Robust and powerful - PowerPoint Presentation

Slide1

Robust and powerful sibpair test for rare variant association

Sebastian Zöllner

University of MichiganSlide2

Acknowledgements

Matthew

Zawistowski

Keng

-Han Lin

Mark

ReppellSlide3

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?Slide4

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 TestsSlide5

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 stratificationStratification may differ from common variants in magnitude and pattern.Challenges of Rare Variant AnalysisSlide6

(202 genes, n=900/900

,

MAF < 1%, Nonsense/nonsynonymous variants)

Stratification in European PopulationsSlide7

Variant Abundance across Populations

African-American

Southern Asia

South-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 Size

Expected Number of variants per kbSlide8

Allele Sharing

Median EU-EU: 0.71

Median EU-EU: 0.86Median EU-EU: 0.98

Measure of rare variant diversity.

Probability of two carriers of the minor alleles being from different populations (normalized).Slide9

Select 2 populations.

Select mixing parameter r.

Sample 30 variants from the 202 genes.Calculate inflation based on observed frequency differences.General Evaluation of StratificationSlide10

Inflation by Mixture Proportion

Zawistowski et al. 2014Slide11

Inflation across ComparisonsSlide12

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 StratificationSlide13

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=1Slide14

Twice as many non-shared as shared chromosomes.Null hypothesis determines test:Shared alleles : Non-shared alleles=1:2

Test for linkage or associationShared alleles : Non-shared alleles=Shared chromosomes : Non-shared chromosomes Test for association onlyBasic PropertiesSlide15

IBD sharing is known.Individuals

don’t need phase

to identify shared variants.Except one configuration: IBD 1 and both sibs are heterozygousUnder 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-sharedSlide16

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=1Slide17

Classic Case-Control

Selected Cases

Enriching Based on Familial Risk

S=0

S=2

S=1

Internal ControlSlide18

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.

StratificationSlide19

Robust to Population StratificationSlide20

Realistic rare variant models are unknownTypical allele frequencyNumber of risk variants/gene

Typical effect

sizeDistribution of effect sizesIdentifiabillity of risk variantsGoal: Create a model that summarizes these unknowns intoSummed allele frequencyMean effect sizeVariance of effect sizeEvaluating Study DesignsSlide21

Assume many loci carrying risk variants.

Risk alleles at multiple loci each increase the risk by a factor independently.

Frequency of risk variant: Independent casesOn shared chromosome

Basic Genetic Model

A

Affected

AA

Affected relative pairRRisk locus genotypeSlide22

Relative risk is sampled from distribution f with mean , variance

σ

2.Simplifications: Each risk variant occurs only once in the population.Each risk variant on its own haplotype.Then the risk in a random case isEffect Size Model

A

Affected

r

1

,r

2

Carrier status of chromosome 1,2

m1,m2Relative risk of risk variants on 1,2Mean effect sizeσ

2Variance of effect sizeSlide23

To calculate the probability of having an affected sib-pair we condition on sharing S.For S>0, the probability depends on

σ

2. E.g. (S=2):Effect in Sib-pairs

AA

Affected

rel

pair

riCarrier stat chrom i

miRelative risk of variant on ifDistribution of RR

Mean RRσ2Variance of RRS

Sharing statusSlide24

Select μ, σ

2

and cumulative frequency fCalculate allele frequency in cases/controls P(R|A).Calculate allele frequency in shared/non-shared chromosomes. => Non-centrality parameter of χ2 distribution. Analytic Power AnalysisSlide25

Minor Allele Frequency

Conventional Case-Control

Internal ControlSelected CasesSlide26

Power Comparison by Mean Effect SizeSlide27

Power Comparison by VarianceSlide28

Gene-gene interaction affects power in families.For broad range of interaction models, consider two-locus model.

G now has alleles g

1,g2. The joint effect isWe compare the effect of  while adjusting L and G to maintain marginal risk.

Gene-Gene InteractionSlide29

Power for Antagonistic InteractionSlide30

Power for Positive InteractionSlide31

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.ConclusionsSlide32

Questions?Thank you for your attention