing

genotypes for 129 children + 258 parents across 103 loci (phases given for children)

• For each test set, make ρ fraction of data missing• Retain model parameters from model learned from training

data, then draw 1000 samples over missing data• Compute fill-in error rate over 1000 samples, for all

missing data

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Prediction error for Crohn’s/5q31 data

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Comparative performance for Crohn’s/5q31 data

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Establishing haplotype block boundaries

• Define the recombination prior γ on transition probabilities– Different γ correspond to different “blockiness” of data

• For each locus k, can compute the probability of transition pk

– Can establish a threshold t and establish block boundaries

• Once blocks are defined, can assign block labels lb = (m,n)

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Haplotype block structure in the ENm006 region

• 573 SNP markers for 270 individuals from 3 sub-populations:– 90 Yoruba individuals (30 parent-parent-offspring trios) from Ibadan,

Nigeria (YRI);– 90 individuals (30 trios) of European descent from Utah (CEU)– 45 Han Chinese individuals from Beijing (CHB+JPT)/45 Japanese

individuals from Tokyo (JPT)

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Part II: Linking haplotype block structure and gene expression data

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A model for linking haplotype structure to quantitative trait measurements

Observed quantitative trait profile

+

x 1.0

x 0.0

Relevance variable

=

Latent block profile

Haplotype block 2

Individual 1

Individual 2

Individual 3

Individual 4

Individual 5

Individual 1

Individual 2

Individual 3

Individual 4

Individual 5

Haplotype block 1

Label 1

Label 2

Label 3

Label 4

x

x

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Sbj

zgj

μbg

wbg

ρg

individuals j = 1,…,J

blocks b = 1,…,B

quantitative traits g = 1,…,G

ºº

α0,β0

τ0,μ0

Noise precision

Latent block profile

Relevance variable

Observed trait

Block label

π0

A Bayesian model for linking haplotype structure to quantitative

measurements

Tbj

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Linking haplotype blocks to phenotype• 387 individuals with Crohn’s (+1) or non-Crohn’s (-1) phenotype;• Link 10 haplotype blocks from 5q31 to phenotype• Average cross-validation error: 23.1% + 3.45%

Haplotype blocks 2 and 10 most relevant to Crohn’s phenotype (p < 4.76 x 10-5)

Test cases (sorted)

Test data splits

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Linking haplotype blocks to gene expression• ENm006 data set:

• 19 haplotype blocks (573 SNPs)• 28 gene expression profiles in ENm006 region

(Stranger et al., 2007)

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Addressing population stratification

…whereas variation between individuals is the effect we’re interested in

The population variable affects phenotype/gene expression…

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Associations between haplotype blocks and gene expression

GDI1 - HapBlock2 (YRI) GDI1 - HapBlock5 (CHB+JPT)

p < 2.5 x 10-4 p < 3.33 x 10-4

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Summary

• Enhanced version of Jojic et al. (UAI 2004) model for haplotype inference/ discovering block structure

• Novel Bayesian model for associating haplotype blocks to gene expression

• We re-discover population-specific block structures across populations in the HapMap data

• Predictions for Crohn’s disease from Chromosome 5q31 data• Cis- associations between blocks and gene expression in

ENm006 in presence of non-genetic factors

• Cis- association between HapBlocks 2 and 5 and GDI1

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The road ahead…

• Applying to larger portions of the HapMap data• Finding trans- associations• Non-linear models for associating block structure to

quantitative traits• Joint learning of haplotype block structure and

associations• Accounting for patterns of gene

co-expression/similar phenotypes

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Acknowledgements

• Manolis Dermitzakis and Richard Durbin, Wellcome Trust Sanger Institute

• Nebojsa Jojic, Microsoft Research Redmond

• Paul Scheet, University of Michigan - Ann Arbor

• US National Science Foundation (NSF)