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Associating Genomic Variations with

Phenotypes

Model comparison, rare variants, and analysis pipeline

Qunyuan Zhang

Division of Statistical Genomics & Genome Institute

Washington University School of Medicine

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Data & Question

Relationshipbetween X and Y ?

nmnnn

m

m

xxxyn

xxxy

xxxy

XYi

..

.....................

...2

...1

21

222212

112111

Genotypes:SNP

InsertionDeletion

DuplicationInversion

Translocation…

Phenotypes(quantitative,categorical)

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Linkage & Association

Association: (Y,X)

Linkage: (Y,Q)Q is unobservable

...

.....................

...2

...1

221

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1212111

nnnn xqxyn

xqxy

xqxy

XYi Genotypes

Phenotype

Putative QTL

r1 Q r2

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A Fixed-effect Mixture Model For LinkageCommonly used in plant genetics

r1 Q r2

P1 X P2

F1

F2

3

1

),|()(j

iji rXQPyf

2)(

2

1exp

2

1

j

jiy

j

n

iiyfYL

1

)()(

SNP A SNP B

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A Variance-component Model For Linkage

Commonly used in human genetics

r1 Q r2

)()(

2

1exp

||)2(

1)( 1

2/12/

YYYL T

nV

V

222)( eggQQYCov IΔΔV

Background IBD matrix

QTL IBD matrix

Diagonal unit matrix

QΔ

SNP A SNP B

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Variance-component Model = Random-effect Linear Model

222eggQQ IΔΔV

eγZγZμ ggQQY

),0( 2QQMVN Δ ),0( 2

ggMVN Δ ),0( 2eN

)()(

2

1exp

||)2(

1)( 1

2/12/

YYYL T

nV

V

Random effects

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From Linkage to Association

22egg IΔV

eγZγZμ ggQQY

)()(

2

1exp

||)2(

1)( 1

2/12/

XYXYYL T

nV

V

eγZXβμ ggY

marker effect(s)

Family-based association model

Linkage model

QTL effect(s)

fixed effect(s)

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A Simple Association ModelFor Unrelated Subjects

2eIV

)()(

2

1exp

||)2(

1)( 1

2/12/

XYXYYL T

nV

V

eXβμ Y

n

i e

i Xy

e1

2)(2

1exp

2

1

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Covariate(s): Adjusting For Confounder(s)

eβXXβμ CCY

Observed confounders: age, sex etc.Hidden confounders: population structure

Population structure can be estimated by:-PCA-Clustering-Admixture/ancestry

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Modeling Hidden Genetic CorrelationBetween Subjects

22egg IΔV

eγZβXXβμ ggCCY

marker fixed effect(s)

Family data, pedigree => IBD matrixPopulation data, hidden, marker data => IBS matrix

covariate fixed effect(s)

Genetic background random effects

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Modeling Rare Variants

eγZβXXβμ ggCCY

...11 XY μ

......2211 kkXXXY μ

Common variants, tested individually, H0: β1=0. One p-value per variant

Rare variants, tested as an entire group (burden test), usually by geneH0: β1= β2=…=βk=0 . One p-value per group of variants

Incorporated with variable selection, with loose criteria

β can be treated as random effects, variance components test, can be weighted by prior information

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Collapsing Model

......2211 kkXXXY μ

... XY μ

1

1

0

0013

1102

0001321 XXXXsubject

Collapsing multiple variables into one

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Weighted Sum Model

......2211 kkXXXY μ

...)(1

k

jjjXwY μ

2.0

8.0

0.0

0013

1102

00013.05.02.0 1

3

1

2

1

1 S

w

X

w

X

w

Xsubject

Weighted sum score

... SY μ

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Weighting Variants

Base on allele frequency, continuous or binary(0,1) weight, variable threshold;

Based on function annotation/prediction;Based on sequencing quality (coverage, mapping quality,

genotyping quality, validated or not etc.);Data-driven, using both genotype and phenotype data,

learning weights (including effect directions) from data, requiring permutation test;

Any combination …

Grouping VariantsBy gene By transcript By exonBy gene set / pathway By protein domain……

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Modeling More Data TypesGeneralized Linear (Mixed) Model

eXβμ ...)(Yg

Link function

For binary Y, logistic model

)0(1

)1(log)(log)(

YP

YPYitYg

1)...exp(

)...exp()1(

eXβμ

eXβμYP

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Longitudinal Data (quantitative)

Fixed effect, time as covariate

Repeated measures, random effect, correlation within subjects

Time

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Longitudinal Data (binary)

Linear model, time as covariate

Survival analysis, CoxPH model etc.

Time

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Tools

SAS ProceduresREG, LOGISTIC, GENMOD, MIXED, HPMIXED, GLIMMIX, PHREG/LIFETEST

R Functions/Packageslm (), glm()gee, nlme, kinship2/coxme, lme4, survival

Other ProgramsSOLAR, MMAP, EMMA, EMMAX, SKAT

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Pipeline

job1 job2 …..Job N

Input (data + options)

Options.jobi => self-programmed modules (SAS, R,…)

Options.jobi => external program modules (MMAP, SKAT,..)

Result 1

Result 2

….. Result N

Job generating/submitting module

Job number controlling module

Job status monitoring module (all done ?)

Yes

Result summarizing module

no

Wait …

LSF bsub

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gwas.sh options.gwa

#!/bin/shOPFILE=$1...…

[DATA]database=SASgenotype_dir=/dsg1/gwas/fhsgenogenotype_file=

phenotype_file=fhs100markerinfo_file=mapallmarker_selection=MAF>0.01pedigree_file=pediallsubjectID=subjectpedgreeID=famidmarkername=snp…[ANALYSIS]phenolist_file=pheno_list=bmi/qtcovariates=program=SASGLManalysis=mixed[OUTPUT]output_dir=/dsguser/qunyuan/fhs/bmioutput_file=output_replace=no[RUN]clusterjobname=bmimixedmemsize=1000Mmaxjobn=300…

Pheno type covar program analysis runBmi qt age,sex SASGLM mixed YESObes ql NA SASGLM gee YESHD ql age SASGLM gee NOAge …Sex ……

Program language location Maintainer SASGLM SAS /dsg1/code/sas/glm.sas Q.ZhangGSTAT R /dsg1/code/R/gstat.R Q.ZhangMMAP C /dsg1/code/sas/mmap.sh J. Czajkowski…

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Thanks !