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A Method for Detecting Pleiotropy. Ingrid Borecki, Qunyuan Zhang, Michael Province Division of Statistical Genomics Washington University School of Medicine. Biological question : Does a genetic variant have independent effects on both of two traits? . Pleiotropy. Statistical question :

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a method for detecting pleiotropy

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?

Pleiotropy

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:

pleiotropy

Hypotheses & Models

Y1

Y2

X

Y1

Y2

Y1

Y2

Y1

Y2

X

X

X

statistical parameter of pleiotropy hypotheses to be tested

Statistical Parameter (δ) of Pleiotropy& Hypotheses to Be Tested

Compound null:

no pleiotropy

Alternative:

pleiotropy

estimating

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

q q plot under the null

Q-Q Plot under the null

Testing δ

Pleiotropy Estimation Test (PET)

Estimated by bootstrapre-sampling 100 times

with replacement

-LOG10(P)

other methods for comparison

=Residual of Y1 adjusted by Y2

=Residual of Y2 adjusted by Y1

  • 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

Testing if β1≠0 and β2≠0

power comparison

Power Comparison

PET

FCP

MANOVA

RCM

SUM

power comparison1

Power Comparison

PET

FCP

MANOVA

RCM

SUM

application

Correlation (WC, HOMA)= 0.542

Application

Correlation (TG, CAC)= 0.089

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.

Conclusions

acknowledgement

Acknowledgement

Ling-Yun Chang (programming & testing)

Mary Feitosa (GWAS data and application)