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# A Method for Detecting Pleiotropy

## Presentation on theme: "A Method for Detecting Pleiotropy"— Presentation transcript:

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

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?

Hypotheses & Models Compound null: no pleiotropy Alternative:
X Y1 Y2 Y1 Y2 Y1 Y2 X X X

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

Estimating δ Two traits are simultaneously fit into a mixed model
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 model When including X in the model

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

Other Methods for Comparison
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) Testing if β1≠0 and β2≠0 =Residual of Y1 adjusted by Y2 =Residual of Y2 adjusted by Y1

Power Comparison PET FCP MANOVA RCM SUM

Power Comparison PET FCP MANOVA RCM SUM

Application SNP WC HOMA PET Cov(%) 1 3.33E-06 8.35E-06 2.87E-09 1.74 2
Correlation (WC, HOMA)= 0.542 SNP WC HOMA PET Cov(%) 1 3.33E-06 8.35E-06 2.87E-09 1.74 2 1.77E-04 8.96E-06 8.33E-07 1.29 3 2.25E-03 8.06E-06 1.93E-06 1.39 4 2.29E-04 4.04E-06 5.68E-06 1.15 5 2.28E-04 4.15E-06 4.91E-05 6 1.92E-04 9.84E-06 7.18E-05 1.28 7 1.42E-02 3.02E-05 7.68E-05 1.04 Correlation (TG, CAC)= 0.089 SNP TG CAC PET Cov(%) 1 1.83E-18 5.95E-01 2.57E-01 3.63 2 7.47E-01 3.28E-09 6.76E-01 0.42 3 2.61E-02 1.85E-05 1.30E-04 5.36

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.

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

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