Robust and powerful sibpair test for rare variant association
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Transcript of Robust and powerful sibpair test for rare variant association
Robust and powerful
sibpair test for rare variant association
Sebastian ZöllnerUniversity of Michigan
Acknowledgements
Matthew Zawistowski
Keng-Han Lin
Mark Reppell
GWAS have been successful. Only some heritability is explained by common variants. Uncommon coding variants (maf 5%-0.5%) explain less. Rare variants could explain some ‘missing’ heritability.
◦ Better Risk prediction.◦ Rare variants may identify new genes.◦ Rare exonic variants may be easier to annotate functionally and
interpret.
Rare Variants –Why Do We Care?
Testing individual variants is unfeasible.◦Limited power due to small number of
observations.◦Multiple testing correction.
Alternative: Joint test.◦Burden test (CMAT, Collapsing, WSS)◦Dispersion test (SKAT, C-alpha)
Burden/Dispersion Tests
Gene-based tests have low power.◦ Nelson at al (2010) estimated that 10,000 cases &
10,000 controls are required for 80% power in half of the genes.
Large sample size required More heterogeneous sample =>Danger of
stratification Stratification may differ from common variants
in magnitude and pattern.
Challenges of Rare Variant Analysis
(202 genes, n=900/900, MAF < 1%,
Nonsense/nonsynonymous variants)
Stratification in European Populations
Variant Abundance across Populations
African-American
Southern AsiaSouth-Eastern Europe
Finland
South-Western Europe
Northern Europe
Central EuropeWestern Europe
Eastern EuropeNorth-Western Europe
A gradient in diversity from Southern to Northern Europe
Sample SizeExpe
cted
Num
ber o
f var
iant
s pe
r kb
Allele Sharing
Median EU-EU: 0.71 Median EU-EU: 0.86 Median EU-EU: 0.98
• Measure of rare variant diversity.• Probability of two carriers of the minor alleles being
from different populations (normalized).
1. Select 2 populations.2. Select mixing parameter
r.3. Sample 30 variants from
the 202 genes.4. Calculate inflation based
on observed frequency differences.
General Evaluation of Stratification
Inflation by Mixture Proportion
Zawistowski et al. 2014
Inflation across Comparisons
If multiple affected family members are collected, it may be more powerful to sequence all family members.
Family-based tests can be robust against stratification. TDT-Type tests are potentially inefficient. How to leverage low frequency?
◦ Low frequency risk variants should me more common in cases.◦ And even more common on chromosomes shared among
many cases.
Family-based Test against Stratification
• Consider affected sibpairs.• Estimate IBD sharing.• Compare the number of
rare variants on shared (solid) and non-shared chromosomes (blank).
Any aggregate test can be applied.
Family Test S=0
S=2
S=1
Twice as many non-shared as shared chromosomes.
Null hypothesis determines test:
Shared alleles : Non-shared alleles=1:2Test for linkage or association
Shared alleles : Non-shared alleles=Shared chromosomes : Non-shared chromosomes
Test for association only
Basic Properties
IBD sharing is known. Individuals don’t need phase to identify shared variants. Except one configuration: IBD 1 and both sibs are heterozygous
Under null, probability of configuration 2 is allele frequency. Under the alternative, we need to use multiple imputation.
Haplotypes not required
Configuration 1
+1 shared
Configuration 1
+2 non-shared
Assume chromosome sharing status is known for each sibpair.
Count rare variants; impute sharing status for double-heterozygotes.
Compare number of rare variants between shared and non-shared chromosomes with chi-squared test (Burden Style).
Evaluation of Internal Control
S=0
S=2
S=1
Classic Case-Control
Selected Cases
Enriching Based on Familial Risk
S=0
S=2
S=1
Internal Control
Consider 2 populations. p=0.01 in pop1, p=0.05 in pop2. 1000 sibpairs for internal control design. 1000 cases, 1000 controls for selected cases. 1000 cases and 1000 controls for case-control. Sample cases from pop1 with proportion . Test for association with α=0.05.
Stratification
Robust to Population Stratification
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.4
0.8
Proportion
Type
I E
rror
Rat
e
Internal ControlSelected CasesConventional
Realistic rare variant models are unknown◦ Typical allele frequency◦ Number of risk variants/gene◦ Typical effect size◦ Distribution of effect sizes◦ Identifiabillity of risk variants
Goal: Create a model that summarizes these unknowns into◦ Summed allele frequency◦ Mean effect size◦ Variance of effect size
Evaluating Study Designs
Assume many loci carrying risk variants. Risk alleles at multiple loci each increase
the risk by a factor independently. Frequency of risk variant:
◦ Independent cases
◦ On shared chromosome
Basic Genetic Model
)()|()|( RPRAAPAARP
A Affected AA Affected relative
pairR Risk locus
genotypeP(A|R)P(R)ARP )|(
Relative risk is sampled from distribution f with mean , variance σ2.
Simplifications: ◦ Each risk variant occurs only once
in the population.◦ Each risk variant on its own
haplotype. Then the risk in a random case
is
Effect Size Model
2121 )()(),|( 212121rrrr mfmfmmrrAP
A Affected r1,r2
Carrier status of chromosome 1,2
m1,m2
Relative risk of risk variants on 1,2
Mean effect sizeσ2 Variance of effect
size
To calculate the probability of having an affected sib-pair we condition on sharing S.
For S>0, the probability depends on σ2. E.g. (S=2):
Effect in Sib-pairsAA Affected rel pairri Carrier stat
chrom imi Relative risk of
variant on if Distribution of
RR Mean RRσ2 Variance of RRS Sharing status
2121 )()()( 2222 rrrr fEfE
)()(
)2,,|(
2122
21
21
21 mfmfmm
SrrAAPrr
Select μ, σ2 and cumulative frequency f Calculate allele frequency in
cases/controls P(R|A). Calculate allele frequency in shared/non-
shared chromosomes.=> Non-centrality parameter of χ2 distribution.
Analytic Power Analysis
Minor Allele Frequency
1 2 3 4 5
0.0
0.2
0.4
0.6
f=0.2f=0.01
sMA
F
1 2 3 4 5Mean Relative Risk
1 2 3 4 5
Conventional Case-Control Internal
ControlSelected Cases
Power Comparison by Mean Effect Size
1.0 2.5 4.0
0.0
0.4
0.8
Pow
er
f=0.01
1.0 2.5 4.0
sapp
ly(x
, fun
ctio
n(x)
pow
er.s
as(m
u =
x, s
igm
a2 =
sig
ma2
, f =
0.0
5,
n
_sb
= n1
))
f=0.05
Mean Relative Risk1.0 2.5 4.0
sapp
ly(x
, fun
ctio
n(x)
pow
er.s
as(m
u =
x, s
igm
a2 =
sig
ma2
, f =
0.2
,
n_s
b =
n1))
f=0.2
Internal ControlSelected CasesConventional
Power Comparison by Variance
0 1 2 3 4
0.0
0.4
0.8
Pow
er
f=0.01
0 1 2 3 4
sapp
ly(x
, fun
ctio
n(x)
pow
er.s
as(m
u =
mu,
sig
ma2
= x
, f =
0.0
5,
n
_sb
= n1
))
f=0.05
Variance of Relative Risk0 1 2 3 4
sapp
ly(x
, fun
ctio
n(x)
pow
er.s
as(m
u =
mu,
sig
ma2
= x
, f =
0.2
,
n_s
b =
n1))
f=0.2
Internal ControlSelected CasesConventional
Gene-gene interaction affects power in families. For broad range of interaction models, consider
two-locus model. G now has alleles g1,g2. The joint effect is
We compare the effect of while adjusting L and G to maintain marginal risk.
Gene-Gene Interaction
))((2121
21212121),,,|( ggrrggG
rrLggrrAP
Power for Antagonistic Interaction
0.2 0.4 0.6 0.8 1.0
0.0
0.4
0.8
Pow
er
Interaction Coefficient
IC SRR=2IC SRR=8Conventional
Power for Positive Interaction
1.0 1.2 1.4 1.6 1.8 2.0
0.0
0.4
0.8
Pow
er
Interaction Coefficient
IC SRR=2IC SRR=8Conventional
Stratification is a strong confounder for rare variant tests.
Family-based association methods are robust to stratification.
Comparing rare variants between shared and non-shared chromosomes is substantially more powerful than case-control designs.
All family based methods/samples depend on the model of gene-gene interaction. Under antagonistic interaction power can be lower than a population sample.
Conclusions
Questions?Thank you for your attention