1
Identifying Rare Variants with Bidirectional Effects on
Quantitative Traits
Qunyuan Zhang, Ingrid Borecki, Michael Province
Division of Statistical GenomicsWashington University School of Medicine
2
Quantitative Trait & Bidirectional Effects
Distribution of Quantitative Trait
Enriched with negative-effect
(-) variants
Enriched with positive-effect
(+) variants
Enriched with non-causal (.) variants
3
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
4
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
5
(+) (+) (.) (.)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
6
(+) (+) (.) (.) (-) (-)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
7
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
8
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
9
Q-Q Plots Under the Null
Inflation of type I error Corrected by permutation test(permutation of phenotype)
10
Sum Testi
m
iigws
1
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
11
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)
13
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
14
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
15
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