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

2. 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?

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

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

5. 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

6. 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)

7. 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

8. Power Comparison
PET
FCP
MANOVA
RCM
SUM

9. Power Comparison
PET
FCP
MANOVA
RCM
SUM

10. 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

11. 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.

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