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A Method for Detecting Pleiotropy Ingrid Borecki, Qunyuan Zhang, Michael Province Division of Statistical Genomics Washington University School of Medicine

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Pleiotropy Biological question: Does a genetic variant have independent effects on both of two traits? Statistical question: Can the correlation or a portion of the correlation between two traits be explained by a genetic variant?

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Hypotheses & Models X Y1Y2 X Y1Y2 X Y1Y2 X Y1Y2 Alternative: pleiotropy Compound null: no pleiotropy

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Statistical Parameter (δ) of Pleiotropy & Hypotheses to Be Tested Compound null: no pleiotropy Alternative: pleiotropy

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Estimating δ T is the trait indicating variable; R is block diagonal covariance matrix (after re-ordering by individuals), with blocks corresponding to the individuals and each block having the compound-symmetry structure When excluding X from the modelWhen including X in the model Two traits are simultaneously fit into a mixed model

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Q-Q Plot under the null Testing δ -LOG10(P) Estimated by bootstrap re-sampling 100 times with replacement Pleiotropy Estimation Test (PET)

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MANOVA (Wilks' test, wrong null) FCP: Fisher’s combined p-value test (meta-analysis ignoring correlations, wrong null) RCM: Reverse compound model (two tests) SUM: Simple univariate model (two tests) Other Methods for Comparison =Residual of Y 1 adjusted by Y 2 =Residual of Y 2 adjusted by Y 1 Testing if β 1 ≠0 and β 2 ≠0

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Power Comparison PET FCP MANOVA RCM SUM

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Power Comparison PET FCP MANOVA RCM SUM

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Application SNPWCHOMAPETCov(%) 13.33E E E E E E E E E E E E E E E E E E E E E SNPTGCACPETCov(%) 11.83E E E E E E E E E Correlation (WC, HOMA)= Correlation (TG, CAC)= 0.089

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Conclusions The PET Method Tests proper compound null for pleiotropy; Gives estimation of covariance due to pleiotropy; Has greater power other alternatives; Under mixed model framework, can easily be expanded to other data (covariates, family data etc.) ; Practical to GWAS data (with 300 blades, R version takes less than 1 day for the analysis of 2M SNPs and ~3000 subjects) ; Must be fit to primary phenotype and (typed or imputed) genotype data.

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Acknowledgement Ling-Yun Chang (programming & testing) Mary Feitosa (GWAS data and application)

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