Estimation of quantitative genetic parameters from distant ... 8 L4 P… · Estimation of...

Estimationofquantitativegeneticparametersfromdistant

relativesusingmarkerdata

PeterM.Visscherpeter.visscher@uq.edu.au

1

Keyconcepts• DenseSNPpanelsallowtheestimationoftheexpected

geneticcovariancebetweendistantrelatives(‘unrelateds’)• AmodelbaseduponestimatedrelationshipsfromSNPsis

equivalenttoamodelfittingallSNPssimultaneously• ThetotalgeneticvarianceduetoLDbetweencommonSNPs

and(unknown)causalvariantscanbeestimated• GeneticvariancecapturedbycommonSNPscanbeassigned

tochromosomesandchromosomesegments

2

1886

3

4

100yearslaterHeritabilityofhumanheight

h2 ~ 80%5

6

Disease Number of loci

Percent of Heritability Measure Explained

Heritability Measure

Age-related macular degeneration

5 50% Sibling recurrence risk

Crohn’s disease 32 20% Genetic risk (liability)

Systemic lupus erythematosus

6 15% Sibling recurrence risk

Type 2 diabetes 18 6% Sibling recurrence risk

HDL cholesterol 7 5.2% Phenotypic variance

Height 40 5% Phenotypic variance

Early onset myocardial infarction

9 2.8% Phenotypic variance

Fasting glucose 4 1.5% Phenotypic variance

WhereistheDarkMatter?

7

Hypothesistestingvs.Estimation

• GWAS=hypothesistesting– Stringentp-valuethreshold– Estimatesofeffectsbiased(“Winner’sCurse”)

• E(bhat|test(bhat)>T)>b{bfixed}• var(bhat)=var(b)+var(bhat|b){brandom}

• CanweestimatethetotalproportionofvariationaccountedforbyallSNPs?

8

Basicidea• Estimatesofadditivegeneticvariancefromknownpedigreeisunbiased– Ifmodeliscorrect– Despitevariationinidentitygiventhepedigree– PedigreegivescorrectexpectedIBD

• Unknownpedigree:estimategenome-wideIBDfrommarkerdata– Estimateadditivegeneticvariancegiventhisestimateofrelatedness

• Ideaisnotnew– (Evolutionary)geneticsliterature(Ritland,Lynch,Hill,others)

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Closevsdistantrelatives

• Detectionofcloserelatives(fullsibs,parent-offspring,halfsibs)frommarkerdataisrelativelystraightforward

• Butcloserelativesmayshareenvironmentalfactors– Biasedestimatesofgeneticvariance

• Solution:useonly(very)distantrelatives

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AmodelforasinglecausalvariantAA AB BB

frequency (1-p)2 2p(1-p) p2

x 0 1 2effect 0 b 2bz=[x-E(x)]/sx -2p/√{2p(1-p)} (1-p)/√{2p(1-p)} 2(1-p)/√{2p(1-p)}

yj = µ’ +xijbi +ej x=0,1,2{standardassociationmodel}

yj = µ +zijuj +ej u=bsx;µ =µ’+bsx

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Multiple(m)causalvariants

yj = µ +Szijuj +ej

= µ +gj +ej

y = µ1 +g +e

= µ1 +Zu +e

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Equivalence

Letubearandomvariable,u~N(0,su2)

Thensg2 =msu

2 and

var(y) =ZZ’su2 +Ise

2

=ZZ’(sg2/m)+Ise

2

=Gsg2 +Ise

2

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Model with individual genome-wide additive values using relationships (G) at the causal variants is equivalent to a model fitting all causal variants

We can estimate genetic variance just as if we would do using pedigree relationships

Butwedon’thavethecausalvariantsIfweestimateG fromSNPs:

– loseinformationduetoimperfectLDbetweenSNPsandcausalvariants

– howmuchwelosedependson• densityofSNPs• allelefrequencyspectrumofSNPsvs.causalvariants

– estimateofvarianceàmissingheritability

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LetA betheestimateofG fromNSNPs:

Ajk =(1/N)S {xij – 2pi)(xik – 2pi)/{2pi(1-pi)}

=(1/N)S zijzik

Data• ~4000 ‘unrelated’ individuals• Ancestry ~British Isles• Measurement on height (self-report or clinically measured)• GWAS on 300k (‘adults’) or 600k (16-year olds) SNPs

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Lack of evidence for population stratification within the Australian sample

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Methods• Estimate realised relationship matrix from

SNPs• Estimate additive genetic variance

22)var( eg ss IAVy +==

)1(2),cov(

)var()var(),cov(

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iikiij

iikiijijk pp

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axaxA

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Base population = current population

ïïî

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22

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Statistical analysis

22)var( eg ss IAVy +==

y standardised ~N(0,1)

No fixed effects other than mean

A estimated from SNPs

Residual maximum likelihood (REML)

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h2 ~ 0.5 (SE 0.1)

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Partitioning variation• If we can estimate the variance captured by

SNPs genome-wide, we should be able to partition it and attribute variance to regions of the genome

• “Population based linkage analysis”

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Genome partitioning

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• Partition additive genetic variance according to groups of SNPs– Chromosomes– Chromosome segments– MAF bins– Genic vs non-genic regions– Etc.

• Estimate genetic relationship matrix from SNP groups

• Analyse phenotypes by fitting multiple relationship matrices

• Linear model & REML (restricted maximum likelihood)

Application: the GENEVA Consortium• Data

– ~14,000 European Americans• ARIC• NHS• HPFS

– Affy 6.0 genotype data• ~600,000 after stringent QC

– Phenotypes on height, BMI, vWF and QT Interval

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QC of SNPs

• 780,062 SNPs after QC steps listed in the table.

• Exclude 141,772 SNPs with MAF < 0.02 in European-ancestry group.

• Exclude 36,949 SNPs with missingness > 2% in all samples.

• Include autosomal SNPs only.

• End up with 577,778 SNPs.23

Results (genome-wide)

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1

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789

101112

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1819

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0

0.01

0.02

0.03

0.04

0.05

0 50 100 150 200 250

Varia

nceexplainedbyeachchromosom

e

Chromosomelength(Mb)

Slope=1.6×10-4

P =1.4×10-6

R2 =0.695

Height(combined)

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2122

0

0.005

0.01

0.015

0.02

0.025

0 50 100 150 200 250

Varia

nceexplainedbyeachchromosom

eChromosomelength(Mb)

Slope=2.3×10-5

P =0.214R2 =0.076

BMI(combined)

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Genome-partitioning: longer chromosomes explain more variation

1

234

5

6

7

8

9

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13 14

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1819

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21 22

R²=0.511

0.000

0.002

0.004

0.006

0.008

0.010

0.00 0.01 0.02 0.03 0.04 0.05

Varia

nceexplainedbyGIANTheightSNPson

eachch

romosom

e

Varianceexplainedbyeachchromosome

Height (11,586 unrelated)

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2

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5

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1516

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2122

0.000

0.004

0.008

0.012

0.016

0.020

0.000 0.004 0.008 0.012 0.016 0.020

Varia

nceexplainedbychrom

osom

e(adjustedfortheFTO

SNP)

Varianceexplainedbychromosome(noadjustment)

BMI(11,586unrelated)

FTO

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Results are consistent with reported GWAS

1

234

5

6

78

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1011

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151617

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192021220.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 50 100 150 200 250

Varia

nceexplainedbyeachchromosom

e

Chromosomelength(Mb)

Slope=6.9×10-5

P =0.524R2 =0.021

vWF(ARIC)

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Inference robust with respect to genetic architecture

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1011

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151617

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192021

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0.00

0.03

0.06

0.09

0.12

0.15

0.00 0.03 0.06 0.09 0.12 0.15

Varia

nceexplainedbychrom

osom

e(adjustedfortheABO

SNP)

Varianceexplainedbychromosome(noadjustment)

vWF(6,662unrelated)

ABO

0

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Varia

nceexplained

Chromosome

intergenic(± 20Kb)

genic(± 20Kb)

Height(combined)17,277proteincoding geneshGg

2 =0.328(s.e.=0.024)hGi

2 =0.126(s.e.=0.022)Coverageofgenicregions=49.4%P(observedvs.expected)=2.1x10-10

0

0.005

0.01

0.015

0.02

0.025

0.03

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Varia

nceexplained

Chromosome

intergenic(± 20Kb)

genic(± 20Kb)

BMI(combined)17,277proteincoding geneshGg

2 =0.117(s.e.=0.023)hGi

2 =0.047(s.e.=0.022)Coverageofgenicregions=49.4%P(observedvs.expected)=0.022

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Genic regions explain variation disproportionately

Using imputed sequence data

• How much information is gained by using SNP array data imputed to a fully sequenced reference?

• How much is lost relative to whole genome sequencing?

29Yang et al. 2015 (Nature Genetics)

Accounting for LD and MAF spectrum allows unbiased estimation of genetic variance (GREML-LDMS)

30

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Very little difference in “taggability” between SNP chips

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Genetic variation captured after imputation96% due to common variants73% due to rare variants

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n = 45k data on height and BMI

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Totals~60% for height~30% for BMI

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SlidebyRobertMaier 33

h2 overestimation?untaggedrarevariants?

better tagging of ungenotyped variants

samplesize/power

Partitioning variance of height

TotalvarianceHeritability (based on Twin or family studies)SNP heritability from imputation to sequenced referenceSNP-heritability (variance explained by all genotyped SNPs ontheChip)VarianceexplainedbygenomewidesignificantSNPs

missingheritability60%

Scaling revisitedu = bsx ~ N(0, su

2) implies

b2 proportional to su2/[2p(1-p)], so rare variants have larger allelic effect: natural

selection

If b2 = su2 then no relationship between frequency and effect size: neutral

model

In between: b2 = su2 [2p(1-p)]-s

Variance explained by SNP: 2p(1-p)su2[2p(1-p)]-s

= su2 [2p(1-p)]1-s

s = 0: common SNPs explain more variations = 1: all SNPs explain the same amount of variation

34

Multiple methods to estimate additive genetic variance

• Individual-level data– GREML– Haseman-Elston regression(yjyj) = µ + bAij

• Summary dataLDscore regression

• Consideration:– data availability– model assumptions– computation

35

Key concepts• Dense SNP panels allow the estimation of the expected

genetic covariance between distant relatives (‘unrelateds’)

• A model based upon estimated relationships from SNPs is equivalent to a model fitting all SNPs simultaneously

• The total genetic variance due to LD between common SNPs and (unknown) causal variants can be estimated

• Genetic variance captured by common SNPs can be assigned to chromosomes and chromosome segments

36