### Hardy-Weinberg Equilibrium, Imputation, Meta-Analysis

Objectives
• Cover some of the essential concepts for GWAS that
have not yet been covered
• Hardy-Weinberg equilibrium
• Meta-analysis
• SNP Imputation
• Review what we have learned about the genetics of
common disease from GWAS
• Where do we go from here? What do we go with GWAS
results.
• functional characterization of GWAS loci
• clinical applications
Hardy-Weinberg Law

In a large, randomly mating population, genotypes at a given
locus will be in Hardy Weinberg Equilibrium (HWE)
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Aa : alleles at a single locus;
p = relative frequency of A;
q = relative frequency of a;
p+q=1
Under random mating
Genotype
AA
Aa
aa
Probability
PAA= p2
PAa = 2 p q
Paa = q2
HWE and genotyping

HWE provides useful check for genotyping
errors


For a rare disease (or no/modest genetic effects),
genotype frequencies in controls should (nearly)
HWE test:

Chi-square test (χ2)



H0: HWE
Ha: no HWE
Compare observed frequency for a class with
that expected if the null hypothesis were true
Genotype
AA
Aa
aa
Number obs.
36
47
23
106
Frequency exp.
p2
2pq
q2
1
33.4
52.2
20.4
106
2.6
-5.2
2.6
0.20
0.52
0.33
Number exp.
Deviation
χ2
Total
χ2 = 1.05 d.f. =1; P≥0.05
Fail to reject H0: HWE holds
1.05
Meta-Analysis
• Most current GWAS studies actually combine the
results of multiple distinct cohorts
• mega-analysis versus meta-analysis
• How does meta-analysis work?
combine the association results
ORs/Betas and standard errors
fixed effects – assume one true effect for SNP
random effects – account for a range of possible true
effects
• heterogeneity – Cochrane’s Q or I-squared
•
•
•
•
Meta-Analysis Results are
Displayed as Forest Plots
Castaldi et al, Human Molecular Genetics 2010
Imputation – Using LD and Hapmap/1000
Genomes to Impute Untyped SNPs
• Most current GWAS studies take their genotyped SNPs
and then impute SNPs from the HapMap project or the
1,000 Genomes project (~8 million SNP).
• This is very computationally intensive
• Mach
• Beagle
• Basic principle is to use a densely genotyped reference
panel, compare it to your study sample, and infer untyped
SNPs.
• Imputation allows for combining studies that used
different genotype chips
Imputation Works by Inferring Haplotypes
and Comparing to a Reference
Marchini et al, Nature Reviews Genetics 2011
Using Principal Components Analysis
(PCA)as a Surrogate for Genetic Ancestry
• DNA contains a tremendous amount of information