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Identifying Rare Variants with Bidirectional Effects on

Quantitative Traits

Qunyuan Zhang, Ingrid Borecki, Michael Province

Division of Statistical GenomicsWashington University School of Medicine

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Quantitative Trait & Bidirectional Effects

Distribution of Quantitative Trait

Enriched with negative-effect

(-) variants

Enriched with positive-effect

(+) variants

Enriched with non-causal (.) variants

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apo A-I Milanoapo A-I Marburgapo A-I Giessenapo A-I Munsterapo A-I Paris

High-density lipoprotein cholesterol (HDL)

Apolipoprotein A-I (apoA-I)(An example of gene with bidirectional variants)

-560 A -> C -151 C ->T 181 A -> G

.

Variants(+) with positive effects

Variants(-) with negative effects

Low HDL

High HDL

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When there are only causal(+) variants …

(+) (+)Subject V1 V2 Collapsed Trait

1 1 0 1 3.002 0 1 1 3.103 0 0 0 1.954 0 0 0 2.005 0 0 0 2.056 0 0 0 2.10

0 11.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Collapsed Genotype

Trai

t Collapsing (Li & Leal,2008)

works well, power increased

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(+) (+) (.) (.)Subject V1 V2 V3 V4 Collapsed Trait

1 1 0 0 0 1 3.002 0 1 0 0 1 3.103 0 0 0 0 0 1.954 0 0 0 0 0 2.005 0 0 0 0 0 2.056 0 0 0 0 0 2.107 0 0 1 0 1 2.008 0 0 0 1 1 2.10

0 11.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Collapsed Genotype

Trai

tWhen there are causal(+) and non-causal(.) variants …

Collapsing still works, power reduced

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(+) (+) (.) (.) (-) (-)Subject V1 V2 V3 V4 V5 V6 Collapsed Trait

1 1 0 0 0 0 0 1 3.002 0 1 0 0 0 0 1 3.103 0 0 0 0 0 0 0 1.954 0 0 0 0 0 0 0 2.005 0 0 0 0 0 0 0 2.056 0 0 0 0 0 0 0 2.107 0 0 1 0 0 0 1 2.008 0 0 0 1 0 0 1 2.109 0 0 0 0 1 0 1 0.95

10 0 0 0 0 0 1 1 1.00

0 10.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

Collapsed Genotype

Trai

tWhen there are causal(+) non-causal(.) and causal (-) variants …

Power of collapsing test significantly down

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P-value Weighted Sum (pSum) Test(+) (+) (.) (.) (-) (-)

Subject V1 V2 V3 V4 V5 V6 Collapsed pSum Trait1 1 0 0 0 0 0 1 0.86 3.002 0 1 0 0 0 0 1 0.90 3.103 0 0 0 0 0 0 0 0.00 1.954 0 0 0 0 0 0 0 0.00 2.005 0 0 0 0 0 0 0 0.00 2.056 0 0 0 0 0 0 0 0.00 2.107 0 0 1 0 0 0 1 -0.02 2.008 0 0 0 1 0 0 1 0.08 2.109 0 0 0 0 1 0 1 -0.90 0.95

10 0 0 0 0 0 1 1 -0.88 1.00t 1.61 1.84 -0.04 0.11 -1.84 -1.72

p(x≤t) 0.93 0.95 0.49 0.54 0.05 0.062*(p-0.5) 0.86 0.90 -0.02 0.08 -0.90 -0.88

Rescaled left-tail p-value [-1,1] is used as weight

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P-value Weighted Sum (pSum) Test

-1.000 -0.800 -0.600 -0.400 -0.200 0.000 0.200 0.400 0.600 0.800 1.0000.8

1.2

1.6

2.0

2.4

2.8

3.2

pSum

Trai

t

Power of collapsing test is retained

even there are bidirectional variants

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Q-Q Plots Under the Null

Inflation of type I error Corrected by permutation test(permutation of phenotype)

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Sum Testi

m

iigws

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Collapsing test (Li & Leal, 2008)wi =1 and s=1 if s>1

Weighted-sum test (Madsen & Browning ,2009)wi calculated based-on allele freq. in control group

aSum: Adaptive sum test (Han & Pan ,2010)wi = -1 if b<0 and p<0.1, otherwise wj=1

pSum: p-value weighted sum testwi = rescaled left tail p valueincorporating both significance and directions

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random sampling two-tail sampling two-tail plus central sampling

Simulation Allele frequency: 0.002 Variant numbers: n(+), n(-), n(.) Additive effect: 0.5 or -0.5 SD Total N: 2000 Sample size: 300 Three designs (below)

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Collapsing test (Li & Leal)

pSum test

aSum test (Han & Pan)

n(+)=10, n(-)=10, n(.)=10

n(+)=10, n(-)=0, n(.)=10

n(+)=0, n(-)=10, n(.)=10n(+)=10, n(-)=10, n(.)=10

n(+)=0, n(-)=10, n(.)=10n(+)=10, n(-)=10, n(.)=10

n(+)=10, n(-)=0, n(.)=20

n(+)=0, n(-)=10, n(.)=20n(+)=10, n(-)=10, n(.)=10

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n(+)=10, n(-)=0, n(.)=10

n(+)=0, n(-)=10, n(.)=10

Collapsing test (Li & Leal)

pSum

aSum test (Han & Pan)

n(+)=10, n(-)=10, n(.)=10n(+)=10, n(-)=10, n(.)=10n(+)=0, n(-)=10, n(.)=10

n(+)=10, n(-)=10, n(.)=10

n(+)=10, n(-)=0, n(.)=20

n(+)=0, n(-)=10, n(.)=20n(+)=10, n(-)=10, n(.)=10

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n(+)=10, n(-)=0, n(.)=10

n(+)=0, n(-)=10, n(.)=10

Collapsing test (Li & Leal)pSum testaSum test (Han & Pan)Weighted-sum test (Madsen & Browning)

n(+)=10, n(-)=10, n(.)=10