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Kinship adjusted armitage trend test for ENDGAME meeting 2008
 

Kinship adjusted armitage trend test for ENDGAME meeting 2008

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    Kinship adjusted armitage trend test for ENDGAME meeting 2008 Kinship adjusted armitage trend test for ENDGAME meeting 2008 Presentation Transcript

    • Modifying the Cochran-Armitage trend test to address population Modifying the structure in GWAS Gary K. Chen Department ofCochran-Armitage trend test to Preventive Medicine USCaddress population structure in 1. Background 2. Proposed GWAS Method 3. Simulations Gary K. Chen Department of Preventive Medicine USC August 25, 2008
    • Modifying theOutline Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC1. Background 1. Background 2. Proposed Method 3. Simulations2. Proposed Method3. Simulations
    • Modifying theGenome wide association studies of Cochran-Armitage trend test to address populationcases and controls structure in GWAS Gary K. Chen Department of Interested in differences between cases and Preventive Medicine controls USC Estimate the correlation between predictors 1. Background 2. Proposed (e.g. genotypes) and outcomes (disease Method status) 3. Simulations Common methods: logistic regression, Pearson’s χ2 , Cochran-Armitage trend test Confounding can be a serious problem: inflate type I errors Some non-causal SNPs can be correlated to case control status: Population structure Artifacts from sample preparation and/or genotyping
    • Modifying theExisting approaches: genomic Cochran-Armitage trend test to address populationcontrol structure in GWAS Gary K. Chen Department of Let T be a test statistic Preventive Medicine Estimate Var (T ) at some random markers USC assumed to be unlinked to disease 1. Background Define inflation factor as λ = (Rp1 p2 (T ) )) var (1+F 2. Proposed Method T now scaled by λ0.5 3. Simulations Controls type I error to nominal rates Can be anti-conservative (Marchini et al, Nat. Gen. 2004) New GCF method compares against F instead of T distribution P-values are not re-ordered. Other approaches may yield more interesting rankings.Reference: Devin and Roeder, Biometrics 1999
    • Modifying theExisting approaches: structured Cochran-Armitage trend test to address populationassociation structure in GWAS Gary K. Chen Department of Preventive Medicine Parameters estimated by MCMC Gibbs USC sampling 1. Background Estimate P, describing population specific 2. Proposed Method allele frequencies 3. Simulations Estimate Q, describing individual specific admixture proportions Significance tested through likelihood ratio: ˆ ˆ Pr1 (C ;P1 ,Q) Λ= ˆ ˆ Pr0 (C ;P0 ,Q) Computationally intensiveReference: Pritchard et al, Genetics 2000
    • Modifying theExisting approaches: principal Cochran-Armitage trend test to address populationcomponents structure in GWAS Gary K. Chen Department of Preventive Medicine Axes of variation (ancestry vectors) USC computed by singular value decomposition 1. Background Regress genotypes on ancestry vector. 2. Proposed Method Residuals are adjusted genotypes. 3. Simulations Perform analogous regression with phenotypes. Method can be very sensitive to small differences between case-controls e.g. differences in genotyping errors Can lead to power loss if researcher ignores these effectsReference: Price et al, Nat Gen 2006
    • Modifying theAn outline Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC1. Background 1. Background 2. Proposed Method 3. Simulations2. Proposed Method3. Simulations
    • Modifying theOur proposed method Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC Combines ideas from genomic control and 1. Background principal components 2. Proposed Method A common correlation matrix is imposed 3. Simulations on each SNP However, p-values can be re-ordered when structure is present For SNP j: Yj = µj + βj Sj + Σj
    • Modifying theA potential model for variance Cochran-Armitage trend test to address populationstructure of SNP Sj structure in GWAS Gary K. Chen Department of Preventive Medicine Beta-binomial model: Balding and USC Nichols, 1995 1. Background 2. Proposed Var (Sj ) = 2pj (1 − pj )k Method 3. Simulations Given a population l = 1, 2, ..L Diagonal of k:1 + Fl Off-diagonal of k:2F or 0 m Sj∗ Sj∗T s −2pˆ ˆ k= j=1 ∗ where sn,j = √ n,j j M 2pj (1−pj ) ˆ ˆ Ancestral freq pj difficult to estimate ˆ Can use half the sample mean as pj , but ˆ maybe biased
    • Modifying theVariance structure for new method Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC For SNP j, Σj = σj2 K 1. Background σj2 is variance of pooled sample 2. Proposed Method K is an empirically estimated kinship matrix 3. Simulations Genotype correlation between subject m and n km,n element in K matrix: M (snj −2pj )(smj −2pj ) ˆ ˆ j=1 2pj (1−pj ) ˆ ˆ
    • Modifying theMean structure Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC 1. Background For SNP j, µj = C βj 2. Proposed Method µj is vector across N individuals 3. Simulations C is Nx2 matrix βj is a length 2 vector
    • Modifying theBest Linear Unbiased Estimates Cochran-Armitage trend test to address population(BLUE) structure in GWAS Gary K. Chen Department of Preventive Medicine USC ˆ βj = (C T K −1 C )C T K −1 Sj 1. Background 2. Proposed ˆ ˆ Vj = σ 2 (C T K −1 C )−1 Method j 3. Simulations ˆ SjT (K −1 −H)Sj σj2 = N−2 H = K C (C T K −1 C )−1 C T K −1 −1 Assess significance with Wald statistic: 2 βˆ j2 Tj = vˆ 2 j2
    • Modifying theAn outline Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC1. Background 1. Background 2. Proposed Method 3. Simulations2. Proposed Method3. Simulations
    • Modifying theSimulation Study Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC Goal: simulate up to 10 hidden 1. Background sub-populations 2. Proposed Simulate data for 100,000 SNPs Method 3. Simulations Draw ancestral allele freq U ∼ [.1, .9] Strata specific freq: Balding Nichols model Beta ∼ (p 1−Fi , (1 − p) 1−Fi ) Fi Fi Induce a 1% genotyping error in cases (N ∼ (0, .01))
    • Modifying theEmpirical type I errors Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC 1. Background Alpha %Geno Arm. GC PC New 2. Proposed Method Error Test 3. Simulations .05 0 .265 .047 .056 .050 1 .261 .047 .055 .050 −4 1e 0 .011 5e −5 7e −5 8e −5 1 .025 6e −5 2.3e −4 1.9e −4
    • Modifying thePower Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC Alpha %Geno Arm. GC PC New 1. Background Error Test 2. Proposed Method .05 0 .55 .31 .65 .65 3. Simulations 1 .75 .34 0 .40 −4 1e 0 .90 .40 .90 .95 1 .75 .41 0 .65
    • Modifying theSummary Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Accounting for population structure Department of Preventive Medicine improves power, reduces false positives USC Methods need to be efficient 1. Background 2. Proposed New method shares principles from GC Method and PC 3. Simulations Reranks p-values in contrast to GC Can be more powerful than PC when genotyping error is present Caveat: markers should be mostly unlinked We can simulate more realistic scenarios (e.g. LD)
    • Modifying theAcknowledgements Cochran-Armitage trend test to address population structure in GWAS Gary K. Chen Department of Preventive Medicine USC 1. Background 2. Proposed MethodCyril S. Rakovski 3. SimulationsDaniel O. Stram