Generalized Linear Mixed Model (GLMM) & Weighted Sum Test (WST) Detecting Association between Rare Variants and Complex Traits Qunyuan Zhang, Ingrid Borecki, Michael A. Province Division of Statistical Genomics Washington University School of Medicine St. Louis, Missouri, USA 1
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Generalized Linear Mixed Model (GLMM) & Weighted Sum Test (WST) Detecting Association between Rare Variants and Complex Traits Qunyuan Zhang, Ingrid Borecki,
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Generalized Linear Mixed Model (GLMM)& Weighted Sum Test (WST)
Detecting Association between Rare Variants and Complex Traits
Qunyuan Zhang, Ingrid Borecki, Michael A. Province
Division of Statistical Genomics
Washington University School of Medicine
St. Louis, Missouri, USA
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Collapsing/Collective Testing Methods
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CAST (Morgenthaler and Thilly, 2006)
CMC (Li and Leal, 2008)
WSS (Madsen and Browning, 2009)
VT (Price et al, 2010)
aSum (Han and Pan, 2010)
KBAC (Liu and Leal, 2010)
C-alpha (Neale et al, 2011)
RBT (Ionita-Laza et al, 2011)
PWST (Zhang et al, 2011)
SKAT( Wu et al, 2011)…
GLMM & WST
Y : quantitative trait or logit(binary trait)α : interceptβ : regression coefficient of weighted sum m : number of RVs to be collapsed wi : weight of variant igi : genotype (recoded) of variant iΣwigi : weighted sum (WS)X: covariate(s), such as population structure variable(s)τ : fixed effect(s) of XZ: design matrix corresponding to γγ : random polygene effects for individual subjects, ~N(0, G), G=2σ2K, K is the kinship matrix and σ2 the additive ploygene genetic variance ε : residual
ZXgwY i
m
ii
1
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Some special instances:
Mgenthaler and Thilly’s CAST, wi =1 for all RVs;
Li and Leal’s CMC, wi =1 for all RVs, limiting the sum ≤1;
Madsen and Browning’s WSS, wi based on allele frequency in controls;
Han and Pan’s aSum test, wi = 1 or -1, according to the direction of regression coefficient and a cutoff of p-value;
Zhang et al’s PWST, wi defined as a rescaled left-tailed p-value
Weighted Sum
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i
m
ii gw
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Base on allele frequency, continuous or binary(0,1) weight, variable threshold;
Based on function annotation/prediction;
Based on sequencing quality (coverage, mapping quality, genotyping quality etc.);
Data-driven, using both genotype and phenotype data, learning weight from data, permutation test;
Any combination …
More Weighting Methods
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Using re-scaled left-tailed p-value as weight to incorporate directionality of effects into a test, P-value Weighted Sum Test (PWST, Zhang et al, 2011, Genetic Epidemiology).